Dynamics and Control of Energy Integrated Distillation Column Networks

200 American Control Conference Marriott Waterfront, Baltimore, MD, USA June 30-July 02, 200 ThA4.4 Dynamics and Control of Energy Integrated Distillation Column Networks Sujit S. Jogwar and Prodromos Daoutidis Department of Chemical Engineering and Materials Science University of Minnesota, Minneapolis, MN 55455, USA Abstract Networks of distillation columns, used for multicomponent separations, show the potential for energy integration via couing of some of the energy sources and sinks. Energy integration in such networks results in significant energy savings, but it also comes at the expense of control challenges. In this paper, we analyze various networks of distillation columns with significant energy integration. We identify key dynamic characteristics of such networks, which help in addressing the corresponding control problem. A case of a double effect distillation column is considered for a more detailed dynamic analysis and control study. I. INTRODUCTION Distillation is one of the most energy consuming separation processes. In a typical chemical ant, it accounts for about 40% of the total energy consumption. Motivated by this, the design of energy integrated distillation columns has been an area of research for quite some time, resulting in configurations such as vapor recompression distillation columns, multi-effect distillation columns, thermally coued (divided wall) columns, etc (see e.g. 2, 3). Multicomponent separations typically result in a network of distillation columns. The design of such networks has been an area of rich research activity (e.g. 4, 5). In a single distillation column, energy is input in the reboiler (energy sink) and is taken out of the column in the condenser (energy source). In a network of distillation columns, some of these energy sources and sinks can be coued through the use of combined reboiler-condensers, thus allowing for energy integration. The design of energy integrated distillation column networks has attracted significant attention 6, 7. It has been well documented that such integrated configurations lead to significant energy and thus cost savings (e.g. 8). However, these benefits come at the expense of operating and control challenges. The couing of heating and cooling requirements results in the reduction of available degrees of freedom. For exame, in the case of a combined reboilercondenser, the condenser and reboiler duties can not be manipulated independently. Apart from this, such a couing also results in feedback interactions, which can further comicate the control problem. However, not much effort has been put towards analyzing the dynamics of such networks and its impact on control. In this paper, we consider various networks of distillation columns with significant energy integration. Our objective is two-fold: To establish, through the use of energy flow diagrams, that most of these integrated distillation column configurations are interconnections of two fundamental classes of energy integrated networks (large energy recycle networks 9 and large energy throughput 0 networks), which have been analyzed previously in a different context; To focus on a particular exame of a double effect distillation column and illustrate, in detail, the use of the proposed analysis and control framework. The theoretical results presented in the paper are demonstrated with the help of a simulation case study. II. ENERGY INTEGRATED DISTILLATION COLUMN NETWORKS We will consider some representative exames of energy integrated distillation column networks and use energy flow diagrams to characterize the energy flows in such networks. In such energy flow diagrams, the hot and cold sides of a process-to-process heat exchanger are represented by separate blocks connected via an energy transfer stream as shown in Figure. Fig.. Energy flow diagram for a process-to-process heat exchanger A. Double effect distillation columns Double effect distillation is an integrated configuration with two columns operating at different pressures so that the condensing vapor in the high pressure (HP) column provides energy for the vaporization of the bottoms stream in the low pressure (LP) column in a combined reboiler-condenser. The duties of the remaining condenser (of the LP column) and the reboiler (of the HP column) constitute the external energy inputs. Depending on the product of interest, different configurations of double effect distillation, such as feed sit, light sit/forward, light sit/reverse configurations have been proposed (see 2). In this paper, we consider, for illustrative purposes, the light sit/reverse configuration shown in Figure 2(a). Figure 2(b) shows the energy flow diagram for this system. Note that the contribution of latent heat to the enthalpy 978--4244-7425-7/0/$26.00 200 AACC 2835

