Dynamic simulation for internally heat-integrated distillation columns (HIDiC) for propylene–propane system

Dynamic simulation for internally heat-integrated distillation columns (HIDiC) for propylene–propane system

Computers and Chemical Engineering 33 (2009) 1187–1201 Contents lists available at ScienceDirect Computers and Chemical Engineering journal homepage...

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Computers and Chemical Engineering 33 (2009) 1187–1201

Contents lists available at ScienceDirect

Computers and Chemical Engineering journal homepage: www.elsevier.com/locate/compchemeng

Dynamic simulation for internally heat-integrated distillation columns (HIDiC) for propylene–propane system Tsung-Jen Ho a,1 , Chi-Tsung Huang b,∗ , Jhih-Ming Lin b , Liang-Sun Lee a,∗ a b

Department of Chemical and Materials Engineering, National Central University, Chung-li 32001, Taiwan Department of Chemical Engineering, Tunghai University, Taichung 40704, Taiwan

a r t i c l e

i n f o

Article history: Received 15 November 2007 Received in revised form 14 January 2009 Accepted 21 January 2009 Available online 31 January 2009 Keywords: Distillation Heat integration Variable column pressure Dynamic simulation with control

a b s t r a c t This paper reports a dynamic simulation study of the internally heat-integrated distillation column (HIDiC) using equilibrium-based models. First, three different HIDiC structures, i.e. an ideal HIDiC, a HIDiC with a pre-heater, and a HIDiC with a reboiler, are analyzed by control degrees of freedom (DOF). The reboiler is considered to be a necessary part of the HIDiC from DOF analysis, thermodynamic analysis, and engineering judgment. Then, a heuristic HIDiC control configuration including a bottoms reboiler control is proposed. A modular structured simulator for dynamic distillation columns using MESH equations is developed. The simulator also considers: (1) variable column pressure on each tray of the rectifying section, (2) dynamic vapor holdup, and (3) dynamic energy balance. In addition, the SRK equation of state is employed for estimating thermodynamic properties. A typical medium-pressure HIDiC for separation of propylene and propane explored by Olujic et al. [Olujic, Z., Sun, L., de Rijke, A., & Jansens, P. J. (2006). Conceptual design of an internally heat-integrated propylene–propane splitter. Energy, 31, 3083] is adopted as numerical examples for dynamic simulation studies. © 2009 Elsevier Ltd. All rights reserved.

1. Introduction Distillation is one of the most popular methods of separation in chemical and petrochemical industries. However, this process is also energy intensive in the process industries. In order to reduce energy consumption of distillation columns, many new techniques have been proposed since 1950s. One of the efficient ways of saving energy is the internally heat-integrated distillation column (HIDiC). The HIDiC can be considered as one kind of heat pump-assisted distillation columns. Many authors have done several theoretical and experimental research studies since 1985. Nakaiwa et al. (2003), recently, gave a detailed review about the relevant research including thermodynamic analysis, practical process design and operation, and also found that discussions on dynamic modeling seem to be relatively scarce. These authors pointed out that experimental-based development of process configurations is very expensive, and the development of HIDiC configurations based on process models is thus highly desired. Huang, Nakaiwa, Akiya, Aso, and Takamasu (1996) proposed the first HIDiC dynamic modeling using a simplified stage model assuming ideal vapor–liquid equilibrium (VLE) relationship and a control configuration for a

∗ Corresponding authors. Fax: +886 4 2359 0009. E-mail address: [email protected] (C.-T. Huang). 1 Present address: Pilot Process and Applications of Chemical Engineering and Technology Division, Industrial Technology Research Institute, Hsinchu, Taiwan. 0098-1354/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.compchemeng.2009.01.004

HIDiC with a pre-heater. They have also done extensive simulation studies, which include process dynamics, startup, and control strategies (Nakaiwa et al., 2003). In addition, Huang et al. (1996) proposed a HIDiC control scheme, in which the bottoms composition is controlled by the feed pre-heater. Furthermore, this control scheme has been investigated by Huang and his colleagues using different control algorithms including relative gain array analysis, frequency domain analysis, closed-loop PI control, internal model control, nonlinear process model-based control, etc. A more detailed review about these control studies can also be found in the work of Nakaiwa et al. (2003). After that, Nakaiwa et al. (2000) proposed a new intensified HIDiC configuration using the same control structure. Naito et al. (2000) reported an experimental study for the HIDiC, in which a trim condenser and a trim reboiler are necessary for startup operation. Huang, Matsuda, Takamatsu, and Nakaiwa (2006), recently, proposed a more rigorous HIDiC model, which includes the consideration of vapor holdups and pressure dynamics. They stated that the dynamics of pressure distribution should be taken into account in the HIDiC control system design. Controllability analysis for the HIDIC under such control configuration including the influences of pressure distribution, multivariable analysis, closed-loop control, etc. has also been explored by Huang, Matsuda, Takamatsu, et al. (2006) and Huang, Matsuda, Iwakabe, Takamatsu, and Nakaiwa (2006). Moreover, Huang, Wang, Iwakabe, Shan, and Zhu (2007) proposed a temperature control scheme for the HIDiC with a pre-heater. The main purpose of their study is using tray temperatures to infer

