Realistic Models for Distillation Columns with Partial Condensers

Jun 5, 2012 - ... Lehigh University Bethlehem, Pennsylvania 18015, United States ... Fixing reflux-drum temperature and selecting a reasonable pressur...
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Realistic Models for Distillation Columns with Partial Condensers Producing Both Liquid and Vapor Products William L. Luyben*

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Department of Chemical Engineering Lehigh University Bethlehem, Pennsylvania 18015, United States ABSTRACT: Distillation columns frequently produce both vapor and liquid distillate product streams from the reflux drum when the feed stream contains small amounts of light components that would require high pressures or low temperatures if a total condenser were used to completely condense the overhead product. Since removing heat using cooling water in the condenser is much less expensive than using refrigeration, many columns are designed to operate with reflux-drum temperatures of about 120 °F so that cooling water at 90 °F can be used. Fixing reflux-drum temperature and selecting a reasonable pressure determines the split between the amount of vapor product and the amount of liquid product. In the operation of these systems, we usually want to condense as much as possible so as to minimize compression costs of dealing with the vapor product. Therefore the flow rate of cooling water should be maximized. This paper demonstrates a realistic way to model a partialcondenser distillation system using Aspen simulation.

1. INTRODUCTION Distillation columns come in a wide variety of flavors. The plain vanilla column has a single feed with a liquid bottoms product withdrawn from the base and a liquid distillate product withdrawn from the reflux drum. Most types of reboilers (thermosiphon, kettle, or stab-in) perform as partial reboilers and provide one equilibrium stage since the vapor going up the column is in equilibrium with the bottoms liquid product. Condensers, however, are sometimes partial and sometime total. In most cases, total condensation of the overhead vapor is to be preferred because a vapor stream normally requires further expensive processing, such as compression. Using cooling water in a condenser is relatively inexpensive, so column reflux-drum temperatures are often specified such that cooling water, which is supplied at 90 °F, can be used as the heat sink. Heat-exchanger design heuristics recommend that at this temperature level a 20 to 30 °F temperature differential driving force will result in a reasonable capital investment, as dictated by heat-transfer area. Therefore reflux-drum design temperatures are often set at 120 °F. Using this temperature, the required pressure depends on the composition of the overhead and whether the distillate product is removed as a liquid or as a vapor. In the former case, the reflux drum would operate at the bubblepoint pressure at 120 °F. In the latter case, the reflux drum would operate at the dewpoint pressure at 120 °F. There is no difference in these pressures if the overhead is a single pure component. If the overhead is a mixture of chemical components, the bubblepoint pressure is larger than the dewpoint pressure. If the volatilities of the components are quite different, running with a total condenser (bubblepoint pressure) can require a much higher pressure than running with a partial condenser. This is true even if some of the distillate product is taken off as liquid and some is taken off as vapor. A very frequently encountered situation is when the feed to the column contains a small amount of a very light component in addition to the light and heavy key components. Trying to © 2012 American Chemical Society

totally condense the overhead mixture of the lighter-than-light key and light key components could require a very high pressure for a fixed 120 °F reflux-drum temperature. A good example of this situation is in the methanol process where the feed to the distillation column comes from a flash tank that is operating at high pressure with a gas recycle stream containing large amounts of light components (hydrogen, carbon monoxide, and carbon dioxide). Small amounts of these light components will be present in the flash tank liquid and be fed to the column. Trying to totally condense the overhead (a mixture of these light components and methanol) would require either a high pressure or a very low temperature (refrigeration). The solution to the problem is to take a small vapor stream from the top of the reflux drum, in addition to taking a liquid distillate, which is mostly methanol. Some methanol will be lost in the vapor stream, but the small vapor stream can be compressed and recycled back to the reaction section of the process if the economics justify the additional capital and operating expenses. The normal distillation column with either a liquid or a vapor distillate product (but not both) has two steady-state design degrees of freedom once feed conditions, column pressure, total trays, and feed location are fixed. Distillate flow rate and reflux ratio are usually manipulated to achieve two-product composition specifications (the heavy-key impurity in the distillate and the light-key impurity in the bottoms). A distillation column that is designed to produce both a liquid distillate stream and a vapor distillate stream from the reflux drum has an additional design degree of freedom. This is usually specified to be the reflux-drum temperature. Under these conditions, the split between the flow rates of the vapor and liquid distillates is fixed. The condenser heat duty is also Received: Revised: Accepted: Published: 8334

