Economic Model Predictive Control of an Industrial Fluid Catalytic

Article pubs.acs.org/IECR

Economic Model Predictive Control of an Industrial Fluid Catalytic Cracker Hasan Sildir,† Yaman Arkun,*,† Asli Ari,‡ Ibrahim Dogan,§ and Murat Harmankaya§ †

Department of Chemical and Biological Engineering, Koc University, Rumeli Feneri Yolu, 34450 Sariyer, Istanbul Turkey TUPRAS R&D Center, 41790 Korfez, Kocaeli Turkey § TUPRAS Iż mir Refinery, 35800 Aliaga, Iż mir Turkey ‡

ABSTRACT: Fluid catalytic cracking (FCC) is an important refinery process by which heavy hydrocarbons are cracked to form lighter valuable products over catalyst particles. FCC plants consist of the riser (reactor), the regenerator, and the fractionator that separates the riser effluent into the useful end products. In FCC plants the product specifications and feedstocks change due to varying economic and market conditions. In addition, FCC plants operate with large throughputs and a small improvement realized by optimization and control yields significant economic return. In previous work, we developed a nonlinear dynamic model and validated it with industrial data. In this study, our focus involves the development and application of a real-time optimization framework. We propose a hierarchical structure which includes a two-layer implementation of economic model predictive control (EMPC). EMPC provides the optimal riser and the regenerator temperature reference trajectories which are determined from a dynamic optimization problem maximizing the plant profit. A regulatory model predictive controller (RMPC) manipulates the catalyst circulation rate and the air flow rate to track the reference trajectories provided by EMPC. We consider changes in product prices and the feed content, both of which necessitate online optimization. Dynamic simulations show that the proposed hierarchical control structure achieves optimal tracking of plant profit during transitions between different operating regimes thanks to the combined efforts of EMPC and RMPC.

1. INTRODUCTION The fluid catalytic cracking (FCC) process converts heavy hydrocarbons to lighter products which have higher economic value. The FCC plant under study here involves the reaction and fractionation subsystems as shown in Figure 1. The reaction subsystem is composed of the riser (reactor) and the regenerator units. Heavy vacuum gas oil (HVGO) is fed to the

riser, where cracking reactions take place. During cracking, some amount of coke is produced on the catalyst surface which leads to catalyst deactivation. Therefore, deactivated catalyst is regenerated in the regenerator and recycled back to the riser at elevated temperatures. The vapor products of the cracking reactions are separated into the useful end products in the fractionation unit. These products are off-gas, liquefied petroleum gas (LPG), whole crack naphtha (WCN), light cycle oil (LCO), and clarified oil (CLO). In our previous study,1 we developed a nonlinear dynamic model for the industrial FCC plant shown in Figure 1. The model parameters were estimated from plant data, and the model predictions matched the real plant data closely. The objective of this paper is to utilize this model for real-time optimization and control purposes. In the refinery, the FCC plant operates with large throughputs; therefore, a small improvement realized by optimization and control is expected to offer a significant economic return. Thus, the plantwide control system should enable an economically optimum transition between different operating regimes as well as provide plant safety and stability. Economic impact of the FCC plants has motivated the development of various advanced control architectures, and a significant number of publications have appeared over the years. For example, in ref 2, the transfer function matrix of the plant is obtained and validated through tests on the actual plant

Figure 1. Simplified process flow diagram of FCC plant in the refinery. PT, pressure transmitter; TT, temperature transmitter; GC, gas analyzer.

Received: Revised: Accepted: Published:

© 2014 American Chemical Society

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Industrial & Engineering Chemistry Research

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formed from cracking of the nth PC. For each reaction, φ fraction of the reacting material is assumed to be converted to coke. The differential energy balance at a particular position is given by1

in order to develop a single-step predictive control algorithm. Moro and Odloak3 developed a dynamic matrix control (DMC) structure which drives an industrial FCC unit to the optimum operating regime determined by a linear economic optimization layer. Ansari and Tade4 showed the superiority of the nonlinear controllers over DMC. In addition to controller algorithms, control structure selection can be challenging due to the limited number of manipulated variables. In this regard, the partial control of FCC plants is evaluated in ref 5. Zanin et al. implemented a real-time optimization structure which maximizes the LPG production in an FCC converter.6 Most of the literature on FCC focuses on model based approaches usually due to its proven advantages over decentralized proportional−integral−derivative (PID) controllers.7 In this study, we have designed a hierarchical control structure including an economic model predictive controller (EMPC) which drives the traditional regulatory model predictive controller (RMPC) to maximize the plant profit despite changing economic conditions. To the best of our knowledge, this is the first reported application of EMPC to an industrial FCC plant. A brief summary of the model developed in ref 1 and used here is presented next. After introducing the model, we will focus on the use of the model for optimization and control, which is the main objective of this paper.