(a) (a) (b) Fig. 2. Double effect distillation is generally much greater than that of the sensible heat. Assuming that the kinetic and potential energy contributions to energy are negligible, the energy flow associated with a vapor stream will be larger compared to a liquid stream. The heat transfer in the condenser and the reboiler is dominated by the latent heat, and hence the corresponding input/output flows Q CL, Q BH represent a large energy source and sink respectively. Figure 2(b) highlights in red these large energy flows and suggests that this network is characterized by a high energy throughput. Such networks have been shown to exhibit two time scale behavior, with the energy balance dynamics evolving faster compared to the material balance dynamics 0. B. Sidestream rectifiers/strippers Sidestream rectifiers/strippers are typically used in the petroleum industry as well as in cryogenic air separations (wherein the side stripper is used for the recovery of argon). Figure 3 shows a sidestream rectifier along with its energy flow diagram. Note that no separate reboiler is needed for the side column. Recognizing again the discrepancies in the energy flows arising due to the presence of vapor and liquid flows as well as the heat transfer dominated by latent heat effects, the energy flow structure for this column also points to two large energy throughput loops, one from the reboiler of the parent column to the condenser of the parent column and the other from the same reboiler to the condenser of the side column. C. Heat pump assisted distillation columns In a distillation column, the temperature at which energy enters (in the reboiler) is higher than the temperature at Fig. 3. (b) Sidestream rectifier which it is taken out (in the condenser). This prevents direct couing of these energy sources and sinks. The use of a heat pump cycle, wherein the temperature of the condensing vapor is raised through compression, generates a sufficient temperature difference in a combined reboiler-condenser. Figure 4 shows one such heat pump assisted separation of a ternary mixture. In this particular exame, we can note the presence of two energy recycle loops, one each for the two reboilercondensers. Following the arguments about heat transfer dominated by latent heat effects, it can be established that both these loops exhibit large recycle of energy. It has been shown that networks with large energy recycle show a time scale separation in the energy dynamics itself, with a slow evolution of the total network enthalpy 9. The presence of the large recycle loops in this case suggests the potential for such multi-time scale dynamics. D. Multicomponent separation with five species Figure 5 shows an exame of an integrated system separating a mixture of five species (taken from ). In this system, there are four columns and only five external energy sources/sinks, as the other sources/sinks are shared through two combined reboiler-condensers. The energy flow 2836

(a) Fig. 5. Multicomponent separation with five species Fig. 4. (b) Heat pump assisted distillation diagram for this system is shown in Figure 6. We can note the presence of three large energy throughput branches (two in red and one in blue) in this system. As pointed out earlier in this section, the distillation column networks considered here represent interconnections of networks with large energy recycle or networks with large energy throughput. Both these classes of networks have been analyzed previously, in detail, documenting the presence of corresponding multi-time scale dynamics. Specifically: The networks with large energy recycle show a two time scale dynamics for the energy balance variables with fast evolution of the individual unit enthalpy and slow evolution of the total enthalpy 9. A hierarchical control strategy addressing control objectives related to the energy balance of the individual units in the fast time scale, leaving the control and optimization of the energy utilization at the level of the entire network to be addressed in the slow time scale has been shown to exhibit excellent closed-loop dynamics for such networks. The networks with large energy throughput show a two time scale dynamic evolution with the entire energy balance dynamics evolving in the fast time scale and the material balance dynamics evolving in the slow time scale 0. A hierarchical control strategy with a fast component addressing control objectives pertaining to energy balance and a slow component addressing control objectives related to material balance has also been shown to lead to excellent transition control. The existing framework for such generic classes can in princie be used to address the dynamic analysis and control of these distillation column networks. To this end, let us focus on a particular exame of a double effect distillation column to show, in detail, the use of the proposed framework. III. DYNAMICS AND CONTROL OF DOUBLE EFFECT DISTILLATION Let us consider the double effect distillation configuration shown in figure 2(a). The feed with light component mole fraction x f enters the N f,l tray of a low pressure (LP) column, with N L trays, at a flowrate F. The bottoms stream from the LP column is fed to the high pressure (HP) column at the N f,h th tray. The vapor from the HP column condenses in the reboiler of the LP column. Q C,L and Q B,H are the condenser and reboiler heat duties for the LP and the HP column respectively. For simicity, let us assume constant tray holdups, constant heat capacities and constant relative volatility in each column. Under these assumptions, the dynamic material and energy balance equations of this network can be formulated as: 2837

