Rigorous dynamic models for distillation safety analysis

Rigorous dynamic models for distillation safety analysis

Computers and Chemical Engineering 40 (2012) 110–116 Contents lists available at SciVerse ScienceDirect Computers and Chemical Engineering journal h...

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Computers and Chemical Engineering 40 (2012) 110–116

Contents lists available at SciVerse ScienceDirect

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

Abnormal events management and process safety

Rigorous dynamic models for distillation safety analysis William L. Luyben ∗ Department of Chemical Engineering, Lehigh University, Bethlehem, PA 18015, USA

a r t i c l e

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Article history: Received 27 October 2011 Received in revised form 13 February 2012 Accepted 23 February 2012 Available online 3 March 2012 Key words: Safety analysis Distillation simulation Distillation Dynamic models Aspen simulation

a b s t r a c t Dynamic simulations of distillation columns are widely used to develop effective control structures. The normal distillation models assume instantaneous heat transfer in the condenser and reboiler. However, when dynamic simulations are used in the analysis of safety problems in the event of emergency situations, the basic model does not accurately represent the dynamic response. Accurate response times are essential in the design of safety systems for the column. For example, a failure of the supply of cooling water will lead to rapid increases in pressures and temperatures that occur in seconds. Accurately determining the rates of increase in these important variables and the time period to reach critical limits (safety response time) permits the engineer to quantitatively design effective safety systems. This paper illustrates how rigorous condenser and reboiler models can be developed in Aspen Plus and their dynamics evaluated in Aspen Dynamics. © 2012 Elsevier Ltd. All rights reserved.

1. Introduction Dynamic simulation is widely used for developing control systems to handle normal operation around the desired steady state. However dynamic simulation can also provide a useful tool for predicting how fast variables change in the event of an operating emergency or equipment failure. Modern dynamic simulators can easily be used to provide this type of dynamic information. When an emergency arises, the time it takes to approach a high limit in some critical variables (temperature, pressure or composition) is important because it determines how fast the safety protection equipment (sensors and valves) must be able to respond to the detected event. A common example is a loss of coolant, which could be refrigerant (low-temperature operation), cooling water (medium-temperature operation) or boiler feed water (if cooling is achieved by generating steam). This type of loss can be detected in several ways. The most obvious is a measurement of the flowrate of the coolant. But flow sensors are often noisy due to turbulent flow conditions and have limited reliability. Impulse lines and orifice plates can plug and foul. Shutting down a whole plant due to faulty measurement signal is very undesirable. Therefore other more reliable sensors (temperature or pressure) are often used to infer a loss of coolant. Multiple sensors based on different physical principles are used to improve fault detection reliability. There are several levels of action to be taken as the critical variable moves away from its normal value. As sketched in Fig. 1,

at some percentage of departure from normal pressure, perhaps 10%, an alarm will be activated to alert the operator. At a larger percentage (20%), an override system will begin to adjust other manipulated variables not normally used to maintain the pressure in an attempt to ride through the disturbance without necessitating a complete plant shutdown. For example, the feed flowrate and/or the reboiler heat input could be reduced as the column pressure approaches this “override” limit. If conditions worsen and the pressure continues to rise up to perhaps 30% above normal, an interlock system will be activated that shuts down the process. If these actions are unable to prevent a further rise in pressure, the last line of defense to protect the physical integrity of the vessels is opening of safety valves or blowing of rupture disks at perhaps 40% above normal. Of course, the vent/scrubbing/flaring systems into which these discharges empty must be sized adequately to handle the dynamic loads that occur during the event. A discussion of the safety responses of several chemical reactor systems has recently been presented (Luyben, in press). Reactors often present critical safety issues, and the wide variety of different reactor and reaction types and conditions yield a wide range of safety reaction times. The current paper addresses dynamic simulations for the safety analysis of a typical distillation column. Columns are usually more benign than chemical reactors, and there a fewer types of configurations and ranges of operating variables. A typical numerical example is considered.