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the top and bottoms compositions instead of the on-line analyzer. On the other hand, a conventional approach based on fundamental engineering principles for classic distillations and other unit operations using explicit modular sequential method has also been developed by Franks (1972), Grassi (1992), and others. Such approach usually follows the process topology, solving each physical phenomenon in a structured sequence of steps. Since process systems are normally represented as sets of interconnected unit operations with controllers, many practicing engineers have used it for a long time. The main advantage of such approach is that it is more flexible to link with other unit operations or controllers. In addition, Choe and Luyben (1987) pointed out that vapor holdup and dynamic column pressure should be incorporated into the distillation models. Otherwise, it will lead to a poor prediction of dynamic responses for higher pressure (say greater than 10 bars) columns. The study considers that the previous HIDiC model proposed by Huang et al. (1996) or Huang, Matsuda, Takamatsu, et al. (2006) seems possible to be modified. In order to explore the dynamics and control for HIDiC systems, a dynamic simulator based on the modular structure of Franks (1972) using FORTRAN language has been developed in this study. Based on the equilibrium-based models of Choe and Luyben (1987), the Soave–Redlich–Kwong (SRK) equation of state (Soave, 1972) is employed. A HIDiC for separation of propylene–propane, which was explored by Olujic, Sun, de Rijke, and Jansens (2006), is adopted as numerical examples. In addition, a dynamic column pressure on each tray of the rectifying section using the first-order transfer function is recommended. Furthermore, a heuristic control configuration from practical instrumentation viewpoints for the HIDiC shown in Fig. 1 is proposed. Simulation based on the dynamic model without using any advanced control algorithm (e.g. model-based control) in Fig. 1 is implemented in this study.

Fig. 1. The HIDiC control configuration proposed in this study.

2. Analysis of HIDiC configurations with control The selection of an appropriate control configuration (or structure) is the most important decision when designing distillation control systems. The control configuration implies which controlled variables should be connected to which manipulated variables. Once a plant has been specified, the control configuration design normally requires knowledge of the control degrees of freedom (DOF). For many practical problems, the control DOF is equal to the number of independent material and energy streams that can be manipulated in control loops. Luyben (1996) proposed an equation to predict the control DOF for a broad class of chemical processes as DOF = Nvalves + Nsections + Ngas

reactor

− Nnonreactive

levels

(1)

For a conventional distillation column, there are six control degrees of freedom (Luyben, Tyreus, & Luyben, 1999). Thus, six control valves can be manipulated: feed flow, distillated flow rate, bottoms flow rate, reflux flow rate, cooling flow rate, and heating medium flow rate. The controlled variables are two product compositions (top and bottoms), throughput, column pressure, and liquid levels in the reflux drum and column base. Normally, one of these valves is used to set throughput. Two of the control degrees of freedom must be consumed to control the two liquid levels. A fourth degree of freedom is for column pressure control. Finally, two remaining degrees of freedom are employed to control two product compositions of the column. Fig. 2 shows the DOF analysis for three HIDiC structures using Luyben’s equation. They are: (a) ideal HIDiC, (b) HIDiC with a preheater, and (c) HIDiC with a reboiler. The compressor, which is equivalent to the control valve during the counting of DOF in Fig. 2, is considered to be a manipulated variable. Except for the ideal HIDiC, others have the same DOF as the classic distillation column, i.e. DOF = 6. The proposed control configuration in Fig. 1, which is equivalent to Fig. 2(c), has four control valves and one variable speed controller (SC) to adjust the compressor. A feed valve, not shown in Fig. 1, is usually used to set throughput. In addition, five controlled variables for this configuration are: stripping base level, rectifying base level, rectifying pressure, top product composition (yD ), and bottoms product composition (xB ). As shown in Fig. 1, two valves are utilized to control two base levels. It should be noted that the base level of the stripping (or rectifying) should be controlled; otherwise, the base may surge or empty. The bottoms composition (xB ) is controlled by the reboiler heat duty. At this point in the analysis, a true control problem is encountered. Two control degrees of freedom remain, and either the top product valve or the compressor speed could be manipulated to control the rectifying pressure. However, either of these two variables could also be manipulated to control the top product composition (yD ). Thus, a conceptual control configuration employing a valve-position controller (VPC) for the rectifying section of the HIDiC is proposed in Fig. 1. The technique of VPC was original developed by the industry before the second energy crisis (Shinskey, 1978; Shinskey, 1996). For energy saving, the compressor should operate at minimum speed needed to satisfy the total load, which is variable. As shown in Fig. 1, the top composition (yD ) is controlled by the top pressure, which is controlled by adjusting the top product valve. The VPC minimizes the compressor speed by keeping the valve mostly open for energy saving, e.g. 90% open. In fact, the VPC scheme is a different type of cascade control system. The primary control is the position of the valve. The secondary control is the column pressure of the rectifying section. It should be noted that the pressure of the rectifying section would float up and down under such control scheme in Fig. 1. In addition, the speed controller is recommended for the compressor control in Fig. 1; other compressor control systems (Muhrer, Collura, & Luyben, 1990) are also feasible. However, Shinskey (1996) con-