dm B,j dx B,j dt B,j R j + F j V j B j (R j + F j )(x N,j x B,j ) M B,j V j (y B,j x B,j ) (R j + F j )( h l (T N,j ) M B,j c h l (T B,j )) V j ( h v (T B,j ) h l (T B,j )) + Q B,j where the index j represents the column (LP/HP). h represents molar enthalpy of a stream with subscripts v and l distinguishing between the vapor and liquid streams. The integrated structure leads to the following equality relations: Q B,L Q C,H B L F H As pointed out earlier, the contribution of latent heat to the enthalpy is much larger than the contribution of sensible heat. Therefore, we can define a small parameter ɛ so that, Fig. 6. Energy flow diagram for the distillation column network in Figure 5 dm D,j d,j dt D,j V j R j D j V j (y,j,j ) M D,j V j ( h v (T,j ) M D,j c h l (T D,j )) Q C,j for i N f,j dx i,j V j (y i+,j y i,j ) + R j (x i,j x i,j ) M j dt i,j V j ( h v (T i+,j ) M j c h v (T i,j ))+ R j ( h l (T i,j ) h l (T i,j )) dx Nf,j dt Nf,j for N f,j < i N j dx i,j dt i,j V j (y Nf+,j y Nf,j ) + F j (x f,j x Nf,j ) M j R j (x Nf,j x Nf,j ) V j ( h v (T Nf+,j ) M j c h v (T Nf,j ))+ F j ( h l (T f ) h l (T Nf,j ))+ () R j ( h l (T Nf,j ) h l (T Nf,j )) V j (y i+,j y i,j )+ M j (R j + F j )(x i,j x i,j ) V j ( h v (T i+,j ) M j c h v (T i,j ))+ (R j + F j )( h l (T i,j ) h l (T i,j )) h l (T i,s ) h v (T i,s ) ɛ k i and F L,s h l (T f,s ) Q in/out,s ɛ k in/out where k i and k in/out are O() quantities. The dynamic equations in () can now be cast in a vector form (2): dx f + gu dζ F + g s w s + ɛ g lw l (2) with appropriately defined f, g, F, g s and g l. u represents the vector of scaled material flows and the vectors w s and w l represent, respectively, the scaled energy flows corresponding to small and large energy flows. The presence of the small parameter ε makes the dynamic equations stiff, showing a potential for multie time scale dynamics. We used singular perturbations to investigate these time scale properties. The description of dynamics in the fast time scale τ t/ε can be obtained by substituting τ in Eq. 2 and taking the limit ε 0, to get: dx 0 dτ dζ g l w l (3) dτ We can note that only the energy dynamics (tray temperatures) evolves in this fast time scale. The fast dynamics is influenced only by the scaled inputs corresponding to large energy flows (w l ). These flows serve as potential manipulated inputs to address control objectives in this fast time scale. The control objectives such as temperature regulation of a particular tray should be addressed in this time scale using one of these scaled large internal energy flows or scaled external large energy flows. 2838

This fast dynamics converges to a quasi-steady state captured by the following constraints: 0 g l w l (4) It can be verified that the constraints (4) are linearly independent. As the quasi-steady state constraints are linearly independent, we can solve the constraints (4) to obtain quasi-steady state values for the various temperatures in the network as T k(x, w l, û) (where û are the material flows not set by fast controllers). Thus, the energy dynamics entirely evolves over a fast time scale and the material dynamics corresponds to the slow dynamics of the network. The slow time scale material dynamics can now be given as: dx f(x, T ) + g(x, T )û (5) Eq. (5) can now be used to address control objectives in the slow time scale, such as the regulation of condenser/reboiler holdups, the control of exit concentrations, etc. û represents the subset of the scaled flows which are available for manipulation in the slow time scale. Let us consider a simulation case study to further illustrate these results. IV. SIMULATION CASE STUDY We considered the separation of a benzene-toluene mixture in the double effect distillation configuration shown in Figure 2(a). The nominal values of various parameters for the double effect distillation configuration are given in table I. The system was modeled with gproms2. The distillation columns and the heat exchangers were modeled using Process Model Library v3. and the inbuilt IPPFO package was used for property estimation. We considered that the two distillate streams are mixed together to obtain a total benzene-rich distillate stream. TABLE I NOMINAL VALUES OF PARAMETERS FOR THE DOUBLE EFFECT DISTILLATION CONFIGURATION,L 0.939 kg/kg,h 0.7484 kg/kg x B,L 0.4493 kg/kg x B,H 0.2587 kg/kg x f,l 0.56 kg/kg x f,h 0.4493 kg/kg D L.37 kg/s D H.539 kg/s B L 3.863 kg/s B H 2.324 kg/s F L 5.000 kg/s F H 3.863 