2. Process studied ∗ Tel.: +1 610 758 4256; fax: +1 610 758 5057. E-mail address: [email protected] 0098-1354/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.compchemeng.2012.02.019

The binary separation of methanol and water is used an example column. A feed of 82 mol% methanol and 18 mol% water is fed to a

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Fig. 1. Safety constraints and actions; pressure limitations.

column with 40 trays (42 stages in Aspen terminology with feed on Stage 27 and the condenser labeled as Stage 1). Condenser pressure is 1 bar, condenser pressure drop is 0.1 bar and tray pressure drop is 0.01 bar per tray (giving a base pressure of 1.5 bar). Product purities are 99.9 mol% methanol in the distillate and 99.9 mol% water in the bottoms. The required reflux ratio is 0.8569. Column diameter is 5.61 m. Reboiler heat input is 64.1 MW. Condenser heat removal is 60.0 MW. The NRTL physical property package is used. 2.1. Basic Radfrac models The basic Aspen “Radfrac” model incorporates implicitly a condenser and a reboiler. The process flow diagram of this base model is shown in Fig. 2. The dynamics of the system depend on the column diameter, the tray weir height and the holdups in the column base (reboiler) and reflux drum (condenser). This basic model has several options for handling the dynamics of the heat exchangers. A. Constant duty model: The default mode is “Constant duty” in which heat-transfer rates (QC in the condenser and QR in the reboiler) are set immediately with no dynamic lags. These heattransfer rates are directly manipulated in the dynamic model and their effects are immediately felt by column. There is no consideration of heat-transfer area, temperature driving forces or heat-transfer coefficient. The holdup of material on the utility-side of the heat exchanger is not considered. In normal control studies, this assumption is valid because the composition dynamics of the column trays, column base and reflux drum are typically much slower than the dynamics of the heat exchangers. For predicting rapid responses to safety scenarios, the dynamics of the heat exchangers should not be neglected. B. Constant temperature model: The temperature of the cooling medium in the condenser or the temperature of the heating medium in the reboiler is set, and then Aspen calculates the required “UA” product (overall heat-transfer coefficient U and heattransfer area A) from the known heat-transfer rate and temperature differential driving force. This temperature is manipulated in the dynamic simulations. No heat-exchanger dynamics are considered. C. LMTD model: If the condenser uses the flowrate of a cooling medium (typically cooling water) or if the reboiler used the flowrate of a heating medium (hot oil), a model using a log-mean temperature differential driving force (temperature differentials at outlet and inlet ends) can be used. The inlet medium temperature and the minimum approach temperature difference between the process and the medium are specified. Then Aspen calculates the required

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“UA” product (overall heat-transfer coefficient U and heat-transfer area A) and the required flowrate of the medium from the known heat-transfer rate. The flowrate of the medium is manipulated in the Aspen Dynamic simulations, not QC or QR directly. However, this model contains no dynamics. The holdup of medium in the heat exchanger is not considered. Medium flowrate changes produce instantaneous changes in temperature driving forces and subsequent heat-transfer rates. D. Condensing or evaporating medium models: An Evaporating model can be used in the condenser, and a Condensing model can be used in the reboiler if the cooling/heating medium undergoes a phase change. If the reboiler is heated by a condensing vapor (typically steam), the difference in temperature between the condensing steam at a specified temperature and the column base temperature is used to calculate the “UA” and the flowrate of the steam from the known reboiler duty QR . The flowrate of the steam is manipulated in the Aspen Dynamics simulations, not QR directly. If the condenser is cooled by a vaporizing liquid (boiler feed water in high-temperature columns or liquid refrigerant in lowtemperature columns), the difference in temperature between the specified temperature of the vaporizing liquid and the temperature of the process in the condenser is used to calculate the “UA” and the flowrate of the coolant from the known condenser duty QC . The flowrate of the coolant is manipulated in the Aspen Dynamics simulations, not QC directly. E. Dynamic model for reboiler: There is one heat-exchanger model in the standard model that considers heat-exchanger dynamics, but is only available for the reboiler. The dynamic model uses the holdup of the heating medium in the reboiler. The medium is assumed to be at a single temperature (perfectly mixed). The inlet medium temperature and the approach temperature to the process are specified. Then Aspen calculates the required “UA” and the medium flowrate from the known heat-transfer rate QR . The larger the medium holdup, the more slowly the perfectly mixed medium temperature changes for a change in medium flowrate. So this model is the only built-in model that considers dynamic lags in the heat exchanger equipment associated with the column. However, this model can only be realistically used when the reboiler heating medium is a hot liquid stream, and the holdup of this liquid on the shell or tube side is significant. If the reboiler is heated with a condensing vapor, which is much more frequently the case, this dynamic model is not applicable.