March 27, 2012 May 8, 2012 June 5, 2012 June 5, 2012 dx.doi.org/10.1021/ie300818b | Ind. Eng. Chem. Res. 2012, 51, 8334−8339

Industrial & Engineering Chemistry Research

Research Note

Figure 1. Column flowsheet: DME/methanol/water at 2 psia.

fixed. Specifying a reasonable design minimum temperature differential temperature (at the either the cold or the hot end of the condenser) and a reasonable overall heat-transfer coefficient fixes the heat-transfer area. This also fixes the required flow rate of the cooling water since both the inlet and exit cooling water temperatures are known. All these sizing calculations are performed at the design stage to select the correct equipment (column and heat exchangers). Once the column is built and the condenser area is fixed, the normal operating objective is to minimize the vapor flow rate by maximizing condenser heat removal. This is achieved by maximizing cooling water flow rate. A numerical example is considered in a later section to illustrate this situation.

1. Fixed reflux flow rate: pressure controlled by the flow rate of the vapor distillate and reflux-drum level controlled by condenser heat removal 2. Fixed condenser heat removal: pressure controlled by the flow rate of the vapor distillate and reflux-drum level controlled by the flow rate of the reflux 3. Fixed reflux ratio: pressure controlled by the condenser heat removal, reflux-drum level controlled by the flow rate of the reflux, and the flow rate of the vapor distillate ratioed to the flow rate of the reflux The present paper explores the situation in which both vapor and liquid product streams are removed from the reflux drum, and the optimum operation is to produce as little vapor and as much liquid as possible. Hori and Skogestad3 studied alternative control structures for a cryogenic deethanizer with a partial condenser using Aspen simulations and reported a test of a control structure on a real column. They considered single-end and dual temperature control structures in addition to having different pairings in the pressure and level loops. In their deethanizer example, the vapor distillate was very small (1% of the feed). Despite its small flow rate, manipulating vapor to control pressure was found to be effective as long as a temperature controller manipulating reboiler duty was on automatic.

2. PREVIOUS WORK The design and control of partial condenser systems were examined in the pioneering work of Shinskey1 over three decades ago. The advantages of various process configurations and of alternative control structures were discussed but only in qualitative terms. No dynamic simulations with performance comparisons were presented. Some aspects of the control of distillation columns with partial condensers were quantitatively discussed almost a decade ago.2 The system studied in that work produced only a vapor distillate. The condenser only condensed enough of the overhead vapor leaving the column to provide liquid for the column reflux. The condenser and reflux-drum system had three variables that could be manipulated: reflux flow rate, vapor distillate flow rate, and condenser heat removal. These manipulated variables permit the control of three variables. Two variables that must be controlled are the column pressure and the reflux-drum level. There are strong interactions among the pressure, temperature, and level loops, and pairing and tuning of these loops are more difficult than in a totalcondenser column. Three alternative control structures were explored in which various controlled/manipulated variable pairings were evaluated. In all these control structures, the temperature of a sensitive tray was controlled by manipulating reboiler duty.

3. PROCESS STUDIED The numerical example considered in this paper has 500 lbmol/h of feed that is a ternary mixture of 5 mol % dimethyl ether (DME), 45 mol % methanol, and 50 mol % water. The DME is a lighter-than-light key component that is mostly removed in a vapor stream from the top of the reflux drum. Most of the light-key component methanol comes off in the liquid distillate, and most of the heavy-key component water leaves in the bottoms. Figure 1 shows the flowsheet. The column has 36 stages (Stage 1 is the reflux drum and stage 36 is the base). Feed is introduced on stage 17. The reflux-drum pressure is set at 25 psia and the reflux-drum temperature is 120 °F. A tray pressure 8335

dx.doi.org/10.1021/ie300818b | Ind. Eng. Chem. Res. 2012, 51, 8334−8339

Industrial & Engineering Chemistry Research

Research Note

Figure 2. Fix partial condenser temperature.

Figure 3. Select LMTD dynamic model in partial condenser.