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Fig. 2. Control degrees of freedom analysis for various HIDiC structures.

siders that the speed manipulation for compressor control is more effective and efficient for all. Subsequently, there is a throttling valve between the bottom of the rectifying section (higher pressure) and the top of the stripping section (lower pressure). The throttling valve here is used for reducing pressure. In practice, it is more convenient to employ a pressure regulator (PCV) as shown in Fig. 1. The pressure regulator is a self-contained control loop requiring no external energy, which incorporates a sensor, a controller, and a valve into one device. The PCV in Fig. 1 can reduce and regulate the downstream pressure of the pipeline. More details about the pressure regulator including hardware and applications can be found in Liptak (1995). Furthermore, the top product, which is considered to be a saturated vapor, can be used to preheat the feed or even an auxiliary reboiler, or it can be used in other process heat integrations for energy saving (Smith, 2005). On the other hand, Fukushima, Kano, and Hasebe (2006) recently have investigated several HIDiC structures including an ideal HIDiC, a HIDiC with condenser and reboiler, a HIDiC with preheating the feed by distillated vapor, and a HIDiC with condenser and preheating the feed by distillated vapor. Using the Aspen simulator, they compare the energy efficiency, dynamics, and controllability of these HIDiCs. Based on energy efficiency and controllability, Fukushima et al. (2006) have recommended adopting the structure in which the feed is preheated by distillated vapor product, a condenser is used, and a reboiler is not used. Their HIDiC structure is significantly different from the proposed HIDiC structure, in which a condenser is not recommended. Fig. 3(a) shows the schematic HIDiC system of Fukushima et al. (2006); it is also called System 1 in this study. Under the same separation conditions (i.e. the feed, the distillate product, and the bottoms product are the same), the top vapor product of the proposed HIDiC can be used to heat an auxiliary reboiler and the feed. The proposed HIDiC system, which is called System 2, is shown in Fig. 3(b). Now let HFeed = F × hFeed , HTop = D × hTop , and HBot = B × hBot ; where all h’s in Fig. 3 are specific enthalpies. From the first law of thermodynamics, one has H = Q + Ws for open systems if the kinetic energy and potential energy are negligible, where Ws is the shaft work (Kyle, 1999, p. 29). Furthermore, the total energy balance of System 1 from the first law perspective is H1 = HTop + HBot − HFeed = WS1 − QCond

(2)

Similarly, the total energy balance for System 2 is H2 = WS2 + QReb

(3)

It should be noted that both QCond and QReb in the above equations are all positive quantities. Under the same conditions, i.e. H1 = H2 , Eqs. (2) and (3) are combined to form as WS1 = (WS2 + QReb ) + QCond

(4)

It is obvious that the compressor shaft work of System 1 (WS1 ) is higher than the total energy required of System 2, which is

Fig. 3. Schematic diagrams of different HIDiC structures. (a) System 1 and (b) System 2.

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stage is carried out by solving the SRK equation of state (Soave, 1972). A fast convergence technique recommended by King (1980) is employed in this algorithm. The King’s convergence technique (King, 1980), which is an algebraic iteration method without using any derivative as in Newton’s method, is considered to be reliable for VLE calculations using the SRK equation of state. Then, using the modular structure of Franks (1972), a VLE stage modular (or called subroutine) as shown in Fig. 4 is developed. In addition, based on the basic control configuration shown in Fig. 1, one can see that the output pressure of the compressor (Pout ) should “synchronize” with the base pressure of the rectifying section, which is also influenced by the top valve. Thus, the effects of variable pressure should be incorporated in the dynamics of the rectifying section, since the HIDiC control scheme can cause large changes in operating pressures. In order to simulate such phenomena, a modular simulation diagram for the HIDiC system, as shown in Fig. 5, is developed in this study. The modeling for the equilibrium stages of the rectifying or the stripping section is described in the previous paragraph. Heat transfer between the corresponding stages (Qj ) shown in Fig. 5 is calculated by Fig. 4. An equilibrium stage.

WS2 + QReb . It can also be interpreted as that a HIDiC with condenser needs bigger compressor and consumes more energy than the proposed HIDiC without any condenser. In addition, it is found in Fig. 2 that the ideal HIDiC has DOF = 5, and others have DOF = 6. The ideal HIDiC configuration might have difficulties in practical control, since it loses one DOF. Also, from the first law of thermodynamics (i.e., H = Q + Ws ), the total energy required (i.e., Q + Ws ) for Fig. 2(b) is the same as that of Fig. 2(c), if they are operated under the same separation conditions. Huang, Matsuda, Iwakabe, et al. (2006) have pointed out that a HIDiC with a reboiler requires more steam flow rate (Q) than a HIDiC with a pre-heater. It can also be interpreted as that a HIDiC with a reboiler needs less compressor shaft work (Ws ) than one with a pre-heater. Furthermore, to control of the bottoms composition (xB ) by adjusting the feed pre-heater, which was recommended by Nakaiwa et al. (2003), it might normally produce a very large undesired timedelay owing to the tray hydraulic lag (Luyben & Luyben, 1997, p. 460; Luyben et al., 1999, p. 196). Accordingly, the HIDiC control configuration shown in Fig. 1, which adjusts the reboiler duty to maintain the bottoms composition, is adopted for simulation studies in this paper.