∂(Mċ p ,avgT + Ṁ cat cp ,catT ) ∂z

N n>i

Ṁ n (1 − ε)ρcat Φ vg

i=1

Ṁ i (1 − ε)ρcat Φ vg (2)

3. CONTROL PROBLEM FORMULATION FCC units have to run under economically optimum operating conditions while maintaining stability and adhering to operational constraints. Therefore, closed-loop control strategies have to address two types of objectives: regulatory control objectives and economic control objectives. Furthermore, these objectives have to be continuously met in the face of external disturbances. Plant disturbances can be classified according to their frequencies and impact.10 Slow disturbances with high economic impact require reoptimization and may initiate a change in the operating conditions. For example, changes in the feed quality and product types and prices belong to this class of disturbances which may persist for a relatively long period. For such cases the model parameters can be updated online and economic optimization is repeated to determine the new operating conditions. Since these economic disturbances do not change frequently, the closed-loop plant dynamics are favorable to undergo the necessary transition between the different optimum operating conditions. For faster disturbances or for those without significant economic impact, online optimization is not warranted. The adverse effects caused by these disturbances are handled by the regulatory controllers. Economic and regulatory objectives are addressed in real time through a two-layer approach as shown in Figure 2a.11 In practice, most of the time, the optimizing control layer performs steady-state optimization to compute the optimal steady-state operating point (yss,uss) from the solution of

Ṁ ∂(Ṁ i ) = −ki i (1 − ε)ρcat Φ vg ∂z

∑ p(i , n)(1 − φ)kn

∑ ΔHiki

where Ṁ is the total mass flow rate of PCs, cp,avg is the average heat capacity; ΔHi is the heat of cracking of the ith PC. The regenerator is modeled by two separate phases. The dense phase is the bottom part of the regenerator and is highly concentrated with catalyst (see Figure 1). The dilute phase is the top part of the regenerator and, in contrast to the dense bed, contains a negligible amount of catalyst particles. As input air travels through the dense bed, oxygen reacts with coke. A significant amount of heat is released because of combustion reactions. In our case, the dense phase dominates the dynamic behavior of the plant and is modeled as a dynamic continuous stirred-tank reactor (CSTR) as in other works.9 The dilute phase can be approximated by pseudo-steady-state operation due to high superficial velocity of the gaseous phase. It is modeled as an adiabatic plug flow reactor in which CO is burnt homogeneously only. Important model parameters including the yield function and kinetic rate constants were estimated using real plant data. For the details, the readers are referred to ref 1.

2. PLANT MODELING The FCC unit is very complex, and it is a challenging task to model it. At the same time the model should have enough accuracy for optimization and control. While developing the model expressions, the basic idea was to keep it simple (with small number of parameters) and to explain the literature observations from pilot plants and industry. The developed model captures the fundamental physics of the process; it provides the right steady-state and dynamic trends and thus it is suited for optimization and control purposes. In the riser the vapor hydrocarbon cracks on the solid catalyst surface. Cracking reactions are very complex because of the high number of species involved in the reactions. To deal with this complexity, we have defined pseudocomponents (PCs), which are the petroleum fractions boiling in a specific temperature range, and estimated their properties using their average normal boiling points (NBPs).8 The riser is modeled as an adiabatic, one-dimensional, twophase moving bed reactor. The riser dynamics are very fast relative to the much slower regenerator which dominates the overall dynamic behavior. Therefore, the riser can be assumed to be at pseudosteady state and its modeling equations are derived only for steady-state conditions. The mass balance for a specific PC at any axial position, z, is given by1

+

N

=

(1)

where Ṁ i is the mass flow rate of the ith PC; ki is the cracking rate constant of the ith PC; Φ is the catalyst activity coefficient. The first term on the right-hand side of eq 1 denotes cracking of the ith PC to smaller molecules; the second term is the formation of that component from cracking of larger molecules. The yield function p(i,n) determines the amount of ith PC

max Lss(y , u , d)

(3a)

y = fss (u , d)

(3b)

u

s.t.