kg/s T D,L 347.8 K T D,H 43.8 K T B,L 36.7 K T B,H 43.8 K Q C,L 0.87 MW Q B,H.33 MW M D,L 59.9 kg M D,H 56.6 kg M B,L 987.2 kg M B,H 45.8 kg P L 0.8 bar P H 3.8 bar N L 2 N H 8 N f,l 0 N f,h 2 Following our analysis, in the fast time scale, we addressed the control of the temperature in the reboiler of the HP column (T B,H ), which indirectly regulates the bottoms stream composition (x B,H ). We used the reboiler duty (Q B,H ), which is a large energy flow, as a manipulated input to address this control objective. A sime PI controller (6) was used. τ ) w B + (er K + τi er dτ 0 where w B Q B,H /Q B,H,s, er T B,H,sp T B,H and K 0.05 K, τ I min. In the slow time scale, we addressed the control of the total distillate composition ( ) using a model based controller using the distillate flow from the HP column (D H ) as a manipulated input. The slow model (5) was used for the synthesis of a state feedback input/output linearizing controller. We requested a first order response of the form: β d (6) + v (7) where β 50 min. Apart from this controller, we imemented sime proportional controllers to stabilize various holdups in the network. In the first simulation run, the set point of controller was increased from to 0.88 and the corresponding ots are shown in Figure 7. Note that the fast and slow controllers, derived on the basis of the reduced order models, enable efficient transition between the two steady states. In the next simulation run, the feed flow rate of the system was increased by 0% and the corresponding ots are shown in Figure 8. The proposed control strategy demonstrates very good performance in this case too. V. CONCLUSIONS In this paper, we analyzed the impact of energy integration on the dynamics and control of distillation column networks. We considered some representative exames of such networks and investigated the underlying energy flow structure with the help of energy flow diagrams. We identified a connection between these energy flow structures and some generic classes of integrated networks studied previously. We focused on the case of a double effect distillation column network and showed the presence of two time scale dynamics with fast evolution of the energy balance dynamics and slow evolution of the material balance dynamics. Exoiting this time scale multiicity, we proposed a hierarchical control strategy addressing the temperature control in the fast time scale and the concentration/holdup control in the slow time scale. Through a simulation case study, we demonstrated the performance of the proposed control strategy. The analysis presented in this paper can be extended to more comex distillation column networks (e.g. Figure 5). The analysis and control of such networks is one direction of our future work. ACKNOWLEDGEMENTS Partial financial support for this work by the National Science Foundation, grant CBET-0756363 is gratefully acknowledged. 2839

0.89 43.8 0.88,set 43.8.6,set.55 0.87 43.79.5 43.78 0.86 0.85 K 43.77 43.76 D H kg/s.45.4 0.84 43.75.35 43.74 0.83 43.73.3 0.82 43.72.25.65 0.264.6 0.263.55 0.262 Q B H MW.5.45 x BH 0.26.4 0.26.35 0.259.3 0.258 Fig. 7. Closed loop performance for a set point change ( to 0.88) in 432..9,set 432,set.85 43.9.8 K 43.8 43.7 43.6 43.5 43.4 D H kg/s.75.7.65.6 43.3.55 43.2.5.55 0.276 0.274.5 0.272 0.27 Q BH MW.45.4 x BH 0.268 0.266 0.264 0.262.35 0.26 0.258.3 0.256 Fig. 8. Closed loop performance for a 0% increase in feed flow REFERENCES J. Humphrey, Separation Process Technology; McGraw-Hill, 997. 2 C. J. King Separation Processes, 2 nd ed.; McGraw-Hill: New York, 980. 3 O. Annakou and P. Mizsey, Rigorous Comparative Study of Energy- Integrated Distillation Schemes, Ind. Eng. Chem. Res., vol. 35, 996, 877-885. 4 M.F. Doherty and M.F. Malone, Conceptual Design of Distillation Systems, McGraw-Hill, Boston, 200. 5 R. Agrawal, Synthesis of Multicomponent Distillation Column Configurations, AIChE J., vol. 49, 2003, pp. 379-40. 6 B. G. Rong, A. Kraslawski and I. Turunen, Synthesis of Functionally Distinct Thermally Coued Configurations for Quaternary Distillations, Ind. Eng. Chem. Res., vol. 42, 2003, pp. 204-24. 7 J. A. Caballero and I. E. Grossmann, Design of Distillation Sequences: From Conventional to Fully Thermally Coued Distillation Systems, Comput. Chem. Eng., vol. 28, 2004, pp. 2307-2329. 8 E. Rev, M. Emtir, Z. Szitkai, P. Mizsey and Z. Fonyo, Energy Savings of Integrated and Coued Distillation Systems, Comput. Chem. Eng., vol. 25, 200, pp. 9-40. 9 S. S. Jogwar, M. Baldea, and P. Daoutidis, Dynamics and Control of Process Networks with Large Energy Recycle, Ind. Eng. Chem. Res., vol. 48, 2009, pp. 6087-6097. 0 M. Baldea and P. Daoutidis, Modeling, Dynamics and Control of Process Networks with High Energy Throughput, Comput. Chem. Eng., vol. 32, 2008, pp. 964-983. M. J. Andrecovich and A. W. Westerberg, An MILP Formulation for Heat-integrated Distillation Sequence Synthesis, AIChE J., vol. 3, 985, pp. 46-474. 2 gproms v3.2 User Guide. 2009, Process Systems Enterprise Ltd. 2840