Qj = UA · Tj

(5)

where A is the heat-transfer area; U is the overall heat-transfer coefficient; Tj is temperature difference between the paired stages. Also, UA in this study is assumed to be constant for all thermally coupled stages. Furthermore, the top portion of the HIDiC rectifying section is considered as Fig. 6. The top pressure is manipulated by a control valve using a pressure controller (PC). Assuming the temperature of the top portion is the same as that of stage 1, one has the following material balances: dM1V dt

= V1 − VD

d(M1V yi,D ) dt

(6)

= V1 yi,1 − VD yi,D

for i = 1, 2, . . . , NC

(7)

where M1V is the vapor holdup of the top stage (stage 1); V1 is the vapor flow rate from stage 1; VD is the vapor flow rate of the top distillate, which is manipulated by the pressure controller (PC). It should be noted that during the calculations of stage 1 the vapor holdup is neglected, which is different from the previous equilibrium stage. Combing Eqs. (6) and (7), one has dyi,D V1 (yi,1 − yi,D ) = dt MV

for i = 1, 2, . . . , NC

(8)

1

3. Modeling of the HIDiC with variable column pressure The basic module for a HIDiC is a vapor–liquid equilibrium (VLE) stage, as shown in Fig. 4. The assumptions for formulating such model are: (1) each liquid (or vapor) phase is perfect mixing; (2) heat of mixing is negligible; (3) temperature (or pressure) on each stage is uniform; (4) the liquid and vapor streams leaving each stage are in phase equilibrium; (5) the liquid flow rate on each stage is calculated by Francis weir formula; (6) the heat loss between the HIDiC column and the surrounding is negligible. Under the above assumptions, the fundamental equations for an equilibrium stage (stage j) are dynamic MESH (mass balances, equilibriums, summations, and heat balance) equations. Moreover, Choe and Luyben (1987) have reported that neglecting vapor holdup gives a process time constant about 50% less than the actual value on an ethylene-ethane splitter operating at 30 atm. Thus, dynamic material balances of a VLE stage as shown in Fig. 4, which include liquid holdup (MjL ) and vapor holdup (MjV ), are considered in this study. The detailed equations for dynamic material and energy balances can be found in Choe and Luyben (1987). In addition, the VLE calculation on each

Thus, both the top vapor composition (yi,D ) and M1V at each time point can be calculated from Eqs. (6) and (8) using the 4th-order Runge-Kutta method. Once M1V is obtained, the top pressure (P1 ) at each time point can be calculated by P1 = zM1V

RT VOL

(9)

where VOL is a constant vapor volume of the top portion. Moreover, z and T are obtained during the equilibrium calculation of stage 1 using the SRK equation of state. Since the top pressure is floating, the pressures on each stage of the rectifying section may also vary. There are several ways to incorporate floating pressure in the classic distillation model. A more complex and rigorous approach, which considers variable tray pressure drop, is called “vapor hydraulic” model. This method, however, requires more computer time for executing a software package. Choe and Luyben (1987) gave a more detailed description about this method. To avoid too complex computation for the variable column pressure of a HIDiC, a simple technique using transfer functions is proposed in this study.

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Fig. 5. Schematic representation of a HIDiC simulation diagram.

Normally, a constant pressure drop between two consecutive stages (Pstg ), say Pstg = 0.006 bar, is considered for steady-state design. Thus, if the top pressure of the rectifying section is P1 , the base pressure of the rectifying section is P1 + Pstg × (N − 1), where N is the number of rectifying stages. In this study, not only the steady-state pressure drop per stage (Pstg ) is considered, but also the pressure dynamics for each stage using the transfer function, as ˆ shown in Fig. 5, is considered. Let X(s) represents the deviation variˆ able of the top pressure, and X(t) = P1 (t) − P1s . Where P1 (t) is the real-time pressure of the top; P1s is the steady-state top pressure. Similarly, let Yˆ j (t) is the deviation variable of the jth-stage pressure, and Yˆ j (t) = Pj (t) − Pjs . Where Pj (t) is the real-time pressure of stage j; Pjs is the steady-state pressure of stage j. The dynamic relationship between the jth-stage pressure and the top pressure, i.e. Yˆ j (s) ˆ vs. X(s), can be represented by the first-order transfer function as Yˆ j (s) Xˆ j (s)

=

1 1 = j s + 1 (j − 1) s + 1

(10)

where  is the time constant between two consecutive stages. It can also say that the time constant between the top stage and stage j is  j , and  j = (j − 1). Practically, the numerical value of  can normally be estimated from the column geometry. In this simulation study,  = 0.1 min is chosen. Then, the dynamics of variable column pressure on each stage of the rectifying section is incorporated with

its steady-state pressure as Pj (t) = Pjs + Yˆ j (t)