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xk + 1 = f (xk , uk , dk) h(xk , uk , dk) ≤ 0

xN ∈ X f

(3c)

where y is the vector of outputs; u is the vector of inputs or decision variables; d is the vector of economic disturbances; fss is the steady-state plant model; Lss(y,u,d) is the economic performance index, i.e., plant profit in this case. Optimal solution (yss,uss) is supplied to the lower regulatory layer as a constant set point (ysp,usp). Usually, in complex multivariable and constrained industrial applications, the regulatory layer consists of a model predictive controller (RMPC)12 which tracks the set points. The classical tracking optimization problem solved by RMPC is given by N

min JRMPC =

u1, u 2 ,..., uN

∑ (yk

− y sp )T Wy(yk − y sp )

k=1

+ (uk − u sp)T Wu(uk − u sp)

(4a)

s.t.

xk + 1 = f (xk , uk , dk)

(4b)

yk = g (xk , uk , dk)

(4c)

h(xk , uk , dk) ≤ 0

k = {1, ..., N }

(4d)

where k is the sample time; N is the horizon; yk is the output vector at time k; dk is the vector of disturbances at time k; uk is the vector of inputs; Wy and Wu are weighting matrices of the outputs and inputs, respectively. Determining steady-state set points first, followed by tracking, is clearly suboptimal when compared with a dynamic optimization formulation which directly optimizes the economic objective function. Economic dynamic optimization performed over a specified time horizon is bound to provide better economic performance since it minimizes the transient cost incurred during transition between different steady-state operations.13−15 The economic impact of EMPC becomes even more significant when the best performance is achieved under non-steady-state operation (e.g., cyclic processes16). Therefore, a single layer architecture that integrates optimizing and regulatory control tasks has been proposed recently. In particular, economic model predictive control (EMPC)13 is such a strategy. EMPC converts the open-loop dynamic optimization into a feedback control strategy by performing it at each sampling time after updating the initial state. Specifically, EMPC implements in real time the solution of the following dynamic optimization problem:

u1, u 2 ,..., uN

∑ L(xk , uk) + C(xN ) k=1

(5c) (5d)

4. HIERARCHICAL CONTROL STRUCTURE The hierarchical control structure designed for the FCC plant under consideration is shown in Figure 3. Next we describe the function of each block and its interaction with and contribution to the overall hierarchy. 4.1. Management. The highest level in the hierarchy is the management layer, which provides prices of all individual products considering product demand in the refinery and the market. In addition, product specifications and operating constraints are also defined here.

N

min JEMPC =

k = {1, ..., N }

As in RMPC, the first optimal control move uk is applied to the plant, and optimization is repeated at the next sampling time after estimation of the new state from output measurements. In eq 5a, L(xk,uk) is the economic stage cost, e.g., negative profit; C(xN) is the terminal cost. In eq 5d Xf is a compact terminal region containing the steady-state operating point in its interior. Unlike RMPC, the stability of EMPC is more challenging due to primarily the nonconvex form of the economic objective function. In refs 13 and 17 stability is ensured by using a terminal state constraint xN = xss (final steady state) instead of the terminal region constraint xN ∈ Xf and eliminating the terminal cost term C(xN). Later Amrit et al.18 relaxed the terminal constraint to a terminal region constraint xN ∈ Xf in order to provide more flexibility. Other techniques to handle stability exist as well.19,20 Real-time implementation of the dynamic optimization as a feedback control law requires solving eq 5a at each sampling time to account for disturbances, modeling, and initial state errors. For large scale complex industrial processes, this can be computationally demanding especially when large prediction horizons have to be used to enhance stability and performance. In order to cope with these disadvantages of real-time optimization, a two-layer implementation of EMPC21−24 has been proposed as shown in Figure 2b. Here EMPC acts as a supervisory controller driving RMPC by supplying economically optimal time-varying reference trajectories for the plant outputs. RMPC tracks these trajectories by implementing the necessary changes in the control inputs. Note that this two-layer implementation is proposed on the premise that plant disturbances can be separated into slow (economic) and fast (noneconomic) disturbances as discussed earlier. In this case the sampling time for EMPC can be chosen much larger than the sampling time of RMPC so that slow (economic) disturbances are handled by EMPC and fast (noneconomic) disturbances are rejected by RMPC. Integrating EMPC with RMPC in a twolayer hierarchy offers significant computational advantages by reducing the frequency of the optimization cycle. Two-layer EMPC implementation benefits from both the economic features of EMPC and the well-established advantages of RMPC such as stability, fast convergence, robustness, and constraint handling. In addition, in most industrial plants RMPC is already in place and is widely used with success. This is indeed the case with the FCC plant under study here as well. In section 4 we present how we apply EMPC to the FCC plant.