°F, which is much higher than the reflux-drum temperature. This occurs because of the large difference between the boiling points of DME (−12.7 °F) and methanol (148.5 °F) and the 25 psia operating pressure. The condenser is designed for a 10 °F approach, so the cooling water exit temperature is 161 °F. In some plant cooling-water systems, the cooling-water chemistry imposes a limit on the permitted change in the cooling water temperature (20 to 30 °F). In this situation the design approach temperature would be increased, which would require a higher flow rate of cooling water and a smaller area condenser.

drop of 0.1 psi per stage is assumed. NRTL physical properties are used in the Aspen simulations. There are three design degrees of freedom in this partial condenser column. They are selected to be 0.1 mol % water in the liquid distillate, 0.1 mol % methanol in the bottoms, and 120 °F reflux-drum temperature. The resulting small vapor distillate flow rate is 30.08 lb-mol/h and the larger liquid distillate flow rate is 221.9 lb-mol/h. Column diameter is 3.06 ft, and the reflux flow rate is 208 lb-mol/h. The heat removal rate in the condenser is 6.894 × 106 Btu/h, which requires 96,390 lb/h of 90 °F cooling water. Notice that the temperature of the overhead vapor from the column is 171 8336

dx.doi.org/10.1021/ie300818b | Ind. Eng. Chem. Res. 2012, 51, 8334−8339

Industrial & Engineering Chemistry Research

Research Note

Figure 4. Throughput increase.

4. STEADY-STATE DESIGN The feed conditions, the pressure, the total stages and the feed stage are specified in the steady-state design using Aspen Plus (Version 7.3). Two Aspen design spec/vary functions are set up to achieve the desired product specifications of 0.001 mol fraction water in the liquid distillate and 0.001 mol fraction methanol in the bottoms. Figure 2 shows how the third specification is fixed in Aspen Plus. Under the C1 column block, the Setup item is selected and the Condenser page tab is opened. The condenser specification is selected to be a fixed temperature (120 °F). In preparation for exporting into dynamics, the reflux drum and the column base are both sized in the normal way to provide 5 min of liquid holdup when half full. The column diameter is determined from the Tray Sizing item in the column block. The Aspen Plus default dynamic conditions for the reboiler and condenser are Constant duty. When the Aspen Plus file is exported into Aspen Dynamics, the heat duty in the condenser will be fixed. It can be manipulated to control some variable, usually pressure. However, there are other options for setting up the condenser, which can be used to obtain more realistic models. Figure 3 shows that clicking the drop-down arrow on the right of the Heat transfer option gives several options. The Constant duty option is the default and produces a dynamic model in which condenser heat removal is the manipulated variable. The Constant temperature option assumes that the temperature of the cooling medium is the same at all axial positions in the condenser. This situation can be used when the cooling medium is a liquid that is being vaporized in the condenser by the heat of condensation of the process vapor stream. The medium could be a vaporizing refrigerant in low-temperature columns or vaporizing boiler feedwater to generate steam in high-temperature columns. The Constant temperature option produces a dynamic model in which the temperature of the cooling medium is the manipulated variable.

The Evaporating option is similar to the Constant temperature option except that the flow rate of the cooling medium is the manipulated variable. The most realistic option for partial condenser modeling is the LMTD option. The cooling medium is a liquid that enters a counter-current heat exchanger at a specified inlet temperature. The minimum approach differential temperature is specified. The process inlet and outlet temperatures are known, so the log-mean temperature differential driving force is known. With the known condenser duty, the required product of the overall heat-transfer coefficient and the condenser heat-transfer area (UA) is calculated. The required flow rate of the cooling medium can also be calculated. The LMTD option produces a dynamic model in which the flow rate of the cooling medium is the manipulated variable. This is the model that will realistically provide a prediction of how the partial condenser system responds to disturbances.

5. DYNAMIC SIMULATION Two files were exported into Aspen Dynamics with the two alternative condenser models (Constant duty and LMTD). Three cases were explored. The Constant duty model was used in the first two cases, and the LMTD model was used in the third. In the first case (constant QC), the condenser duty was held constant. In the second case (constant TC), the reflux-drum temperature was controlled by manipulating condenser heat duty. In the third case (constant CW), the flow rate of cooling water was held constant (using the LMTD model). Disturbances in the flow rate and composition of the feed to the column were made. In all cases, the basic control structure used the following conventional control loops. The only difference among the cases was how the condenser heat duty was determined. 1. Feed was flow controlled 2. Pressure was controlled by manipulating the flow rate of the vapor distillate 8337

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Industrial & Engineering Chemistry Research

Research Note

Figure 5. Throughput decrease.

