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Jun 6, 2012 - The hot reactor effluent is recycled back to a feed preheater to provide all or a portion of the energy required to preheat the reactor ...
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New Control Structure for Feed-Effluent Heat Exchanger/Reactor Systems William L. Luyben* Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015, United States ABSTRACT: Feed-effluent heat exchangers (FEHEs) are widely used in high-temperature exothermic adiabatic tubular reactor systems to conserve energy. The hot reactor effluent is recycled back to a feed preheater to provide all or a portion of the energy required to preheat the reactor feed to the optimum reactor inlet temperature. Several alternative flowsheets have been presented in the literature for this type of configuration. Some use bypassing of cold material around the FEHE, some use a furnace after the FEHE and before the reactor, and some use a cooler (steam generator) after the reactor. A number of control structures have been proposed to control the reactor inlet temperature, which is critical for the steady-state performance (achieving the desired conversion and staying below some maximum temperature). It is also critical for dynamic performance since these systems can be openloop unstable as a result of the positive feedback of energy from the reactor back to the preheat system. The control structure must prevent quenching to low temperatures (“blowout”) and temperature runaways (“blowup”). The most commonly suggested control structure recommends controlling the temperature of the mixed stream after the FEHE by manipulating the bypass flow and controlling the reactor inlet temperature by manipulating fuel to the furnace. This paper presents an alternative process and control configuration that reduces furnace energy consumption while maintaining good dynamic control in the face of very large disturbances.

1. INTRODUCTION There is a long and fairly rich literature that discusses the design and control issues involved in systems with high-temperature exothermic adiabatic tubular reactors. The design of the reactor in isolation is fairly straightforward. If the reaction is irreversible, there is usually a maximum temperature limitation due to catalyst degradation, undesirable side reactions, or materials-of-construction limitations. In this case, there is an optimum design in terms of reactor size, reactor inlet temperature, and per-pass conversion. The last of these design optimization variables impacts recycle flow rates and separation costs. The colder the reactor inlet temperature, the higher the conversion can be without exceeding the maximum temperature limitation. This reduces the required amount of recycle of unconverted reactants, which lowers separation costs. However, the size of the reactor increases as reactor inlet temperature is decreased, which increases capital investment in the reactor vessel and catalyst. If the reaction is reversible and exothermic, there is also an optimum design in terms of reactor size and reactor inlet temperature. But now the effect of temperature on the chemical equilibrium constant establishes the reactor inlet temperature that maximizes conversion. The reactor must be large enough to approach this limiting conversion. The maximum temperature limitation is usually not an issue. A number of alternative flowsheets have been studied for this type of system, which is sometimes referred to as an “autothermal” reactor. Some of these configurations are illustrated in Figure 1. Heat-exchanger bypassing with no furnace is shown in flowsheet A in Figure 1. This configuration has only one manipulated variable and can prevent a temperature runaway but cannot prevent a quench. Note that dual split-ranged valves are used to regulate the flows through and around the heat © 2012 American Chemical Society

exchanger. A gas-phase system is assumed with a valve on the gas stream leaving the unit, which holds pressure in the gas system. The dual-valve setup is permitted in a gas system where pressures vary from location to location. This setup would not work in a liquid system since there would be two valves in series in a single liquid line. Heat-exchanger bypassing with a furnace before the reactor is shown in flowsheet B in Figure 1. Now there are two control degrees of freedom (bypassing and furnace heat input). This configuration has the potential of being able to prevent both a quench (using furnace heat input to maintain reactor inlet temperature) and a temperature runaway (using bypassing) Flowsheet C in Figure 1 shows a process in which a cooler (steam generator) is used on the hot reactor effluent before it enters the heat exchanger. The system also has two control degrees of freedom. Flowsheet D in Figure 1 illustrates the use of multiple FEHEs with multiple coolers, which increases the number of manipulative variables available for control. Five decades ago, Douglas et al.1 presented one of the earliest papers that studied the control of FEHE/reactor systems. Analog simulation was the high-tech tool used in this pioneering work. The investigation showed the tendency of these systems to either quench (“blowout” or “extinguish” to a low-temperature steady state) or runaway (“blowup” to a high-temperature steady state) because of the inherent positive feedback of energy from the adiabatic reactor back to the heat exchanger. A higher reactor inlet temperature produces a higher reactor exit temperature that then raises the reactor inlet temperature coming from the heat Received: Revised: Accepted: Published: 8566

