Analysis of Inverse-Acting Column Base Levels

Jul 1, 1996 - in the average life, size, and number of bubbles. Since the level is maintained by a rising current of bubbles, as the average size of t...
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Ind. Eng. Chem. Res. 1996, 35, 2640-2644

Analysis of Inverse-Acting Column Base Levels Himal P. Munsif and James B. Riggs* Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409

Distillation column base levels are known to exhibit inverse action in certain cases, and this is detrimental to column control performance when reboiler duty is set by the base level controls. This inverse response behavior in level is known to arise due to two factors, namely the reboiler swell and the froth density effects. Inverse action due to reboiler swell effects depends upon the operating pressures and also on the reboiler type. Inverse action due to the froth density effects is dependent on the operating regime and tray design. It was found that, in general, for high-pressure columns, inverse action is unlikely due to either the froth density or the reboiler swell effects. For low-pressure columns, inverse action can be significant. Contrary to the reported literature, it was concluded that froth density effects are not as likely to be a significant cause of inverse action in reboiler levels as reboiler swell. Introduction In many chemical processes, the output variable subjected to a step change in the manipulated variable will give an initial response in the opposite direction to where the output variable goes at steady state. This behavior, which is referred to as “inverse response”, is caused by competing factors, one of which has a relatively large short-term effect and the other cause is the dominating long-term response. There are a wide range of chemical engineering systems that exhibit inverse action, among them are a number of boiling systems: waste heat and utility boilers and distillation column reboilers. Inverse action in column base levels is caused primarily by two factors. The first factor is the reboiler swell/ surge effect. Inverse response occurs when additional bubbles are generated due to an increase in the heat rate leading to a rise in the liquid level (swell) momentarily before the level starts decreasing due to the overall material balance (Shinskey, 1979). The second factor which can cause inverse action is the froth density effect which is dependent on the operating regime and tray design (Buckley et al., 1975). This latter mechanism of inverse action in reboiler levels occurs mainly in the froth regime when the froth density changes sharply with changes in the vapor flowrate. When a positive step change is provided in the vapor rate, the density of the mixture over the tray decreases, resulting in an increase in volume. Since there exists a sideways (horizontal) motion for the fluid on the tray, the excess volume is displaced and ends up in the downcomer, increasing the flow over the weir. This occurs on all the trays. Hence the short-term effect is a rise in the liquid level of the reboiler due to the excess liquid displaced over the downcomer via a reduction in froth density followed by a reduction in level due to an increase in boiling rate, thereby leading to inverse action. Figure 1 is a schematic representation of both of the above effects. Inverse-acting base levels are generally not a problem unless the base level controller sets the column reboiler duty. Base level is used to set reboiler duty for columns with a large boilup to bottoms product ratio and for columns for which the bottoms flowrate is set externally to the column (e.g., bottoms product is fed to a reactor * Author to whom correspondence should be addressed. Fax: (806) 742-3552. Email: [email protected].

Figure 1. Factors responsible for inverse-acting levels: (a) froth density effect; (b) reboiler swell effect.

for which it is desired to maintain a specified feed rate). For both cases the relative changes in column heat duty and degree of inverse action are likely to be largest during column feed rate changes. In any case, when significant inverse action occurs for a column which sets reboiler duty off of level control, it can result in a significant operational problem affecting the reliability and overall control performance for distillation columns. The following sections study the different factors which lead to an inverse response in the column base level. The individual effects and the magnitude of these factors are analyzed under different operating regimes/ systems in an attempt to suggest guidelines to the control engineer as to when will a particular column