2.2. Radfrac model with explicit heat-exchanger dynamics Fig. 3 gives a process flow diagram of a more rigorous Aspen simulation that explicitly incorporates separate units for the condenser and the reboiler. Fig. 4 gives a detailed flowsheet of operating conditions and equipment sizes. The column itself is Radfrac column, but it has no reboiler and no condenser. These are added externally as standard Aspen HeatX models, as are a separate reflux drum and liquid circulation from the base of the column through the reboiler. A. Column: The top tray is now labeled Stage 1 in this absorber model. So the feed stage and the bottom stage must be decreased by one to make this column equivalent to the basic column. The feed and reflux are fed to column along with a partially vaporized stream from the reboiler. This vessel has no design specifications. Top pressure is 1.1 bar. Base pressure is 1.5 bar. B. Condenser: The overhead vapor from the column is condensed in a water-cooled heat exchanger. The design specification for this HeatX model is the exit temperature of the hot stream at 64.2 ◦ C (the bubble-point temperature of the distillate at 1 bar). Cooling water flows through the condenser (3.7 × 106 kg/h), entering at 32.2 ◦ C and exiting at 47.6 ◦ C. With a heat-transfer rate of 60.06 MW and

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Fig. 2. Base Aspen distillation column model.

an overall heat-transfer coefficient of 730.9 kcal h−1 m−2 K−1 , the required area is 2788 m2 . The volume of the tubes is estimated by assuming tubes 0.05 m in diameter and 5 m in length. The number of tubes required to give the necessary heat-transfer area is calculated and the inside volume of these tubes (35 m3 ) is used to give dynamics in the HeatX model. Shell volume is set equal to tube volume. In the Dynamics section of the HeatX block, the default is Instantaneous. Use the drop-down arrow to select Dynamic, and enter the inlet and outlet volumes on both hot and cold sides of the heat exchanger. The dynamic capacitance of the tube metal in the condenser can also be included if it is significant compared to that of the cooling water in the tubes. The mass of cooling water times its heat capacity is (35 m3 ) (1000 kg/m3 ) (4.184 kJ/kg K) = 145,600 kJ/K. Assuming a metal tube wall thickness of 0.00127 m, the volume of the tube metal is 3.54 m3 . Then using a metal density of 7750 kg/m3 and a heat capacity of 0.836 kJ/kg K, the product of metal mass times heat capacity can be calculated: (3.53 m3 ) (7750 kg/m3 )

(0.836 kJ/kg K) = 22,940 kJ/K. Thus the metal heat capacitance is only 15% of the water capacitance. C. Reflux drum: An Aspen Flash2 model is used for the reflux drum with pressure set at 1 bar and design specification of a vapor fraction of 10−5 , which makes the drum essentially adiabatic. A small vapor flowrate is necessary so that the control valve in this vent line can be sized. In the Aspen Dynamics simulation, the valve is completely closed. The liquid holdup in the drum is set to give 5 min at 50% full (diameter 3 m and length 6 m). D. Liquid split: Liquid from the drum is pumped up to 4 bar and split into a reflux stream (set at exactly the value used in the base case, 2826 kmol/h) and the distillate. See Fig. 3 (Splitter S1). As discussed below, the conditions in the reboiler will be adjusted to drive the distillate to be the same as in the base case (3297.7 kmol/h). D. Reboiler: Liquid from the column base is split (Splitter S2 in Fig. 3) between the bottoms and a circulating stream that flows through a HeatX model used for the reboiler. The bottoms flowrate is set equal to that found in the base case (720.7 kmol/h). Note that

Fig. 3. Rigorous Aspen distillation column model; steady state.

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Fig. 5. Flowsheet Equation.