February 23, 2012 May 2, 2012 June 6, 2012 June 6, 2012 dx.doi.org/10.1021/ie3004896 | Ind. Eng. Chem. Res. 2012, 51, 8566−8574

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not considered. They presented a design procedure to produce a design with large enough FEHE, furnace, and cooler to yield an openloop stable process. The resulting conservative design may be expensive in terms of capital investment and energy consumption (furnace duty). Morud and Skogestad6 studied instability in an industrial ammonia reactor with an FEHE. An extensive discussion7 of reactor/FEHE systems covered the effects of bypassing and adding a furnace. The HDA process was used as an example in which a reactor exit quench stream provided an additional manipulated variable. Chen and Yu8 extended the work of Terrill and Douglas, demonstrating that the use of multiple FEHE’s improved disturbance rejection capability. Reactor/FEHE systems were explored9 using both linear analysis and nonlinear simulations to develop control structures. The recommended control structure had the following loops: (1) The temperature of the mixed stream (hot heat-exchanger exit plus cold bypass) is controlled by manipulating the bypass flow rate. (2) Temperature of the reactor inlet is controlled by manipulating fuel to the preheat furnace. A recent study by Jogwar et al.10 explored process networks with large energy recycles. All these studies demonstrated that the primary control issue is to maintain the reactor inlet temperature. If it drops too much, reaction rates slow up and the reactor exit temperature drops. Since this flows back to the heat exchanger as its hot inlet stream, the temperature of the stream leaving the heat exchanger (and entering the reactor) drops. A “quench” can easily occur. Mathematically this is equivalent to the system going to a stable low-temperature steady state. In this condition, nothing is reacting in the reactor (zero conversion). These studies demonstrated quantitatively that control is improved when a larger fraction of the total feed flow rate is bypassed around the heat exchanger. However, this requires a larger heat exchanger, which means higher capital investment. Bypassing can prevent reactor temperature runaways. However, it cannot prevent quenching. Using a cooler on the reactor effluent is similar to FEHE bypassing in that it changes the temperature of the stream leaving the heat exchanger and entering the reactor (or furnace). However, bypassing and mixing hot and cold streams gives much faster dynamics than manipulating heat removal in a cooler because the dynamics of the cooler are involved. These studies also demonstrated that using a furnace improves dynamic control. In particular, a furnace can prevent quenching. However, use of a furnace increases energy costs. It is therefore desirable to use as little furnace energy input as possible. In this paper we present an alternative process and control structure that has the advantage of reducing furnace energy consumption while still providing effective dynamic control for very large disturbances.

Figure 1. FEHE/reactor alternative flowsheets.

exchanger. These authors studied two systems. In the first, which is similar to the reactor in the ammonia process, there was both heat transfer and reaction in a heat exchanger/reactor in which cold feed flowed in one direction in the tubes and returned in the other direction in the shell. There was no adiabatic reactor section. The second system had both a heat exchanger and an adiabatic reactor. Silverstein and Shinnar2 studied the effects of design parameters on dynamic stability of systems with a FEHE followed by a furnace before the adiabatic reactor. They recommended controlling reactor inlet temperature with the furnace duty. Bypassing of cold material around the FEHE to provide an additional manipulated variable was explored. Terrill and Douglas3 examined the use of multiple feedeffluent heat exchangers in the complex HDA process, which had a furnace before the reactor and used the hot reactor effluent (after quenching to prevent coking) to preheat the reactor feed in several FEHE’s in series. Coolers (reboilers of distillation columns) were installed between these multiple FEHEs. The dynamics of these FEHE/reactor systems can be quite complex as another early paper4 demonstrated and can lead to unconventional controller tuning. The system studied used FEHE bypassing to control reactor inlet temperature. No furnace or cooler was used. Unlike most processes, using integral action in the feedback controller improved dynamics. The reactor can exhibit inverse response to changes in inlet temperature because of the slower heat transfer to the solid catalyst. Bildea and Dimian5 explored the stability and multiplicity of systems with a FEHE, a furnace, a reactor, and a cooler on the reactor effluent before it recycled back to the FEHE. The cooler generated high-pressure steam. Bypassing around the FEHE was