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exhibit inverse response, and if so, which is/are the contributing factor(s) and what are the expected levels of inverse response? Reboiler Swell Under steady state operating conditions, the reboiler contains a certain mass of liquid and vapor below the surface of the liquid. For this mass of liquid and vapor, there is an average mixture density. As long as the reboiler heat rate is constant, the vapor-liquid mixture has the same volumetric proportions, and the average mixture density is constant. If the reboiler heat load is increased, the concentration of vapor bubbles under the liquid surface increases. This results in a change in the volumetric proportions in the vapor-liquid mixture, and the average density of the mixture decreases. Since the mass of the liquid and vapor at this point has not changed significantly while the average density has decreased, the result is an immediate increase in the volume of the vaporliquid mixture. This causes an immediate increase in the liquid level even though additional liquid has not been added. This is schematically represented in Figure 1b. This effect of a sudden increase in the liquid level as the heat rate is increased is known as swell which is a short-term effect. Eventually the material balance takes over, and the level starts to decline steadily since there is more material leaving the reboiler than entering it. Similarly, when the heat load is reduced, there are fewer vapor bubbles in the mixture; hence the average density of the mixture increases, and the volume of the vapor-liquid combination decreases. This leads to an immediate reduction in the liquid level, although the liquid and vapor mass has not significantly changed. This sudden reduction of level due to a decrease in the heating rate is called shrink which like swell is a shortterm effect, and the level will eventually rise in the longterm. The swell and shrink can give rise to the inverse response in reboilers. The swell and shrink described above are due to a step change in the heating rate. Inverse response can also be caused if liquid is introduced at a temperature below that of the boiling liquid. This causes internal condensation of the vapors, and hence a sudden increase in flow can reduce the rate of boiling, and the level momentarily decreases (shrink) before the increasing liquid inventory begins to raise it integrally (Dukelow, 1986). The following sections analyze the effects of reboiler types and bubble dynamics on inverse response. Reboiler Types. Reboilers are an integral part of distillation systems, and there are a variety of reboiler types used in the chemical processing industries. They can be grouped broadly into two categories: (1) natural circulation reboilers like the thermosyphon, kettle, and internal reboilers; (2) forced circulation reboilers like the suppressed and unsuppressed vaporization types. Some of the common types of reboilers are depicted in Figure 2. There is an abundance of literature available as to the advantages and disadvantages of the abovementioned reboiler types and their selection criteria (Kister, 1990). For thermosyphon and forced convection reboilers, the swell effect due to reboiler duty increases results in reducing the liquid holdup around the tube bundle and in the vapor return line, resulting in an increase in the measured base level. That is, liquid holdup removed from around the tube bundle and the vapor return line ends up in the base of the column thus raising the

Figure 2. Common reboiler types (with permission of McGrawHill): (a) vertical thermosophon; (b) horizontal thermosophon; (c) forced convection; (d) kettle; (e) internal.

measured base level. The significance of the swell effect upon the degree of inverse action is dependent upon the fraction of the total liquid holdup in the reboiler that is contained in the vapor return line and around the tube bundle. Direct fired forced convection reboilers, which generally have the reboiler located a significant distance from the base of the column, are particularly susceptable to inverse level response due to the large proportion of liquid holdup in the vapor return line. In a kettle reboiler, the level is measured from a compartment connected to the housing for the tube bundle. Here too, inverse action occurs due to reboiler swell effects. The short-term effect of an increase in boilup rate is an increase in the vapor fraction around the tube bundle which causes additional liquid flow over the weir into the compartment where the reboiler liquid level is measured. Since the compartment has a cross sectional area that is considerably smaller than that for the tube bundle (see Figure 2), it is expected that kettle type reboilers would be the reboiler type that is most susceptable to swell effects. In an effort to reduce the magnitude of the inverse action due to swell in kettle reboilers, industrial practioners have drilled holes at the bottom of the weir (the plate that separates the boiler tubes from the level compartment) in the reboiler (Shinskey, 1996). When extra liquid enters the level compartment as the result of swell, part of it can return to the boiler tube compartment through the holes thus reducing the magnitude of inverse action. Inverse action also occurs in internal reboilers due to the same swell effects. Many times for internal reboilers, the level is inferred based upon a pressure measurement at a point just above the reboiler tubes. This is done in order to reduce the risk of exposing the