Figure 2. Decomposition of control tasks. (a, left) Traditional twolayer approach. (b, right) Two-layer EMPC.

h(x , u , d) ≤ 0

(5b)

(5a)

s.t. 17698



Article ref TRiser,min ≤ TRiser, k ≤ TRiser,max

4.2. EMPC. The plant profit is given by 5

̇ ̇ ∑ PM i p, i − PHVGOMHVGO − U

(6)

i=1

where Pi is the price of the ith product; Ṁ p,i is the mass flow rate of the ith product; PHVGO is the price of the feed; Ṁ HVGO is the mass flow rate of the feed; U is the utility cost. In our case, the utility cost is negligible compared to the economic value of the product and the feed. There are two degrees of freedom and the decision variables are the two inputs: the catalyst circulation rate (Ṁ cat) and the air flow rate (Ṁ air). In addition to economic considerations, there are some hard constraints which are determined by equipment capacities and the catalyst. These are Ṁ air,min ≤ Ṁ air ≤ Ṁ air,max (7a) Ṁ cat,min ≤ Ṁ cat ≤ Ṁ cat,max

(7b)

TRegen,min ≤ TRegen ≤ TRegen,max

(7c)

TRiser,min ≤ TRiser ≤ TRiser,max

(7d)

Typical constraint values are listed in Table 1. Table 1. Plant Constraints variable Ṁ air [m3/h] Ṁ cat [kg/h] TRegen [K] TRiser [K]

min

max

39 484 628 578 945.95 787.55

43 640 694 796 955.00 803.25

(8f)

Equation 8a is solved at each sample time to deliver the sp optimal trajectories Tsp Regen,k, TRiser,k for k ∈ (1, ..., N) to the RMPC layer. The sampling time for EMPC is 1 h and the prediction horizon N = 2. With these choices, plant dynamics allow enough time to track the temperature trajectories and the computational load is kept reasonable. The constraint (Tsp Regen,k, Tsp Riser,k) (eq 8d) where Γ is closed and bounded is included in the optimization to guarantee that the closed-loop system is stable and the optimal reference trajectories can be tracked by RMPC.23 In fact, this additional requirement is imposed by the two-layer implementation of EMPC. The set Γ is constructed in such a way that, for each set point value belonging to Γ, there exist feasible values for the lower layer RMPC control inputs, Ṁ air and Ṁ cat. The set Γ is easily calculated from the steadystate FCC model1 that relates the riser and regenerator temperatures to the catalyst circulation and the air flow rate and their constraint values. In addition to feasibility, closed-loop stability is guaranteed for trajectories belonging to the set Γ by the tuning parameters of RMPC. In our simulations with a single set of tuning parameters, RMPC was able to track the optimal reference trajectories. In case of poor tracking, online tuning of RMPC or deviation from the optimal trajectory may be required. Finally, EMPC starts the optimization from the estimated state xk. In the above formulation, it is assumed that the estimated state xk remains in Γ. Otherwise it has to be projected to this set as done in ref 23. Finally, the regenerator and the riser temperature trajectories are constrained by the plant limits as expressed by the inequalities 8e and 8f. The closed-loop dynamics of RMPC layer are represented by f RMPC in eq 8b. The vector of product flow rates Ṁ p in the objective function is calculated from the empirical fractionator model as explained below.1 4.3. RMPC and the Reaction Unit. RMPC controls TRegen and TRiser. Tracking the optimization problem is given by

Figure 3. Hierarchical FCC control structure.