2. PROCESS STUDIED The chemical system used in this study is the production of dimethyl ether (DME) from methanol. The vapor-phase reaction is exothermic and reversible. 2MeOH ⇔ DME + H 2O 8567

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The kinetics equations for the forward and reverse reactions are 9F = (pMdOH )2 (3.23 × 10−7)e−80300/ RT 9R = (pDME )(pH O )(2.888 × 10−6)e−101860/ RT 2

where 9 = overall reaction rate (kmol/(m3 s)); pj = partial pressure of component j (P); T = temperature (K). Activation energies have units of kilojoules per kilomole. Uniquac physical properties are used in the Aspen simulations. These kinetics show that the reaction is exothermic and that low reactor temperatures would favor high conversions. However low temperatures mean small specific reaction rates, so a very large reactor would be required. The upper graph in Figure 2 gives the dependence of the chemical equilibrium constant on temperature. Figure 3. Reactor outlet temperature with and without heat transfer to catalyst.

Figure 4. FEHE/reactor flowsheet.

3. DESIGN CASES WITHOUT FURNACE The steady-state and dynamic effects are studied for different bypass flow rates. The effect of using a furnace is explored in the next section. 1.1. No Bypass, No Furnace. The design that minimizes the size of the heat exchanger would have no bypass around the heat exchanger, as shown in Figure 5. The cold stream to the

Figure 2. Chemical equilibrium constant; methanol conversion.

The specific reactor used in the example is 1.2 m in diameter and 12 m in length. It is filled with a solid catalyst with void fraction 0.28 and solid density of 1700 kg/m3. There is an optimum inlet temperature for this reactor. Feed flow rate is 295.2 kmol/h. Reactor pressure is 13 atm as set by downstream pressure requirements. The liquid fresh feed has a composition of 95 mol % methanol and 5 mol % water. It is vaporized before entering the FEHE. The lower graph in Figure 2 shows that the optimum inlet temperature for this size reactor is 541 K at which the conversion of methanol is 81.6%. The dynamics of this adiabatic packed tubular reactor are complex. Figure 3 gives the response of the reactor in isolation to an increase in inlet temperature from 541 to 551 K at time equal 0.5 h. The solid line is the response of the reactor exit temperature when heat transfer from the process gas to the solid catalyst is considered in the Aspen Dynamic simulation (which is the realistic case in this heterogeneous reaction). The dashed line is the response in reactor exit temperature if heat transfer to the catalyst is neglected, which is obviously not reality. Figure 4 gives the initial flowsheet of process considered in this paper. An alternative is considered later. The dynamic elements in this process are the vaporizer (sized for 5 min of liquid holdup when half full), the heat exchanger (size varies directly with the required heat-transfer area, which varies with the fraction of total flow that is bypassed), and the tubular reactor.

Figure 5. No bypass and no furnace.

heat-exchanger is saturated vapor at 425 K and 14 atm coming from the vaporizer. The desired reactor inlet temperature is 541 K, so the cold exit stream from the FEHE must be heated to 541 K. The required heat-transfer rate to raise the cold process stream to this temperature is 0.5422 MW. 8568

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The hot reactor exit stream that enters the hot end of the FEHE is at 662 K. Using an overall heat-transfer coefficient of 0.17 kW/(K m2) and the available log-mean temperature differential, the required heat-transfer area is 27.51 m2. This is the smallest heat exchanger that could be used in this system with no furnace. Of course, this system would be completely uncontrollable since there is nothing to manipulate to maintain reactor inlet temperature. Figure 6 demonstrates this openloop instability.

Figure 7. (A) Flowsheet; 20% bypass; no furnace. (B) Control structure; 20% bypass; no furnace. Figure 6. Openloop response.