(11)

On the other hand, there is a pressure regulator (PCV) between the bottom of the rectifying section and the top of the stripping section, as shown in Figs. 1 and 5. The PCV can normally reduce and regulate the downstream pressure of the pipeline, as mentioned before. As shown in Figs. 1 or 5, the downstream pressure of the PCV is adjusted to be the same as the feed pressure, and the feed flow rate normally is a large quantity. The pressure on the top stage of the stripping section (i.e., b1 in Fig. 5), therefore, is considered to be the same as the feed pressure. Moreover, the heat transfer between the corresponding stages in rectifying and stripping sections, or the heat transfer from the reboiler can normally change vapor flow rates in the column (Franks, 1972; Grassi, 1992; Huang et al., 1996). In practice, if the reboiler duty (or other internal heat transfer) increases, the vapor flow rate will also increase, and vice versa. Thus, the pressure drop (Pstg ) between consecutive stages will also change. Similarly, the vapor flow rate on the top of the stripping section, as shown in Figs. 1 and 5, may also change when the pressure elevation of the compressor varies (Shinskey, 1996). Consequently, thePstg will also change. The relationship of the Pstg changes can normally be approximated as (Pstg )2 = (Pstg )1 × (u2 /u1 )2 , where u1 and u2 are two different

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T.-J. Ho et al. / Computers and Chemical Engineering 33 (2009) 1187–1201 Table 1 Steady-state design specifications for the HIDiC. Feed composition (propylene) Top composition (propylene) Bottom composition (propane) Feed flow rate Top flow rate Bottoms flow rate Feed pressure Feed temperature Rectifying pressure Stripping pressure Rectifying stages Stripping stages Overall heat transfer coefficient (U) Heat transfer area (A) Pressure drop (Pstg ) Rectifying section active area Stripping section active area Rectifying section weir height Stripping section weir height Rectifying section weir length Stripping section weir length Rectifying section column diameter Stripping section column diameter Reboiler duty

Fig. 6. The top portion of the HIDiC rectifying section.

vapor velocities (McCabe, Smith, & Harriott, 2005). However, Pstg normally is quite small (say Pstg = 0.006 bar × 4, if u2 /u1 = 2) in comparison with the column pressure (say 11.2 bar). Thus, except for vacuum distillation, the changes of Pstg during the transients are generally neglected in common distillation simulation (Franks, 1972; Grassi, 1992; Huang et al., 1996). Accordingly, the assumption of constant stage pressure is considered for the stripping section, and the uniform pressure drop between consecutive stages (i.e., Pstg = 0.006 bar) is chosen in this study. Furthermore, the dynamics of the compressor is negligible, which is attributed to very rapid response. The output temperature of the compressor (Tout ), however, is calculated by Tout = Tin

P

out

(−1)/

Pin

(12)

where  is the polytropic coefficient. In this study, an ideal compression is considered, and  = 1.4 is chosen. Moreover, in order to “synchronize” with the base pressure of the rectifying section for this simulation, the setpoint of the compressor controller should be set by Pout = P1 + Pstg × (N − 1)

(13)

In fact, Eq. (13) has not been used during simulation, since the base pressure of the rectifying section, which is equivalent to Pout , is already calculated by Eqs. (10) and (11). Fig. 5 shows the schematic representation of basic simulation modules for a HIDiC column. The dynamic simulation of the rectifying pressure in Fig. 5 is very similar to the VPC pressure control system in Fig. 1, although it is not exact resemblance. 4. Simulation for HIDiC control Dual-composition control for a general distillation column, which provides a tighter control over both top and bottoms product purities, has been profitably implemented in process industries. In this section, we are trying to use the proposed dynamic simulator to explore the effectiveness of the dual-composition control in the HIDiC using simple control strategies. A propylene–propane sys-

52 mol% 99.6 mol% 96.5 mol% 112 t/h 57.9 t/h 54.1 t/h 11.2 bar 300 K 14.6 bar 11.2 bar 170 61 1000 W/m2 K 402 m2 /stage 6 mbar/stage 12.82 m2 12.21 m2 0.05 m 0.05 m 4.38 m 4.21 m 9.07 m 8.81 m 7.16 MW