J=

k ∈ (1, ..., N )

J FCC min Ṁ air,1, Ṁ air,2 ,..., Ṁ air, N RMPC Ṁ cat,1, Ṁ cat,2 ,..., Ṁ cat, N N

=

sp sp T ∑ ((TRegen,k − TRegen, k) WRegen(TRegen, k − TRegen, k) k=1

sp sp T + (TRiser, k − TRiser, k) WRiser(TRiser, k − TRiser, k)

)

(9a)

s.t. EMPC uses the profit function as the stage cost and solves the following dynamic optimization: min

sp sp sp , TRegen,2 ,..., TRegen, TRegen,1 N sp sp sp , TRiser,2 ,..., TRiser, TRiser,1 N

N

FCC JEMPC

5

= − ∑ (∑ Pi , kṀ p, i , k − PHVGO, kṀ HVGO, k ) k=1

i=1

xk + 1 = fReaction Unit (xk , Ṁ cat, k , Ṁ air, k )

(9b)

Ṁ air,min ≤ Ṁ air, k ≤ Ṁ air,max

k = {1, ..., N }

(9c)

Ṁ cat,min ≤ Ṁ cat, k ≤ Ṁ cat,max

k = {1, ..., N }

(9d)

ΔṀ air,min ≤ ΔṀ air, k ≤ ΔṀ air,max

(8a)

(9e)

sp sp xk + 1 = fRMPC (xk , TRegen, k , TRiser, k)

(8b)

sp sp Ṁ p, k = g (xk , TRegen, k , TRiser, k)

(8c)

sp sp (TRegen, k , TRiser, k) ∈ Γ

(8d)

TRegen,min ≤ TRegen, k ≤ TRegen,max

(8e)

TRiser,min ≤ TRiser, k ≤ TRiser,max

sp TRegen,min ≤ TRegen, k ≤ TRegen,max

k = {1, ..., N }

k ∈ (1, ..., N )

ΔṀ cat,min ≤ ΔṀ cat, k ≤ ΔṀ cat,max

k = {1, ..., N } (9f)

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k = {1, ..., N }

k = {1, ..., N }

(9g) (9h)



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Figure 4. Riser effluent curves and TCPs.

Figure 5. FCC operating window. (●) Plant initial operating point. (○) Optimal operating regime of t = 0−3 h. (△) Optimal operating regime of t = 3−6 h.

Figure 6. Crucial process variables in the simulation.

ΔṪ Regen,min ≤ ΔṪ Regen, k ≤ ΔṪ Regen,max

open loop plant and are hidden inside the “reaction unit” block. Once RMPC is designed on top of the reaction unit block, it inherently captures the dynamics of the PID loops (which are relatively fast). In addition, the control frequency of RMPC is 3 min and can filter the noisy data at each control action. 4.4. Empirical Separator. In order to compute the profit function used in EMPC, individual product amounts are needed. However, these amounts are available only after fractionation. Detailed modeling of the fractionation plant is out of the scope of this study. Instead we have developed an empirical model based on temperature cut points. The input to the empirical separator model is the riser effluent boiling point curve as shown in Figure 4. Boiling point curves indicate the amount of vaporized petroleum fraction as a function of temperature, and they are used to analyze petroleum fractions. A typical curve for the riser effluent is shown in Figure 4. The solid curve represents the boiling point curve of the riser effluent predicted by the model and it is obtained through eq

k = {1, ..., N } (9i)

ΔṪ Riser,min ≤ ΔṪ Riser, k ≤ ΔṪ Riser,max

k = {1, ..., N } (9j)

While we have used the nonlinear model explicitly in EMPC to exploit its full economic potential, we have used its linearized version for RMPC since empirical linear step response models are already used in the plant satisfactorily. f Reaction Unit represents the linearized reaction unit model which includes both the riser and regenerator. ΔṀ air,k and ΔṀ cat,k are the rates of change of the air flow and the catalyst circulation at time k. Constraints include total and rate constraints on the inputs and the temperatures. In practice, local PID controllers control the air flow rate, the catalyst circulation rate, pressures, and levels in the reaction unit. Those low level PID loops are considered as part of the 17700



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Figure 7. Product flow rates.

Figure 8. Manipulated variables of RMPC.

1.1 The dashed curve represents the real plant riser effluent. Temperature cut points (TCPs) can be used to map the riser effluent to the final product amounts.25 TCPs can be calculated from plant data,1,26 and a typical set of values is shown in Figure 4 with vertical lines. With the use of the cumulative product masses at these cuts, individual product amounts can be computed and used in optimization. Note that when EMPC changes the riser and regenerator temperature reference trajectories, the riser effluent boiling curve changes and affects the product distribution. Cut point temperatures have found applications in many other studies as well (i.e., refs 8 and 27).