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Figure 4. Flow regions for column. Figure 3. Inverse action due to reboiler swell in measure percentage level.

reboiler tubes which could damage them. When an increase in reboiler duty is applied to an internal reboiler, the vapor void fraction for the region around the tube bundle increases, forcing more liquid above the tube bundle which results in a larger reboiler level being sensed. If the level indicator (i.e., pressure senser) were placed below the tube bundles, no inverse action would result because the mass above the level indicator would not have changed. Bubble Dynamics. In most reboilers, the heat transfer occurring can be viewed as essentially consisting of two zones: sensible heat transfer followed by nucleate boiling with convection (Shah, 1979). A rigorous macroscopic balance over the reboiler and the column base does not predict inverse response [Alatiqi et al. (1992)]. To understand the phenomena of reboiler swell, a microscopic balance was studied pertaining to the bubble growth since the size and number of the bubbles decide the swell and shrink which in turn are responsible for the inverse action. Using the equations developed from Tong (1965), the maximum bubble size, the time required to reach this maximum size, and the average bubble size at any time can be calculated. A water-steam system and a hydrocarbon (C8-C9) system were considered for the reboiler. At an operating pressure of about 2 atm, the bubble size was calculated along with the time for bubble collapse. It was found that for the water-steam system, the maximum bubble size was 0.47 cm and the collapse time was 0.95 s. When a step change of 5% was provided in the heating rate, the maximum bubble size obtained was 0.65 cm and the collapse time was 1.00 s. The number of nuclei also increased. For the hydrocarbon system at the base case condition, the maximum bubble size was 0.29 cm and the collapse time was 0.63 s. After the step change, the maximum bubble size increased to 0.44 cm and the collapse time to 0.66 s. It can be seen that when a positive step change is given in the heating rate, the immediate effect is a rise in the average life, size, and number of bubbles. Since the level is maintained by a rising current of bubbles, as the average size of the bubbles and the number of bubbles increase (as indicated by the rise in the number of nuclei), the level rises immediately (as a short-term effect) before the material balance catches up and the level starts decreasing. The reverse happens when a negative step change is provided in the heating rate. Figure 3 shows the inverse action due to the reboiler swell in terms of the inverse acting percent level change as a function of pressure for an internal reboiler. It takes into account changes in the nucleation sites and

bubble volume. Three operating pressures were studied: 0.3 atm (for vacuum columns), 2 atm (for atmospheric columns), and 10 atm (for high-pressure columns). Two cases of change in the heat load were studied, one at 2% and the other at 5%. It was found that vacuum columns are the most susceptible to inverse action. As the pressure increases, the degree of inverse action decreases. For high-pressure columns, the inverse action due to reboiler swell is minimal. This is because at high pressures, the density difference between the vapor and liquid is diminished, whereas under vacuum, this same density difference is enhanced. When the actual liquid holdup is 100%, the measured level reads 100%, and when the actual holdup is 80% of the maximum, the measured level reads 0% as is generally the case in industrial internal reboilers. This procedure is usually applied in order to reduce the likelihood that boiler tubes are exposed and thus damaged. It was assumed that the liquid that resides around the boiler tubes accounts for 25% of the total molar holdup for the reboiler. The results shown in Figure 3 are average values for the water-steam and the hydrocarbon system. These numbers will vary from system to system and also on the reboiler type, but the trend should be similar. Summarizing, for the case of inverse action due to reboiler swell, the operating pressure and the reboiler type are critical factors. For high-pressure columns inverse action is minimal. For low to moderate pressures, there can be significant inverse action. Natural circulation reboilers are susceptible to inverse action, especially kettle reboilers, but forced circulation reboilers are not unless the reboiler is located a significant distance away from the base of the column. Froth Density The plot shown in Figure 4 (Lockett, 1986) illustrates a flow regime diagram indicating how the flow regime on the tray typically changes with the flow parameter. From this figure, generally, vacuum distillation can result in spray regime operation, atmospheric distillation typically involves operation in the froth regime, and high-pressure distillation is usually associated with the emulsion regime. The capacity factor is defined as

CF )

( )

QG FG Ab FLFG

0.5

(1)

The flow parameter is defined as

FP )

()

M L FG MG FL

0.5

(2)

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Figure 5. Change in froth density as function of vapor flowrate.