tem, which was studied by Olujic et al. (2006), is adopted. Table 1 summarizes the main column specifications. Most of the parameters in Table 1 follow those of Olujic et al. (2006); some of them, such as equivalent column diameters, weir height, weir length, etc., are obtained from the engineering practice of tray sizing. Unlike Olujic et al. (2006), in which an ideal HIDiC without reboiler is considered, this study recommends to add a reboiler at the bottom of stripping section. Although an ideal HIDiC without reboiler may reduce some equipment and energy costs, it will lose one DOF as shown in Fig. 2(a), and the bottoms composition (xB ) may not be easily maintained. There are two proposed HIDiC simulation schemes, which are all derived from Fig. 1, in this study. One uses an on-line analyzer to cascade the top pressure as shown in Fig. 7, and named as CS1. The other, shown in Fig. 8, uses a simple inferential scheme to control the top product, and named as CS2. In both CS1 and CS2 cases, a temperature controller is employed instead of an on-line analyzer controller for the bottoms composition. It should be noted that the compressor controller (SC) is always “synchronized” to the top pressure variation using the previous pressure simulation, and will not be discussed in the later part of this work. On the other hand, a practical proportional-integral-derivative (PID) control algorithm dubbed as reset-feedback form shown in Fig. 9 is chosen. The reset-feedback form of PID control algorithm provides a noise filter and avoids “derivative kick”. In addition, a saturation function (between 0 and 1.0) with anti-reset-windup compensation is considered. The saturation function, which corresponds to an actuator, causes the output signal of the PID controller in the normalized range of 0–1.0 (or 0–100%). Details of this PID control algorithm can be found elsewhere (Astrom & Hagglund, 1995; Shinskey, 1996; Smith & Corripio, 2006). Since the reset-feedback PID controller is employed in the dynamic simulation of this study, the controlled variable (e.g. temperature) is converted into the normalized signal of 0–1.0 based on the transmitter range before it enters the controller. The signal, which varies in the normalized range from 0 to 1.0, is an observable evidence of variation in the physical variable through the transmitter range. Similarly, the controller output signal, which varies in the range from 0 to 1.0, is converted into physical variable (e.g. heat duty) by the control valve and then influences the process. Table 2 summarizes transmitter and valve ranges with controller tuning constants for the important loops. Unlike other research works, such kind of dynamic simula-

T.-J. Ho et al. / Computers and Chemical Engineering 33 (2009) 1187–1201

Fig. 7. CS1 simulation scheme.

Fig. 8. CS2 simulation scheme.

Table 2 Transmitter and valve ranges with controller settings. Variables name Top pressure (bar) Top temperature (K) Bottoms temperature (K) Reboiler duty (MW) Top product (mol/min) Top composition (mole fraction)

1193

Maximum

Normal

Minimum

15.6 317.0 315.0 13.6 43,362.0 1.0

14.6 307.0 305.0 7.16 21681.0 0.996

13.6 297.0 295.0 0.0 0.0 0.9

Controller settings

KC (%/%)

 I (min)

 D (min)

Top pressure control Top temperature control Bottom temperature control Composition control

−0.1 0.1 0.1 10.0

5.0 2.0 2.0 1.0

– 0.4 0.4 0.25

tion using normalized signal and the reset-feedback controller is considered to be more realistic for a practical situation. In addition, Smith and Corripio (2006) stated: “Reset windup protection is an option that must be bought in analogy controllers. It is a standard feature in any computer-based controller.” 4.1. CS1 simulation First, a dual-composition control scheme for the HIDiC shown in Fig. 7 using the previous simulator is implemented in this study. The temperature on stage 60 of the stripping section is selected to infer the bottoms composition. In fact, the vapor boilup in Fig. 7 affects all stripping section of the HIDiC quickly. Thus, any stage temperature in the stripping section could be selected as the controlled variable without dynamic problem (Luyben & Luyben, 1997). Since propane

Fig. 9. The reset-feedback PID control loop.

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Fig. 10. Steady-state temperature profile of the HIDiC.

is almost the only component on stage 60, if one can maintain the stage temperature at its bubble point, very little of the propylene can go down to the bottoms. However, a composition controller (CC) with on-line analyzer is required to manipulate the top pressure in order to maintain the top composition. In addition, several modules (subroutines) including the equilibrium stage, PID controller, and variable pressure system have been developed in this study. The HIDiC simulator requires a master-calling program (main program) to assemble these subroutines. The main program just assembles the control system shown in Fig. 7 with the HIDiC modules shown in Fig. 5. The master-calling program starts with the reboiler, and then the bottoms with control, followed by calling the stages up to the top of the column in a sequence of time point. All level controls and PCV in Fig. 7 are assumed to be “prefect control”, i.e. their dynamics are negligible. The reset-feedback PID controllers are employed for these control loops, and PID controller settings, shown in Table 2, are obtained by trial-and-error. In addition, the step size of 0.01 min is chosen for the numerical integration of the complete simulation. However, the sampling period of 6 min is chosen for the composition controller, since an on-line analyzer (e.g. gas chromatograph) normally has a column retention time of 4 min when the sample is injected. The composition control system in Fig. 7, actually, is a sampled-data system with sampling period of 6 min. The steady-state operating conditions of the HIDiC can, therefore, be obtained when the dynamic simulator was run under such

Fig. 12. Steady-state vapor flow rate profile of the HIDiC.

