Economic Model Predictive Control (EMPC) of an Industrial Diesel Hydroprocessing Plant. Erdal Aydın*, Yaman Arkun** Gamze Is***

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1 Preprint, 11th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems Economic Model Predictive Control (EMPC) of an Industrial Diesel Hydroprocessing Plant Erdal Aydın*, Yaman Arkun** Gamze Is*** * Department of Chemical and Biological Engineering, Koc University, Rumeli Feneri Yolu, Sariyer, Istanbul, TURKEY ( aydin@mpi-magdeburg.mpg.de). ** Department of Chemical and Biological Engineering, Koc University, Rumeli Feneri Yolu, Sariyer, Istanbul, TURKEY ( yarkun@ku.edu.tr) *** TUPRAS R&D Center, Korfez, Kocaeli, TURKEY ( GAMZE.IS@tupras.com) Abstract: Diesel hydroprocessing is a refinery process by which the sulfur impurities are removed by hydrodesulfurization and the main product diesel is obtained by hydrocracking. The industrial Diesel Hydroprocessing Plant considered in this study consists of two hydrodesulfurization reactors and one hydrocracking reactor in series. The feed to the plant is a blend of four different raw material streams which are heavy diesel (HD), light diesel (LD), light vacuum gas oil (LVGO) and imported diesel from another refinery. A two-layer, hierarchical Economic Model Predictive Control (EMPC) structure is proposed to maximize the profit of the plant. The plant-wide profit is maximized by computing the optimal set-points by the upper economic model predictive control layer while these set-points are tracked by the regulatory model predictive controllers in the lower level. Set-point tracking and disturbance rejection performances of the proposed EMPC structure are tested through closed-loop simulations. Keywords: Economic model predictive control, non-linear control, hierarchical control, real-time optimization, hydrodesulfurization, hydrocracking. 1. INTRODUCTION The industrial diesel hydro-processing plant (DHP) subject to this study consists of two catalytic hydro-desulfurization (HDS) reactors and a hydro-cracking (HC) reactor in series as shown in Fig.1. The feedstock of the unit is a blend of four streams: HD (straight run heavy diesel), LD (straight run light diesel), LVGO (light vacuum gas oil) and an imported diesel. HD and LD streams are obtained from a crude distillation unit, and LVGO stream is derived from a vacuum distillation unit. These streams are blended in order to obtain a desired T95 value (the temperature at which 95% of the distillate is collected e.g. by ASTM D86 distillation) for the reactor feed. In the first two HDS beds, the organic sulfur impurities are removed. Hydrocracking (HC) occurs in the last bed where heavier hydrocarbons are cracked to lower molecular weight petroleum fractions. Inter-stage cooling by quench hydrogen is used in both reactors to control the bed exit temperatures. Reactor effluent is next fed to the separation unit where the end products naphtha and diesel are obtained. The industrial diesel hydroprocessing plant operates with varying feedstocks and large throughputs. Also, changing market conditions have significant effects on product specifications. Therefore, slight improvements on process conditions may result in high profits. In the presence of such a dynamic environment, the diesel hydroprocessing plant must be controlled in the most profitable and safe way. The main operational objectives are to maximize the overall profit of the plant and to keep the sulfur content of diesel below 10 ppm. Therefore, the optimum operating conditions have to be calculated using an economic objective function, and a proper control configuration has to be implemented. In this study, a nonlinear, plant-wide, hierarchical EMPC structure is designed. Nonlinear first principles and empirical models for both blending, reaction and separation subsystems have been developed and validated using industrial data in our earlier work (Aydın et al., 2015). 2. EMPC DESIGN In classical plant-wide real-time optimization and control (RTO), steady-state set-points are determined first, and these set-points are tracked by the regulatory level controllers. However, a closed-loop implementation of dynamic optimization maximizing the profit over a specified time horizon provides better economic performance since it also maximizes the transient profit. Economic Model Predictive Control (EMPC) is such a strategy (Angeli et al. (2012); Amrit et al.(2013); Würth et al. (2009)). EMPC converts the open-loop dynamic optimization into a feedback control strategy by performing it at each sampling time after updating the initial state based on plant measurements. 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, Copyright 2016 IFAC 568