Figure 6. Increase in DME in feed.

3. Base level was controlled by manipulating bottoms flow rate 4. Reflux-drum level was controlled by manipulating liquid distillate flow rate 5. Reflux flow rate was fixed 6. The temperature on stage 33 was controlled by manipulating reboiler heat input

The dotted lines are when the temperature of the reflux drum is controlled. In Figure 4 the feed flow rate is increases 10%. If condenser duty is fixed (FixedQC), no additional heat transfer occurs in the condenser, so there are large increases in the flow rate of the vapor distillate (DV) and in the reflux-drum temperature. These responses are unrealistic since the increase in the flow rate of the overhead vapor into the condenser should change the condenser heat-transfer rate. If the reflux-drum temperature is fixed (FixedTC) by varying condenser duty (using a temperature controller), the increases in the flow rates of the vapor and distillate are about

5.1. Feed Flow Rate Disturbances. Figures 4 and 5 show the responses of the process to 10% disturbances in feed flow rate. The solid lines are when the flow rate of cooling water is fixed. The dashed lines are when the condenser duty is fixed. 8338

dx.doi.org/10.1021/ie300818b | Ind. Eng. Chem. Res. 2012, 51, 8334−8339

Industrial & Engineering Chemistry Research

Research Note

Figure 7. Decrease in DME in feed.

proportional to the increase in feed flow rate. But these responses are unrealistic since the increase in condenser duty would require a proportional increase in the differential temperature driving force that could only be attained by a large increase in the flow rate of the coolant. The realistic situation is when the cooling water flow rate is fixed (at its maximum since we are trying to minimize the flow rate of the vapor distillate). Flow rate is the only truly manipulated variable. The FixedCW responses show a refluxdrum temperature that increases slightly and a slightly larger ratio of vapor-to-liquid flow rates. Figure 5 gives results for a 10% decrease in feed flow rate. Results are the opposite of those shown for an increase. Unrealistic responses are shown for the FixedQC and the FixedTC cases. Notice that the FixedQC case requires a refluxdrum temperature (TC shown in the bottom right graph in Figure 5) that is lower than the temperature of the available cooling water. 5.2. Feed Composition Disturbances. Figures 6 and 7 give responses for feed composition disturbances with the three alternative condenser models. In Figure 6 the DME concentration in the feed is increased from 5 mol % to 7.5 mol % (with a corresponding decrease in methanol). The flow rate of the vapor distillate DV increases in all cases as expected, but the FixedQC model gives a smaller increase in DV accompanied by an unrealistically large decrease in reflux-drum temperature down to 101 °F. The DME impurity in the liquid distillate xD(DME) shows a large increase. Decreasing the DME concentration in the feed has the opposite effects, as shown in Figure 7. The FixedQC model predicts less change in the flow rate of the vapor distillate and a high reflux-drum temperature. The most realistic predictions are those given by the FixedCW model.

6. CONCLUSION Three different distillation condenser models have been compared for columns producing both vapor and liquid distillate streams. When the objective is to minimize the flow rate of the vapor, we should try to condense as much of the overhead vapor as possible. The realistic means for accomplishing this objective is to maximize the flow rate of the cooling medium. Therefore the model that assumes a fixed flow rate of cooling water gives the most realistic predictions of performance to disturbances.

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AUTHOR INFORMATION

Corresponding Author

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

The authors declare no competing financial interest.

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REFERENCES

(1) Shinskey, F. G. Distillation Control for Productivity and Energy Conservation; McGraw-Hill: New York, 1977. (2) Luyben, W. L. Alternative Control Structures for Distillation Columns with Partial Condensers. Ind. Eng. Chem. Res. 2004, 43, 6416−6429. (3) Hori, A. E. S., Skogestad, S. Control Structure Selection of a Deethanizer Column with Partial Condenser. Proceedings of European Congress of Chemical Engineering (ECCE-6), Copenhagen, 16−20 September, 2007.

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dx.doi.org/10.1021/ie300818b | Ind. Eng. Chem. Res. 2012, 51, 8334−8339