Buckley et al. (1975) mention that an inverse response is partly due to tray design or type and partly due to low F-factors (or vapor rates). They derived theoretical equations to predict inverse response. They found that the change in froth density with a change in the vapor rate strongly influences the presence of inverse action. Figure 5 (Van Winkle, 1967) shows a plot of froth density as a function of the vapor velocity. For low vapor rates or F-factors (Fva from Figure 5) the froth density changes steeply, whereas for high vapor rates the change in froth density is minimal. The latter is true because there is mainly vapor on the trays as froth and the system is tending toward the emulsion regime. When a column is operating in the froth regime, the location along the curve in Figure 5 determines the magnitude of the inverse action. Calculations based on the analysis carried out by Buckley et al. (1975) indicate that for a 2% change in the vapor rate, inverse action due to the froth density change in the measured percent level (where a measured level of 0% corresponds to 80% actual holdup) is as follows: Referring to Figure 5, at point 1 (top of the curve, Fva ≈ 0.1) the froth density change is about 4%, at point 2 (middle of the curve, Fva ≈ 1.0) the change is about 1%, and at point 3 (flat end of the curve, Fva ≈ 2.0) it is minimal. For the case of inverse action due to froth density, the operating regime (operating pressure) and the vapor rate play a critical role. For vacuum columns, the operation lies in the spray regime. Thus inverse action due to the froth density effects is not a factor. Highpressure columns typically operate in the emulsion regime where the inverse action is unlikely. Thus the only columns for which inverse action can occur due to the froth density effects are the frothing systems which typically operate near atmospheric conditions (low to moderate pressures). Even for these columns, the location along the curve in Figure 5 determines the degree of inverse response. For point 1 in Figure 5, the degree of inverse response is higher than anywhere else along the curve. But this point is not realizable physically from an operating standpoint because it corresponds to weeping conditions (the vapor rates are so low so as to cause flooding). Point 2 in Figure 5 is an operating region where the realizable inverse response can be moderate. But this region corresponds to a column operating well below design conditions (typically at 30-40% of flood loading design), i.e., and at low boilup rates. Although there are cases where columns operate in this region, they are still few in number