2 IFAC DYCOPS-CAB, 2016 Fig. 1. Simplified DHP flowsheet. a two-layer real-time implementation of EMPC has been proposed (Helbig et al. (2000); Kadam et al. (2002); Ellis and Christofides (2014)). Sildir et al (2014) has proposed a twolayer hierarchical EMPC strategy for an industrial FCC unit. Here EMPC is designed as a plant-wide controller which supervises the local decentralized MPCs. Similarly, the hierarchical EMPC structure proposed for the industrial DHP plant is shown in Fig. 2. The overall DHP plant consists of Blending, DHP reactors and separator subsystems. Each control layer in the hierarchy has a specific optimizing or regulatory control objective as described next. In this hierarchical approach, EMPC acts as a coordinator by supplying economically optimal time-varying set-point trajectories to the local RMPCs (regulatory MPCs). RMPC follows these trajectories by adjusting their control inputs. 2.1 EMPC Layer The nonlinear constrained dynamic optimization performed in the EMPC layer is given as follows: s.t. N Max { P DieselM Diesel + P Naphtha M Naphtha (u k k=1,2,..m) k=1 C HD M HD C LD M LD C LVGO M LVGO C ImportDiesel M ImportDiesel } k x k+1 = f regulatory (x k, u k ), y k = g(x k, u k ) T out,hc 655 K, T out,hds1 655 K, T out,hds2 655 K S conv > 99.7 %, 378 C FeedT C, 350 C DieselT C 200 M HD 200, 150 M LD 150, 0 = M LVGO, 200 M Im.Diesel 200, 400 M HD 600, (1) 600 M LD 800, 1300 M Im.Diesel 1500, M HD + M LD + M Im.Diesel = 0, 7 K T in,hds 7 K, 7 K T in,hc 7 K Optimization determines the optimal values of the set-points: u k = (Feed T 95sp k, T out,hc spk, T out,hds1 sp k, T out,hds2 sp k ) which are supplied to the lower layer regulatory MPCs. P i s are the prices of the products and C i s are the costs of the raw materials, both of which are set by the refinery management. The functional f regulatory represents the non-linear closedloop dynamics of the regulatory layer. The refinery management also specifies the daily total flow rate of the unit, which is not allowed to change through daily operation. Since the total feed flow-rate is constant during the period of optimization, utility cost can be assumed as constant. The sampling time of EMPC layer is 100 min, Move horizon M=1 and the length of the prediction horizon N is set to 100 min, which is close to the settling time of the plant. All the constraints are well defined by the plant management considering equipment, catalyst capacities and safety regulations. LVGO flow rate is not allowed to change. Other raw materials flow rates are subject to the restrictions imposed by the upstream distillation columns. The main product Diesel must have its T 95 value between 350 and C. Sulfur conversion (Sconv) is constrained in order to reach a Diesel ppm level less than 10 ppm Regulatory MPCs Regulatory MPCs are the decentralized model predictive controllers of the reactors (Regulatory Reactors MPC) and the blending unit (Regulatory Blending MPC). Sampling time of these layers is 6 seconds which is much smaller than the sampling time of the optimization layer to be able to reject 569

3 IFAC DYCOPS-CAB, 2016 Fig. 2. Hierarchical EMPC structure. fast disturbances and track the set-point changes specified by the EMPC layer. Regulatory Reactors MPC controls the reactor exit temperatures at the desired set-points. The available manipulated variables are the set-points of the reactor inlet temperatures as shown in Fig. 3. PID control (inside the DHP reactors block in Fig. 2) is used to adjust the quench flows to control the reactor inlets at the set-points determined by Regulatory MPC. Linear MPC design based on step-response models was used for the regulatory MPCs. These models were obtained by step testing the dynamic DHP plant model. The constraints are given in Table 