3. Dynamic simulations

Fig. 4. Column flowsheet.

the feed and bottoms flowrates are set to same values as the base case. Therefore the distillate flowrate must also be the same. Using the same reflux flowrate should yield exactly the same tray and product compositions, which is indeed true (99.9 mol% purities of both product streams. The circulating stream is pumped to 2.5 bar and enters the reboiler at a high flowrate (7000 kmol/h) and 111 ◦ C. The circulating loop mimics the flowrate found in a thermosiphon reboiler. The heat duty in the reboiler is 64.13 MW, which produces a partially vaporize process exit stream (vapor fraction = 0.8096) at a temperature of 120 ◦ C. Setting up this circulating loop is not trivial. The circulating stream was “torn” and a guessed value for the flowrate of a stream entering the base of the column is assumed. The composition of the stream is known (same as bottoms). The vapor fraction of this stream was varied using an Aspen Flowsheet design spec to drive the distillate flowrate to the desired value. Then another Flowsheet design spec was used to change the flowrate of the steam to produce this vapor fraction. When the recycle loop was closed in Aspen Plus, it would not converge. However, after exporting into Aspen Dynamics, the loop was successfully closed and converged to the steady state. In Aspen Dynamics, the streams “6” and “2” are deleted, as is block “B1” (see Fig. 3), Then the source of stream “10” is reconnected to block “VREB”. The steam used in the reboiler is medium-pressure steam at 11 bar and 180 ◦ C with a flowrate of 104.5 × 103 kg/h. The steam temperature in the reboiler shell is 144 ◦ C, which provide the necessary driving force to transfer 64.13 MW in the 3176 m2 heat exchanger using an overall heat-transfer coefficient of 730.9 kcal h−1 m−2 K−1 . The specification of the reboiler HeatX model in Aspen Plus is a hot stream outlet vapor fraction of zero (liquid condensate leaving from the stream trap). When the file is exported into Aspen Dynamics, the default condition in the reboiler is a fixed steam-side pressure. This, of course, is not what we want since the pressure (and temperature) must vary to change the heat-transfer rate and the steam flowrate. It is necessary to use Flowsheet Equations in Aspen Dynamics to change the specification to have an exit hot stream with a vapor fraction of zero. Fig. 5 shows the equation used. It is also necessary to change the pressure of the hot exit stream from fixed to free so that the system is not over specified.

Both the base case column and the rigorous column/heatexchanger process were exported into Aspen Dynamics. A standard conventional distillation control structure was installed on both processes. Three of the loops are identical in both systems. 1. Reflux-drum level is controlled by manipulating the flowrate of distillate using a proportional control with KC = 2. 2. Column base level is controlled by manipulating the flowrate of bottoms using a proportional control with KC = 2. 3. The reflux flowrate is ratioed to the feed flowrate. The other two loops, a tray temperature controller and a pressure controller, are different in the two cases. 3.1. Base case control structure For the base case, condenser pressure is controlled by condenser heat removal (direct QC ). The Aspen Dynamics default tuning parameters are used (KC = 20 and  I = 12 min). A temperature on Stage 40 is controlled by manipulating reboiler duty (direct QR ). Stage 40 is selected because it is near the bottom but still in the region in which changes in the temperature profile are large, as shown in Fig. 6. A 1-min deadtime is installed in this loop, and a relay-feedback test gives an ultimate gain KU = 2.8 and an ultimate period PU = 3.6 min. The Tyreus–Luyben tuning rules give the temperature controller tuning constants KC = 0.88 and  I = 8 min. 3.2. Rigorous case control structure For the simulation with external heat exchangers for the reboiler and condenser, the temperature and pressure loops have the same controlled variables but different manipulated variables than those used in the base case.

Fig. 6. Temperature profile.

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The tray temperature controller now controls Stage 39 instead of Stage 40 because of the difference in stage numbering in a stripping column (top tray is Stage 1). The temperature and composition profiles are identical in both columns. The temperature controller manipulates the control valve in the steam line, not QR directly. A 1-min deadtime is installed in this loop, and a relay-feedback test gives an ultimate gain KU = 17 and an ultimate period PU = 4.8 min. The Tyreus–Luyben tuning rules give the temperature controller tuning constants KC = 5.5 and  I = 11 min.

3.3. Comparison of dynamic responses

Fig. 7. Control structure for rigorous case.

Fig. 8. Pressure responses: loss of QC or cooling water.

Reflux drum pressure is controlled by manipulating the control valve in the cooling water line as shown in Fig. 7. The Aspen Dynamics default tuning parameters are used (KC = 20 and  I = 12 min).