Figure 8 gives responses for step changes in the set point of the feed flow controller. In Figure 8A, the step disturbances are plus and minus 20% of the design feed flow rate (295.2 kmol/h). The solid lines are 20% increases, and the dashed lines are 20% decreases. The system handles the decrease in throughput with the bypass flow rate Fby increasing to send much less through the FEHE. Reactor inlet temperature TRin (which is the temperature after the furnace) is well-controlled at 541 K with only a 5 K peak dynamic deviation during the transient. The temperature of the stream leaving the heat exchanger TCout increases. For the 20% increase, the bypass flow goes to zero and the reactor inlet temperature drops below the desired 541 K. But, the system is still stable. Figure 8B gives responses for 30% disturbances. Both of these large upsets result in the system quenching to the low-temperature steady state. In the next section, we increase the design bypassing fraction to see if larger disturbances can be handled. 1.3. 40% Bypass, No Furnace. A. Design. If the system is designed for a higher fraction of the feed to be bypassed around the heat exchanger, the temperature of the stream leaving the FEHE must increase in order to achieve the required mixed temperature of 541 K. The FEHE exit temperature is 568 K for a 20% bypass design. For a 40% bypass design, the temperature must be 610 K, as shown in Figure 9. The heat-transfer rate in the FEHE is exactly the same in all cases with any amount of bypassing (in the absence of a furnace). The differential temperature driving force is now reduced to 662 − 610 = 52 K. Therefore more heat-transfer area is required (39.97 m2). B. Control. The control structure is unchanged. Only the flow rates through the heat exchanger and through the bypass are different from the previous design. Disturbance responses are shown in Figure 10. The larger fraction of bypassing with the large heat exchanger permits the system to handle 30% disturbances (Figure 10A). Figure 10B shows that a 40%

No disturbance is made to the system, but temperatures gradually decline and a quench occurs after about 6 h. It should be remembered that the reactor in isolation is openloop stable. The heat exchanger in isolation is also openloop stable. However, the coupled system is openloop unstable because of the positive feedback of energy. 1.2. 20% Bypass, No Furnace. A. Design. If 20% of the feed is bypassed around the heat exchanger, the cold bypass at 425 K is mixed with the stream leaving the FEHE to give the required 541 K. The temperature of the stream from the heat exchanger must be 568 K, as shown in Figure 7. The heat-transfer rate remains the same, as does the exit temperature of the reactor effluent leaving the FEHE (566 K). The differential temperature driving force on the hot end of the heat exchanger changes from 662 − 541 = 121 K in the case of no bypassing to 662 − 566 = 96 K with 20% bypassing. The differential temperature driving force on the cold end is unchanged (566 − 425 = 141 K). Therefore more heat-transfer area is required (increases from 27.51 to 34.12 m2). B. Control. The dynamic control performance of this 20%bypass case is studied using the conventional control structure shown in Figure 7. The reactor inlet temperature controller manipulates the fraction of flow bypassing the reactor using dual split-ranged control valves in the line through the FEHE and in the bypass line. The bypass valve is air-to-close (reverse acting) since the fail-safe situation is to put cold feed into the reactor. The valve in the heat-exchanger line is air-to-open (direct acting). A 1-min deadtime is inserted in the temperature loop to account for temperature measurement lag. The mixing of the hot and cold streams gives very rapid responses, so tight control of the mixed temperature (which is the reactor inlet temperature) is achieved. A relay-feedback test gives an ultimate gain of 4.5 and ultimate period of 2.2 min. Tyreus−Luyben tuning rules are applied to give KC = 1.4 and τI = 4.8 min. 8569

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Figure 8. (A) 20% bypass; no furnace; feed flow rate 20% changes. (B) 20% bypass; no furnace; feed flow rate 30% changes.

Figure 10. (A) 40% bypass; no furnace; feed flow rate 30% changes. (B) 40% bypass; no furnace; feed flow rate 40% changes.

Figure 9. Flowsheet; 40% bypass; no furnace.

Building a bigger furnace to improve the dynamics may not constitute a major incremental capital expense. A. Design. As shown in Figure 5, the total preheat heat duty to raise the vapor stream leaving the vaporizer from 425 to 541 K is 0.5422 MW (1.951 GJ/h). Designing a system with a furnace that adds 20% of this total heat (0.1084 MW) should be a reasonable compromise between steady-state economics (capital investment and energy) and dynamic controllability. There is some reduction in the capital investment in the FEHE. But the furnace consumes fuel, so there is an energy cost. With no operating furnace, the system is “autothermal.” Figure 11 gives a flowsheet with a furnace in which 0.4338 MW of heat are transferred in the FEHE and the remaining 0.1084 MW of heat are added in the furnace. A 40% bypass design is also assumed. Note that the temperature of the stream leaving the FEHE is 576 K while the temperature of the mixed stream entering the furnace is 519 K. The furnace raises the temperature up to the desired 541 K. B. Control with Linear Proportional−Integral (PI) Controllers. Figure 12 shows the conventional control system for this FEHE/furnace/reactor process. The amount of bypassing is manipulated to control the mix temperature. The furnace duty is manipulated to control the furnace exit temperature (the reactor inlet temperature). We now have two temperature controllers and interaction between these two controllers can be a significant problem. Tuning the mix temperature (Tmix) controller is straightforward,

decrease in throughput can also be handled. However a 40% increase causes a quench.