1.The raw material flow constraints are given in ton/day. Inlet temperatures of the reactor beds cannot be increased or decreased by more than 7 0 C. LVGO flow-rate is not available for manipulation; changes in the other flows have upper and lower limits set by the upstream columns; reactor exit temperatures cannot exceed certain maximum values for safety regulations defined by the catalyst company. Fig. 3. Regulatory Reactors MPC inputs and outputs. Regulatory Blending MPC tracks the FeedT 95 value by manipulating the available raw material flow-rates as shown in Fig. 4. Table 1. Constraints for the regulatory MPCs Regulatory Reactors MPC 7 ΔT ΔT ΔT T out,hc T out,hds1 T out,hds2 sp in,hds1 sp in,hds2 sp in,hc 655K 3. RESULTS 655K 655K 7 K 7 K 7 K Regulatory Blending MPC M HD LVGO HD LD LD Im.Diesel 200 M Im.Diesel Initially, the plant is at a suboptimal steady state. At t=10 min, EMPC was initialized. EMPC performs the dynamic profit maximization and computes the optimal temperature set-points. Next, these set-points are tracked by the regulatory model predictive controllers. The closed-loop simulation results are given in Figures 5 and 6. Numbers are scaled without distorting the general trends for proprietary reasons. 0 Fig. 4. Regulatory Blending MPC inputs and outputs. 570

4 Temperature ( C) Conversion Temperature ( C) IFAC DYCOPS-CAB, FIRST HDS EXIT TEMPERATURE SECOND HDS EXIT TEMPERATURE HYDROCRACKER EXIT TEMPERATURE Fig. 5. Closed-loop responses of reactor bed exit temperatures. 355 Sulfur Conversion Diesel T Feed T Fig. 7. Total profit. In order to check the economic disturbance rejection performance of EMPC, the prices of the raw materials are changed as shown in Table 2. After the maximum profit value is reached, the economic disturbance is added to the plant at t=200 min. Table 2. Costs and prices before and after the economic disturbance. BASE DISTURBANCE C HD C LD C ImportDiesel P Diesel P Nafta As shown in Fig. 8, the profit makes a down peak at t=200 min, decreasing from 26 units to 18 units. This is due to the fact that heavy diesel becomes the most expensive raw material at that instant, when it is fed to the reactors with its maximum allowable flow rate. Accordingly, EMPC takes action and rejects the economic disturbance by changing both feed and reactor operating conditions as seen in Figs Fig. 6. Closed-loop responses of feed and product specifications. EMPC increases the exit temperatures of the two hydrodesulfurization reactors in order to satisfy the sulfur conversion constraint. As a result, Sconv reaches the desired level (99.7 %) as shown in Fig. 6. Furthermore, the hydrocracker exit temperature is decreased and less cracking is favored by the EMPC. Accordingly, DieselT 95 value increases to the upper constraint level of C. As a result, both the production rate of Diesel and the total profit increase (see Fig. 7). Fig. 8. Closed-loop profit trajectory for the economic 571

5 Diesel Flow Rate (ton/day) Temperature ( C) Mass Flow Rate (ton/day IFAC DYCOPS-CAB, HD LD Imp.Diesel Fig. 9. Closed-loop raw materials flow rates for the economic Since heavy diesel becomes the most expensive raw material, EMPC minimizes its flow rate to the lower constraint value of 400 ton/day at t=200 min. Meanwhile, the flow rate of light diesel also increases to the upper constraint value; because, it becomes the cheapest raw material. The flow rate of import diesel is adjusted in order to satisfy the daily flow rate constraint as shown in Fig. 9. As a result of these blending raw material changes, FeedT 95 value decreases to C as shown in Fig Feed T Fig. 10. Closed-loop FeedT 95 response for the economic EMPC also re-adjusts the reactor exit temperatures in order to achieve the new most profitable operating conditions. Since FeedT 95 point decreases to C, EMPC decreases the hydrocracker exit temperature to lessen the level of cracking. Further decrease on hydrocracker exit temperature is not possible since the inlet temperature of the hydrocracker cannot be decreased more than 7 K. As a result, maximum allowable diesel product withdrawal of 2618 ton/day is obtained as shown in Fig. 12. Corresponding Diesel T95 behavior is shown in Fig. 13. With these optimal operating conditions, it is