Two types of safety events are explored. In the first, there is a failure in the supply of cooling water to the condenser. In the second, a large surge in steam to the reboiler occurs. A. Condenser cooling failure: With the basic model, this failure is simulated by running at steady state for 10 s, putting the pressure controller on manual and setting controller output signal (which is QC directly) to zero. The dashed line in Fig. 8 shows the response of reflux-drum pressure. There is an immediate rapid rise in pressure from the operating level of 1 bar. It takes only 10 s for the pressure to climb to 1.2 bar. For the rigorous model, the failure is simulated by running at steady state for 10 s, putting the pressure controller on manual and setting controller output signal (which is signal to the air-to-close valve) to 100% (valve completely closed). The solid line in Fig. 8 shows the response of reflux-drum pressure. The rise in pressure is less rapid, taking about 20 s to reach a pressure of 1.2 bar. Fig. 9 shows how several other variables change for the two models. The middle graph on the left shows how the reboiler heat input is unchanged with the base model (dashed lines). However with the rigorous model, the steam flowrate drops off (middle graph on right). This occurs because the base temperature rises as column pressure rises, which reduce the temperature differential in the reboiler and lowers the heat-transfer rate (solid line in middle graph on left). Thus the dynamic response of pressure is slowed down by both the thermal capacitance of the condenser and the rigorous handling of heat transfer in the reboiler.

Fig. 9. Other variable with loss of QC or cooling water.

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Fig. 10. Pressure responses: surge in steam or QR .

Fig. 12. Simultaneous loss of condenser cooling and reboiler heating.

B. Heat-input surge: A second event that could result in over-pressuring the column would be a sudden increase in heatinput. This could be caused by an operator mistakenly putting the temperature controller on manual and opening the steam valve. With the basic model, this failure is simulated by running at steady state for 0.5 min (note the change in the time scale), putting the temperature controller on manual and setting the controller output signal (the reboiler duty) equal to twice the steady-state value. The dashed lines in Fig. 10 show the response of reflux-drum pressure to this disturbance. The pressure rise is much slower and much smaller in magnitude than for a condenser cooling failure. It takes about 1 min for the pressure to rise up to 1.037 bar. For the rigorous model, the failure is simulated by running at steady state for 0.5 min, putting the temperature controller on manual and setting controller output signal (which is signal to the air-to-open valve) to 100% (valve completely open). The solid line in Fig. 10 shows that the response of reflux-drum pressure is slower, taking about 1.4 min to reach 1.037 bar. Fig. 11 compares the responses of the two models for several other variables. The middle left graph shows that there is an

immediate large rise in reboiler duty for the base model, but in the rigorous model, the change in reboiler duty is fairly small. This occurs because the change in the steam flowrate (middle right graph) doubling the control valve opening does not double the steam flowrate, which is set by the heat-transfer rate (as determined by the temperature differential between the steam and column base). Note that the pressure controller is on automatic during this disturbance, so the condenser heat removal is increased in the base model (dashed line in top left graph in Fig. 11) and condenser cooling water flowrate is increased in the rigorous model (top right graph). It is interesting to see what the effect on pressure dynamics would be if an immediate change in the reboiler duty is made when condenser cooling is lost. Responses for the scenario are shown in Fig. 12 for the two models. The rise in pressure is limited to only 1.18 bar in the base model and 1.12 in the rigorous model. Of course the column temperatures would drop and product quality would quickly go off-specification (methanol would drop out the bottom). But over pressuring could be prevented by interlocking the reboiler steam.

Fig. 11. Other variable with surge in steam or QR .

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4. Other issues

5. Conclusion

The numerical example used in this study has a large column (5.61 m in diameter) with large reboiler and condenser duties. Are these results applicable with smaller columns? The answer is yes. All the vessel volumes and heat-transfer areas scale directly with flowrates, so the dynamics should be the same. The only exception is tray liquid hydraulics because weir lengths scale directly with column diameter, not cross-sectional area. So liquid height of the weir is different for different capacities. However, the shortterm pressure responses should not be affected by liquid flowrates.

The standard basic Radfrac model in Aspen simulations does not accurately predict the rapid pressure changes during emergency situations because the default heat-exchanger models do not account for heat-exchanger dynamics (condenser and reboiler). Simulations can be developed that include external heat exchangers whose dynamics can be incorporated with the model of the column vessel. Reference Luyben, W. L. Use of dynamic simulation for reactor safety analysis. Computers and Chemical Engineering, doi:10.1016/j.compchemeng.2012.02.013, in press.