4. DESIGN CASE WITH FURNACE In the studies above, we have seen the limitations of the FEHE/ reactor system without the use of a furnace. Quenching can occur if disturbances are large. In this section we explore the advantages (and disadvantages) of using a furnace. It should be remembered that a furnace is usually necessary to start up the process. The size of the startup furnace will dictate how fast the reactor can be heated to the temperatures required for the reaction to initiate. 8570

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Figure 11. Flowsheet; 40% bypass; furnace 20% of total preheat duty.

Figure 13. 40% bypass; furnace 20% of total Q; feed flow rate 40% changes.

C. Control with Nonlinear PI Controller. This process is fairly nonlinear, so the use of nonlinear control may provide more effective regulation. The tuning parameters of the two controllers were evaluated at three different throughputs: design (295.2 kmol/h), 40% above design (413.3 kmol/h), and 40% below design (171.1 kmol/h). Table 1 shows that there is a large Table 1. Controller Parameters at Different Throughputs feed

Figure 12. Control structure; 40% bypass; furnace 20% of total preheat duty.

TCmix (D = 1) TCRin (D = 2)

and tight control is easy to achieve even with a 1-min deadtime in the loop. However, the dynamics of the furnace are not nearly as fast. A 2-min deadtime is used in the reactor inlet temperature (TRin) controller. With the slow TRin controller on manual, the Tmix controller is tuned using a relay-feedback test and Tyreus−Luyben tuning rules (KC = 0.464 and τI = 2.96 min). Then with this controller on automatic, the TRin controller was tuned using the same procedure. The resulting control was effective for increases in throughput. However, decreases in throughput produced a very oscillatory response as the two loops fought each other. The inverse response characteristics of the heat exchanger (see Figure 3) contributed to this severe interaction problem. The controllers were detuned (smaller gains and larger integral times). Eventually the most effective tuning was found to be the use of a proportional-only Tmix controller (KC = 0.2). This greatly reduced the loop interaction, and throughput disturbances of 40% could be handled as shown in Figure 13. Notice that the temperature of the mixed stream Tmix entering the furnace is not driven to its set point. There is a significant steady-state offset in the Tmix controller due to the absence of integral action. But this does not really matter because the TRin controller can manipulate the furnace duty to drive the reactor inlet temperature to 541 K. Evidence of the loop interaction can be seen in the somewhat oscillatory responses of various temperatures in the system. Notice that the furnace is consuming energy (20 kW) even at the low throughput condition (171.1 kmol/h). At low flow rates there is really no need for the furnace because the FEHE has plenty of area to transfer required heat. The revised flowsheet discussed in the next section eliminates this energy inefficiency.

(% design)

60

100

140

(kmol/h) KC τI (min) KC τI (min)

171.1 0.115 5.26 0.422 9.24

295.2 0.464 3.96 0.622 9.24

413.3 1.58 5.26 0.422 9.24

change in the gain of the TCmix controller as throughput changes. This suggests that a variable-gain controller could be used. A simple quadratic function relating controller gain with throughput was developed using the three data points given in Table 1 and is shown in the following equation. KC = c1 + c 2(F ) + c3(F )2

where c1 = 0.06176, c2 = −0.00129, c3 = 9 × 10−6. The flow rate F has units of kilomoles per hour. The controller gain is dimensionless using a temperature transmitter range of 500 to 600 K and a controller output range of 0 to 100% valve opening. The TCmix controller is reverse acting since the bypass valve is reverse acting (air-to-close) and the heat exchanger valve is direct (air-to-open). A gain-scheduled controller is easily implemented in Aspen Dynamics using Flowsheet Equations, as shown in Figure 14.

Figure 14. Gain-scheduled Tmix controller.