because most columns are loaded up for maximum throughputs for obvious economic reasons. Besides, even for those columns operating in the frothing region, at low boilup rates, and below design conditions, the base level controller may not be used to set the vapor rate. This further reduces the number of cases where the froth density effects can give rise to significant inverse response. When the level is used to set the vapor rate, it can result in inverse-acting levels. If level is not used to set the vapor rate, then inverse action which will still occur but is handled by the level controller as a disturbance to the system. Tray design can also be a criteria in deciding inverse action. Buckley et al. (1975) report that for valve trays, inverse response is predicted over the entire range of normal operation. This is because valve trays are usually operated at low to moderate flowrates where they provide operational advantages, and therefore, a high turndown. Buckley et al. (1975) report that for sieve trays, inverse response is predicted at low boilup rates but at high boilup rates there is no inverse action. Inverse action in base levels will not occur due to the froth density effects in kettle reboilers because the level is usually measured from inside the reboiler rather than the base of the column. In addition, chemical factors, such as surface tension, do not play a primary role in determining whether or not a reboiler will exhibit inverse action. Thus in general, it was found that there are relatively very few cases where inverse action occurs due to the froth density effects, and even if it does, the magnitude is lower than that due to the swell effects. Hence the reboiler swell effects appear to be the dominating factor for deciding inverse response in column base levels. This has also been observed industrially (Kister, 1995). This result is contrary to the published literature (Buckley et al., 1975) where the researchers have attributed the froth density effects to be the dominant factor for deciding inverse action and which has been accepted by certain portions of the technical community (Seborg et al., 1989). Summarizing, inverse-acting levels due to froth density effects are expected to occur much less frequently than those due to reboiler swell effects. The magnitude of inverse action due to froth density effects is also found to be lower than that due to swell effects. Tray design plays an important role in deciding inverse action, and valve trays are susceptible to inverse action because they are designed for a high turndown. Kettle reboilers are not expected to exhibit inverse action due to froth density effects. Conclusions Inverse action in a column base level occurs primarily due to two factors: reboiler swell and froth density. Of these factors it was concluded that reboiler swell was the more dominant effect for determining inverse action in terms of the magnitude of inverse response, the predicted range of operation, and the number of industrial columns likely to experience inverse-acting base levels. This result is contrary to published literature where researchers have attributed the froth density effects to be the prominent factor for determining inverse action in column base levels. In general, it was found that for high-pressure columns, inverse action is unlikely due to either the swell effects or the froth density effects. For low to moderate pressure (atmospheric) columns, inverse action is likely to be moderate from the swell effects;

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inverse action from the froth density effects depends on the operating region and vapor rates, and it can be relatively low to moderate. For vacuum columns, inverse action can be significant from the swell effects but unlikely due to the froth density effects. Inverse action from froth density effects is unlikely unless operation is in the frothing region and is near the weeping point. Kettle reboilers are most susceptible to inverse response due to swell, but direct fired forced circulation reboilers can experience significant inverse action due to swell when the reboiler is located away from the base of the column. Chemical factors like surface tension were determined to be only secondary factors. Acknowledgment The authors would like to thank Henry Z. Kister and Greg Shinskey for helpful discussions on the mechanisms that cause inverse-acting levels. This work was supported by the member companies of the Texas Tech Process Control and Optimization Consortium. Nomenclature Ab ) interfacial area CF ) capacity factor FP ) flow parameter MG ) gas mass ML ) liquid mass QG ) volumetric gas flowrate VVA ) superficial vapor velocity

FG ) gas density FL ) liquid density

Literature Cited Alatiqi, I. M.; Meziou, A. M. Simulation and Parameter Scheduling Operation of Waste Heat Steam - Boilers. Comput. Chem. Eng. 1992, 1 16, 51-59. Buckley, P. S.; Cox, R. K.; Rollins, D. L. Inverse Response in Distillation Columns. Paper presented at the AIChE Spring National Meeting, Houston, TX, 1975. Dukelow, S. G. The Control of Boilers; Instrument Society of America: 1986. Kister, H. Z. Distillation Operation; McGraw Hill: New York, 1990. Kister, H. Z.; Braun, C. F. Personal communication, August 4, 1995. Lockett, M. J. Distillation Tray Fundamentals; Cambridge University Press: Cambridge, 1986. Seborg, D. E.; Edgar, T. F.; Mellichamp, D. A. Process Dynamics and Control; John Wiley & Sons: New York, 1989. Shah, G C. Troubleshooting Reboiler Systems. Chem. Eng. Prog. 1979, 75, 53-58. Shinskey, F. G. Process Control Systems; McGraw Hill: New York, 1979. Skinskey, F. G. Personal communication, January, 1996. Tong, L. S. Boiling Heat Transfer and Two-Phase Flow; John Wiley & Sons: New York, 1965. Van Winkle, M. Distillation; McGraw Hill: New York, 1967.

Received for review September 25, 1995 Accepted February 22, 1996X IE950595K X Abstract published in Advance ACS Abstracts, July 1, 1996.