(○) at the upper right corner in Figure 5, which corresponds to the high-temperature regime. In the lower level, RMPC increases the air flow rate and the catalyst circulation rate to track the optimal temperature trajectories supplied by EMPC. Physically, both the air flow rate and the catalyst circulation have to increase to increase the riser and regenerator temperatures at the same time. When the air flow rate increases, combustion reactions and higher temperatures are favored and the coke content on the catalyst decreases (see Figure 6). In order to carry more energy from the regenerator to the riser and increase the riser temperature, the catalyst circulation rate is also increased. The dynamic profiles of the manipulated variables are shown in Figure 8. At a simulation time of 3, we introduce a change in the product prices which shifts the profit contours drastically (see Figure 5). This change in prices corresponds to a 5% reduction in WCN price, and 5 and 15% increases in LCO and CLO prices, respectively. With these new prices, the heavy products LCO and CLO are relatively more valuable, which is opposite of the scenario during the first 3 h of plant operation. Therefore, lower riser and regenerator temperatures are expected for optimal operation. In fact, EMPC computes lower riser and regenerator temperature set points as shown in Figure 6. RMPC reduces both the air flow rate and the catalyst circulation to track the temperatures (see Figure 8). The lower catalyst circulation and air input eventually reduce the cracking activity after temperatures drop. As a result, the amount of heavy products increases as shown in Figure 7. This reflects itself in the increasing value of plant profit (see Figure 6, t = 3−6 h). The instant drop in profit at t = 3 is due to the sudden price change at t = 3. After implementation of EMPC’s reference trajectories, the new optimal steady state is reached after approximately 2 h and it is marked by a triangle (△) in Figure 5. As shown, the plant now operates in the low-temperature regime.

5. RESULTS We consider two classes of major plant disturbances that have an economic impact. One is the product prices and the other is the feed quality, both of which change according to the market demand and the refinery needs. We consider a 9-h simulation scenario and introduce a significant disturbance every 3 h. Initially the plant is operating at the steady state operating point marked with “●” in Figure 5. During the first 3 h of operation, the product prices remain constant and no other economic disturbance enters the plant. In this scenario the prices for lighter products (off-gas, LPG, and WCN) are higher than the heaver products (CLO and LCO). The optimal reference trajectories computed by EMPC (SV) and the temperature values of the plant (PV) are shown in Figure 6. Both the riser and the regenerator temperatures are increased. Increase in temperatures favors cracking and reduces the amount of less valuable heavy products (CLO and LCO) as shown in Figure 7. At the same time, the lighter and more valuable products (LPG and WCN) increase. Consequently, the plant profit sharply increases as shown in Figure 6 during t = 0−3 h. After implementation of EMPC’s reference trajectories, it takes about 2 h to reach the new steady state marked by circle 17701



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riser temperature at its lower limit (see Figure 8). The increase of the riser temperature which is required to satisfy the constraints favors more cracking and results in some loss of heavy products, and thus overall plant profit decreases slightly as shown in Figure 6. Despite the negative impact of the feed change, EMPC provides the least loss in profit while maintaining feasible operation. Usually, direct economic factors such as changes of prices have higher impacts on the optimal operating regime as we have seen during the first 6 h of operation. The disturbance from the feed content also changes the optimal operating regime, but smaller adjustments are required to satisfy plant constraints while maintaining optimal profit.

The feed to the FCC is obtained after blending products coming from different process units upstream of the riser. Depending on the refinery production planning, the feed quality varies on a daily basis and has an impact on plant economics. In order to assess this impact, we have introduced a change in the feed at a simulation time of 6. The new feed has a relatively higher average boiling point temperature compared to the feed at the beginning of the process (see Figure 9). It is

6. CONCLUSIONS A hierarchical control structure which includes a two-layer economic MPC (EMPC) is developed and applied to an industrial FCC plant for real-time optimization and control purposes. At the upper layer of the hierarchy, EMPC uses a nonlinear dynamic FCC model and maximizes the plant profit by computing the optimal reactor and riser reference trajectories. The lower-layer controller consists of a regulatory MPC (RMPC) which tracks the optimal reference trajectories by manipulating the air flow rate to the regenerator and the catalyst circulation rate. A linear model is used at this layer. Since dynamic optimization and tracking tasks are separated, the sampling time for EMPC can be chosen much larger than the sampling time of RMPC so that slow (economic) disturbances are handled by EMPC and fast (noneconomic) disturbances are rejected by RMPC. Integrating EMPC with RMPC in a two-layer hierarchy offers computational advantages by reducing the frequency of the optimization cycle. In addition, the two-layer implementation benefits from both the economic features of EMPC and the well-established advantages of RMPC such as stability, fast convergence, robustness, and constraint handling. The focus of the study is limited to the “reaction unit” only. Control of the fractionation unit considering the additional constraints (flooding, wet gas compressor, gas plant capacity) is beyond the scope of this paper. A crucial assumption in this study is that these constraints are not violated within our processing regimes; i.e., the fractionation plant’s control system is able to maintain feasible operation when the reaction unit is controlled within the operating regimes provided by EMPC.