Figure 15 gives the responses of the process to 40% disturbances in throughput. Effective stable regulatory control is achieved. 8571

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Figure 16. Modified flowsheet; nonlinear feedforward (FF) control structure. Figure 15. 40% feed disturbances; nonlinear feedback controller.

A. Design. Notice in Figure 16 that the flow rate of the bypassed material (24.74 kmol/h) is smaller than in the conventional designs (59.1 kmol/h in the 20% bypass case and 118.1 kmol/h with the 40%). The control structure shown in Figure 16 controls the reactor inlet temperature at 541 K by mixing the cold bypass stream at 426 K with the hot stream coming from the furnace at 551 K. It is interesting to compare the duties and the areas of the FEHEs for the various alternative designs. (1) No bypassing (Figure 5) (2) 20% bypassing and mixing at the furnace inlet (Figure 7) (3) 40% bypassing and mixing at the furnace inlet (Figure 9) (4) 40% bypassing, mixing at the furnace inlet and using a furnace whose duty is 20% of the total preheat duty (Figure 11) (5) The new flowsheet with mixing at the furnace outlet (Figure 16) Table 2 summarizes the various design parameters around the FEHE. Area increases as bypassing increases despite there being

Maximum transient deviations in the reactor inlet temperature (TRin) are about 10 K for the 40% increase and 20 K for the 40% decrease. Comparing Figure 13 with Figure 15 shows that the nonlinear controller gives smaller reactor inlet temperature deviations for the increase in throughput. The two control structures give different final steady-state furnace duties. For the 40% increase in throughput, the furnace duty is less with the nonlinear controller (150 versus 200 kW) because the proportional-only Tmix controller used in the linear control structure does not return the mix temperature to its set point of 520 K. It ends up at 510 K, which means more energy must be added in the furnace. On the other hand, for the 40% decrease in throughput, the nonlinear controller requires more energy (60 versus 25 kW).

5. NEW CONFIGURATION AND CONTROL STRUCTURE In this section we explore the possibility of developing a slightly modified flowsheet and a different control structure with the objective of being able to handle larger disturbances and preventing either quenching or temperature runaway. Reduction in furnace energy consumption is also achieved. Two features of the FEHE/reactor system are clear. First, the important temperature that must be tightly controlled is the reactor inlet temperature. Even modest drops in this temperature can lead to quenching because of the positive feedback between the reactor and the heat exchanger. The second feature is that tight control is easily achieved using mixing of hot and cold streams. Putting these two facts together leads to the new system. Figure 16 shows the proposed flowsheet and control structure. Instead of mixing the cold bypass stream with the hot stream from the FEHE, the bypass stream is mixed with the stream from the f urnace, and this mixed stream is fed into the reactor. The stream passing through the FEHE is fed directly into the furnace. This setup permits tight control of the important reactor inlet temperature since we are mixing hot and cold streams. A possible disadvantage of this flowsheet is that the furnace outlet temperature is higher than in the conventional flowsheet. This means that a higher-temperature heat source may be required. However in a high-temperature fired furnace system there should be little negative impact in raising the furnace outlet temperature from 541 K (the furnace outlet temperature in the conventional design) to that required in the modified flowsheet of 551 K.

Table 2. Comparison of FEHE Designs bypass (%) case 1 Figure 5 case 2 Figure 7 case 3 Figure 9 case 4 Figure 11 case 5 Figure 16

no 20 40 40 8.38

furnace FEHE area FEHE duty furnace (% total) (m2) (kW) duty (kW) no no no 20 10

27.51 34.12 39.97 25.13 22.99

542.2 542.2 542.2 433.8 485.3

0 0 0 108.4 55.5

no change in duty (cases 1, 2, and 3 above). Adding a furnace reduces both the area and the heat duty in the FEHE (case 3 versus case 4). Notice that the new flowsheet uses in the furnace only 10% of the total feed preheating (55.6 kW) compared to case 4 (108.4 MW). So the new flowsheet saves energy at design conditions. As we demonstrate below, it also saves energy at throughputs smaller than design. B. Control. There is only one temperature to control, and it can be effectively maintained by mixing. The question remains of how to adjust the furnace heat input. The approach to answering this question was to simulate the process at different throughputs (40% larger and 40% smaller than design) and find what furnace heat input is required while still having the bypass valve somewhat open so that control can be maintained. Table 3 gives results for three feed flow rates using the modified process design 8572