control scheme for a long time period. Figs. 10–12 show the steadystate temperature profile, composition profile, and vapor flow rate profile of the HIDiC, respectively. The vapor flow rate profile shown in Fig. 12 is very similar to that of Olujic et al. (2006), which was obtained by the Aspen Plus. Upon reaching the steady state for the simulation system, the simulation time is reset to zero, i.e. t = 0, and the system is going to implement the dynamic testing. Since the major disturbances of the HIDiC come from the feed, six kinds of step change are introduced at t = 2000 min, respectively. They are: (1) Feed flow +10%: the feed flow rate changes from 2601.73 to 2861.90 kmol/h. (2) Feed flow −10%: the feed flow rate changes from 2601.73 to 2341.56 kmol/h. (3) Feed propylene +10 mol%: the feed propylene changes from 0.52 to 0.62. (4) Feed propylene −10 mol%: the feed propylene changes from 0.52 to 0.42. (5) Feed temperature +10 K: the feed temperature changes from 300 to 310 K. (6) Feed temperature −10 K: the feed temperature changes from 300 to 290 K. The simulation results are shown in Figs. 13–15. Figs. 13 and 14 give respectively the more detailed responses for the feed flow rate variation of +10% and −10%. Fig. 15 summarizes the other simulation results. It can be found from these figures that the top product can ultimately return to its setpoint when disturbances occurred. Thus, one can say that there is no offset (or steady-state error) in the top composition control. The bottoms product, for which a temperature controller is employed, has an offset. However, the offset is quite small and can therefore be negligible. If one needs a very precise bottoms composition, it is not difficult to add a composition controller cascading the temperature controller. In addition, the oscillation in these composition responses is considered to be moderate, and it ensures that the CS1 control configuration for the HIDiC is fairly well. 4.2. CS2 simulation

Fig. 11. Steady-state composition profile of the HIDiC.

Several disadvantages of using on-line analyzer for composition control were reported by the industry, namely it usually suffers from large measurement delays, high investment, and high maintenance costs. Thus, controlling a temperature somewhere in the column instead of an on-line analyzer, as shown in the stripping section of Figs. 7 and 8, is normally employed. Moreover, Marlin

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Fig. 13. Response of feed flow +10% in CS1.

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Fig. 14. Response of feed flow −10% in CS1.

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Fig. 15. Response summarization for other tests in CS1.

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Fig. 16. Response of feed flow +10% in CS2.

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Fig. 17. Response of feed flow −10% in CS2.

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Fig. 18. Response summarization for other tests in CS2.

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(2000) has stated: “Far more distillation tower product composition controllers use tray temperature inference than use on-stream analyzers.” However, to infer the top composition in the rectifying section using a single temperature in this study might not perform fairly well since the pressure is floating. Although more complex inferential techniques (Mejdell & Skogestad, 1991; Baratti, Bertucco, Da Rold, & Morbidelli, 1995; Yeh, Huang, & Huang, 2003) can be used, these methods normally need a lot of experimental data and time to develop. In this study, we are trying to employ a simpler inferential technique to test the operability of the HIDiC. A pressure-compensated temperature shown in Fig. 8 is chosen. Normally, top composition (yD ) depends only on temperature and pressure in a binary system: yD = f (T, P)

(14)

Thus, changes in composition depend on changes in temperature and pressure, i.e.



yD =

∂yD ∂P





P + T

∂yD ∂T



T

(15)

P

If one lets k1 = (∂yD /∂P)T and k2 = (∂yD /∂T )P . Values of k1 and k2 can easily be estimated from dew-point calculations. In addition, if yD  0.0 in Eq. (15) is assumed, one has TPC = (−k1 /k2 )·P, where P is the deviation between the measured pressure and its steady-state value. Thus, the pressure-compensated temperature signal (TPC ) in Fig. 8, which is equivalent to a composition signal, can therefore be T PC = Tmeas + T PC

(16)

where Tmeas is the measured temperature. Then, a PID controller is used for the top temperature control in Fig. 8, and its setpoint is the steady-state temperature of the top stage. The temperature controller (TC) then cascades a pressure controller (PC). All level controls and PCV in Fig. 8 are again assumed to be “perfect control”, and their dynamics are negligible. Similar to CS1, six kinds of step change are introduced at t = 2000 min, respectively. Figs. 16–18 present some results of the rigorous dynamic simulation to various disturbances using −k1 /k2 = 3 K/bar. It is found from these figures that the bottoms responses of CS2 are very similar to that of CS1. However, some offset is found in the top composition responses. Fortunately, the maximum deviation of theses offsets is only 0.79 mol% of propylene composition. It may also conclude that CS2 can still work well, even though no on-line analyzer is employed. 5. Conclusions A dynamic simulation study of the HIDiC using classic control strategies is developed in this study. From thermodynamic and DOF analyses together with the engineering judgment, it looks that a reboiler is necessary for the HIDiC in practice. A heuristic control configuration from practical instrumentation viewpoints, including VPC technique for the HIDiC with a reboiler, and furthermore, a simulation technique for variable column pressures using transfer functions are proposed. The control configuration has been checked by the DOF analysis. The developed simulation algorithms including the equilibrium stage, PID control loop, and variable column pressures are considered to be more rigorous than those in the literature (Huang et al., 1996; Huang, Matsuda, Takamatsu, et al., 2006). In addition, the dynamic simulator can also obtain the valuable steady-state operating conditions of a HIDiC for process design.