not possible to withdraw Diesel with T 95 point value of C, which was the optimal value before the economic disturbance. Furthermore, due to the fact that FeedT 95 point decreased to C, total sulfur concentration of the DHP feed also decreased, which in turn, decreased the relative reaction rate of sulfur removal. In order to compensate for that, EMPC increases the inlet temperature of the second HDS reactor, resulting in a 2 0 C increase in the exit temperature of the second HDS. In addition to that, EMPC decreases the inlet temperature of the first HDS by C to decrease the sulfur conversion in the first reactor. By doing this, the intention of EMPC is to increase the reaction rate in the second HDS, where the heavier sulfur components are removed. As a result, overall sulfur conversion constraint is not violated and is kept above 99.7% as shown in Fig FIRST HDS EXIT TEMPERATURE SECOND HDS EXIT TEMPERATURE Fig. 11. Closed-loop reactor bed exit temperatures for the economic HYDROCRACKER EXIT TEMPERATURE Fig. 12. Diesel flow rate for the economic disturbance rejection. 572

6 Sulfur Conversion Temperature ( C) IFAC DYCOPS-CAB, Fig. 13. DieselT 95 for the economic Fig. 14. Sulfur conversion (Sconv) response for the economic 4. CONCLUSIONS In this work, a two-level hierarchical economic model predictive control structure is proposed for an industrial diesel hydroprocessing plant. In this structure, the upper EMPC layer uses a dynamic model of the industrial diesel hydroprocessing plant and maximizes the overall plant-wide profit by computing the optimal reactor exit temperatures and feed characteristics. The lower layer consists of decentralized regulatory MPCs which track the computed optimum trajectories by manipulating the raw material flow rates and reactor inlet temperatures. Linearized plant models are used in this layer. The sampling time of the lower layer is assigned much smaller than the upper layer. In this context, the slow (economical) disturbances are rejected by the EMPC layer while the fast (non-economical) disturbances are rejected by the lower layer. In other words, the dynamic optimization and tracking tasks are separated, which in turn, reduces the frequency of optimization and prevents possible stability and convergence problems. The possible benefits of the proposed structure are checked with closed-loop simulations for both set-point tracking and disturbance rejection cases. The designed two-level economic model predictive control structure is in the process of implementation in the refinery. REFERENCES Angeli, D.; Amrit, R.; Rawlings, J. B., On Average Performance and Stability of Economic Model Predictive Control. Automatic Control, IEEE Transactions on 2012, 57, (7), Amrit, R., Rawlings, J. B., Biegler, L. T. Optimizing process economics online using model predictive control. Computers & Chemical Engineering, 2013;58: Aydın, E., Celebi, A. D., Sildir, H., Arkun, Y., Canan, U., Is, G., Erdogan, M. Dynamic modeling of an industrial diesel hydroprocessing plant by the method of continuous lumping. Computers & Chemical Engineering, 2015;82: Ellis, M., Christofides, P. D. Integrating dynamic economic optimization and model predictive control for optimal operation of nonlinear process systems. Control Engineering Practice, 2014b;22: Helbig, A.; Abel, O.; Marquardt, W., Structural concepts for optimization based control of transient processes. In Nonlinear Model Predictive Control, Springer: 2000; pp Kadam, J.; Schlegel, M.; Marquardt, W.; Tousain, R.; Van Hessem, D.; van den Berg, J.; Bosgra, O., A two-level strategy of integrated dynamic optimization and control of industrial processes a case study. Computer Aided Chemical Engineering, 2002, 10, Sildir, H., Arkun, Y., Ari, A., Dogan, I., Harmankaya, M. Economic Model Predictive Control of an Industrial Fluid Catalytic Cracker. Industrial & Engineering Chemistry Research, 2014;53: Würth, L., Rawlings, J. B., Marquardt, W. (2009). Economic dynamic real-time optimization and nonlinear modelpredictive control on infinite horizons. In Proceedings of the International Symposium on Advanced Control of Chemical Process, Istanbul, Turkey. 5. ACKNOWLEDGEMENTS The authors gratefully acknowledge the financial support of TUPRAS Refineries. 573