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Table 3. Process Parameters at Different Throughputs (Modified Flowsheet with Mixing after Furnace) feed furnace duty TFout TCout Fby Fhx TCRin controller output

% design

60

100

140

(kmol/h) (GJ/h) (kW) (K) (K) (kmol/h) (kmol/h) (%)

171.1 0.009670 2.686 612 611 68.9 102.3 9.30

295.1 0.200 55.56 551 539 24.74 270.4 74.1

413.3 0.661 183.6 545 517 14.33 399.0 89.7

(mixing after furnace). It is clear that the furnace duty must increase as throughput increases. This increase is certainly highly nonlinear, so a simple linear feedforward ratio scheme (furnace heat input to feed) would not work. However, a nonlinear feedforward element can be used. An exponential function is proposed as shown in the following equation. The two parameters A and B are found by fitting the two data points at the high and design throughputs.

Figure 18. Nonlinear feedforward; feed flow rate 40% changes.

ln Q furnace = A + B /feed

where A = 2.5705, B = −1233.5, Qfurnace is in gigajoules per hour, and feed is vapor from the vaporizer (kmol/h). This equation is easily implemented in Aspen Dynamics using Flowsheet Equations (see Figure 17). Remember that metric units

Figure 17. Nonlinear feedforward controller.

must be used in Aspen Dynamics, so the flow rate must have units of kilomoles per hour and heat duty must be in gigajoules per hour. Furnace duty is an exponential function of the flow rate of the vapor coming from the vaporizer. The reactor inlet temperature controller manipulates the two split-range valves. A relay-feedback test at design throughput and Tyreus− Luyben setting gives a gain of 2.67 and integral time of 5.28 min for the reactor inlet temperature controller. The gain was reduced to KC = 1 to keep the system from oscillating at low throughputs. The effectiveness of this control structure is demonstrated in Figure 18. Reactor inlet temperature control is essentially the same as with the nonlinear controller (compare Figure 15 with Figure 18). Furnace duty is lower at design conditions (55 versus 110 kW). It is much smaller at low throughput (5 versus 60 kW). However, furnace duty is somewhat higher (190 versus 150 kW) at the high throughput steady state because the bypass flow rate is somewhat higher (25 versus 15 kmol/h). Figure 19 gives a direct comparison between the nonlinear feedback control structure and the nonlinear feedforward control structure for 40% changes in throughput. The solid lines are using the nonlinear feedforward (FF) controller and the dashed lines are using the nonlinear feedback (FB) controller. The disturbance in Figure 19A is a 40% increase in throughput. The FF control structure provides faster control of the reactor

Figure 19. (A) Comparison; 40% increase. (B) Comparison; 40% decrease.

inlet temperature TRin and smaller transient deviations in the reactor outlet temperature TRout. The furnace duty at design throughput is lower for the FF structure but is higher at the final steady-state conditions for 40% increase in throughput. Note that 8573

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the bottom right graph shows the mixed temperature for the FB structure and the furnace outlet temperature for the FF structure. The disturbance in Figure 19B is a 40% decrease in throughput. There is little difference between the two structures in terms of effective reactor inlet temperature control. However, there is a very large difference in terms of furnace duty. The FF structure gives smaller deviations in the reactor outlet temperature. Notice that the furnace outlet temperature rises to about 620 K, despite the very small furnace duty, because the outlet temperature of the FEHE is quite high as a result of the 662 K reactor outlet temperature. Figure 20 gives results for an even larger throughput disturbance (50%). The increase in throughput causes a large drop in both the

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 610-758-4256. Fax: 610758-5057. Notes

The authors declare no competing financial interest.

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REFERENCES

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Figure 20. (A) Comparison; 50% increase. (B) Comparison; 50% decrease.

reactor inlet temperature TRin and the reactor outlet temperature TRout when the FB control structure is used. Despite these large changes, the system recovers and no quench occurs. The FF structure handles this very large increase very effectively.

6. CONCLUSION A new process configuration and a new control structure have been developed and tested. Dynamic advantages in terms of robustness to large disturbances have been demonstrated. In addition reduction of furnace energy consumption at design and lower throughputs has been achieved. 8574

dx.doi.org/10.1021/ie3004896 | Ind. Eng. Chem. Res. 2012, 51, 8566−8574