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Moreover, dynamic simulation results for the propylene–propane splitter have demonstrated that the proposed control configuration can control the HIDiC very well under various disturbances. Acknowledgement This work is supported by the Industrial Technology Research Institute, Taiwan under the grant D24200N410. References Astrom, K. J., & Hagglund, T. (1995). PID controllers: Theory, deign and tuning (2nd ed.). Instrument Society of America. Baratti, R., Bertucco, A., Da Rold, A., & Morbidelli, M. (1995). Development of a composition estimator for binary distillation columns. Application to a pilot plant. Chemical Engineering Science, 50, 1541. Choe, Y.-S., & Luyben, W. L. (1987). Rigorous dynamic models of distillation columns. Industrial & Engineering Chemistry Research, 26, 2158. Fukushima, T., Kano, M., & Hasebe, S. (2006). Dynamics and control of heat integrated distillation column (HIDiC). Journal of Chemical Engineering of Japan, 39, 1096. Franks, R. G. E. (1972). Modeling and simulation in chemical engineering. John Wiley & Sons, Inc. Grassi, V. G. (1992). Rigorous modeling and conventional simulation. In W. L. Luyben (Ed.), Practical distillation control (pp. 29–47). Van Nostrand Reinhold. Huang, K., Nakaiwa, M., Akiya, T., Aso, K., & Takamasu, T. (1996). A numerical consideration on dynamic modeling and control of ideal heat integrated distillation columns. Journal of Chemical Engineering of Japan, 29, 344. Huang, K., Matsuda, K., Takamatsu, T., & Nakaiwa, M. (2006). The influences of pressure distribution on an ideal heat-integrated distillation column (HIDiC). Journal of Chemical Engineering of Japan, 39, 652. Huang, K., Matsuda, K., Iwakabe, K., Takamatsu, T., & Nakaiwa, M. (2006). Choosing more controllable configuration for an internally heat-integrated distillation column. Journal of Chemical Engineering of Japan, 39, 818. Huang, K., Wang, S.-J., Iwakabe, K., Shan, L., & Zhu, Q. (2007). Temperature control of an ideal heat-integrated distillation column (HIDiC). Chemical Engineering Science, 62, 6486. King, C. J. (1980). Separation processes (2nd ed.). McGraw-Hill Book Co. Kyle, B. G. (1999). Chemical and process thermodynamics (3rd ed.). Prentice-Hall, Inc. Liptak, B. G. (1995). Instrument Engineers’ Handbook: Process Control (3rd ed.). Chilton Book Co. Luyben, W. L. (1996). Design and control degrees of freedom. Industrial & Engineering Chemistry Research, 35, 2204. Luyben, W. L., & Luyben, M. L. (1997). Essentials of process control. McGraw-Hill Book Company. Luyben, W. L., Tyreus, B. D., & Luyben, M. L. (1999). Plantwide process control. McGrawHill Book Company. Marlin, T. E. (2000). Process control: Designing processes and control systems for dynamic performance (2nd ed.). McGraw-Hill Book Company. McCabe, W. L., Smith, J. C., & Harriott, P. (2005). Unit operations of chemical engineering (7th ed.). McGraw-Hill Book Company. Mejdell, J., & Skogestad, S. (1991). Estimation of distillation compositions from multiple temperature measurements using partial least square regression. Industrial & Engineering Chemistry Research, 30, 2543. Muhrer, C. A., Collura, M. A., & Luyben, W. L. (1990). Control of vapor recompression distillation columns. Industrial & Engineering Chemistry Research, 29, 59. Naito, K., Nakaiwa, M., Huang, K., Endo, A., Aso, K., Nakanishi, T., et al. (2000). Operation of a bench-scale ideal heat integrated distillation column (HIDiC): An experimental study. Computers & Chemical Engineering, 24, 495. Nakaiwa, M., Huang, K., Naito, K., Endo, A., Owe, M., Akiya, T., et al. (2000). A new configuration of ideal heat integrated distillation columns (HIDiC). Computers & Chemical Engineering, 24, 239. Nakaiwa, M., Huang, K., Endo, A., Ohmori, T., Akiya, T., & Takamatsu, T. (2003). Internally heat-integrated distillation columns: a review. Chemical Engineering Research & Design, 81, 162. Olujic, Z., Sun, L., de Rijke, A., & Jansens, P. J. (2006). Conceptual design of an internally heat integrated propylene–propane splitter. Energy, 31, 3083. Shinskey, F. G. (1978). Energy conservation through control. Academic Press. Shinskey, F. G. (1996). Process control system (4th ed.). McGraw-Hill Book Company. Smith, C. A., & Corripio, A. B. (2006). Principles and practice of automatic process control (3rd ed.). John Willey & Sons, Inc. Smith, R. (2005). Chemical process design and integration. John Wiley & Sons, Ltd. Soave, G. (1972). Equilibrium constants from a modified Redlich–Kwong equation of state. Chemical Engineering Science, 27, 1197. Yeh, T.-M., Huang, M.-C., & Huang, C.-T. (2003). Estimate of process compositions and plantwide control from multiple secondary measurements using artificial neural networks. Computers & Chemical Engineering, 27, 55.