Figure 9. Boiling point curves of the two feeds.

assumed that the feed composition upset was known instantaneously. The feed amount is fixed at its original value. The steady-state model is used again to calculate the new operating window which is shown in Figure 10. The temperature contours in Figure 10 are different from those in Figure 5 since the feed content affects the cracking reactions in the riser. The ultimate effect is reflected in the product distribution and thus profit contours. Keeping the air flow rate and the catalyst circulation at their values before the feed change, i.e., at point △, violates the lower limit of the riser temperature. The lower allowable limit is 787.55 K, but at point △ in Figure 10, the riser temperature is below this limit. This occurs because the cracking reactions in the riser are endothermic and more energy is consumed when a heavier feedstock is processed, resulting in a temperature drop. EMPC determines the new optimal temperature set points to move the plant from the previous optimal condition (△) to the new optimal operating regime (□) shown in Figure 10. In order to move to the new optimum, the regenerator temperature is increased while the riser temperature is kept at its lower limit (see Figure 6 during t = 6−9 h). This maintains the feasibility of temperatures in case of the feed disturbance. RMPC increases the air flow rate rather aggressively to track the regenerator set point increase and adjusts the catalyst circulation rate only slightly to regulate the

Figure 10. Operating window with the heavier feed. (□) Optimal operating regime of t = 6−9 h. 17702



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Otherwise a detailed fractionation model and a plantwide control system must be considered with all constraints. The fractionation model presented in this paper is not developed for this purpose. It is an empirical fractionation model to calculate the amounts of the individual products from the riser effluent so that their amounts can be used by EMPC. The proposed control system is tested against several economic disturbances including changes in the product prices and feed quality. Dynamic simulations show that maximum profit can be achieved while the plant is in transition between different steady-state optimal operating conditions. The profit obtained through EMPC is always greater than or equal to the performance of a steady-state tracking controller. The additional profit is sometimes significant, e.g., in cyclic operations, and sometimes is small. In our particular case, the economic improvement happens to be small for all the simulation scenarios considered. However, EMPC introduces other types of benefits as well. It is a transparent system which conforms with the plant management layer that plans in terms of profitability rather than steady-state set points. Over the years, set point tracking has become a mature technology (as in MPC) due to its proven stability properties and tuning guidelines. Today it is preferred even when its economic benefits may be small at times. EMPC has similar potential to become a standard technology, and more research is needed to study its properties and to develop implementational frameworks. In this regard, we have shown how EMPC can be applied to an industrially important process within an hierarchical setting. Implementation on an industrial plant is under consideration by the plant management.

■

■

ε = void fraction p(i,n) = yield function φ = coking tendency cp,avg = average heat capacity ΔHi = heat of cracking of ith PC cp,cat = catalyst heat capacity d = vector of economic disturbances fss = steady-state plant model h = vector of inequality constraint functions k = sample time u = input vector Xf = terminal region x = state vector xN = output vector at terminal time y = output vector

REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +90-212 338 1313. Fax: +90212 338 1548. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support of TUPRAS Refineries. NOMENCLATURE C(xN) = terminal cost on outputs JFCC EMPC = performance index of EMPC JFCC RMPC = performance index of RMPC Ṁ cat = catalyst circulation rate Ṁ air = air flow rate Ṁ i = mass flow rate of ith PC Ṁ p,i = mass flow rate of ith product Ṁ HVGO = mass flow rate of feed Ṁ = total mass flow rate Pi = price of the ith product PHVGO = price of feed TRegen = regenerator temperature TRiser = riser temperature YRegen coke = fraction on catalyst U = utility cost ki = cracking rate constant of ith PC Wy = weighting matrices of outputs Wu = weighting matrices of inputs Φ = catalyst activity coefficient 17703



Article

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Economic Model Predictive Control of an Industrial Fluid Catalytic

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