8.19
Distillation: Basic Controls H. L. HOFFMAN, D. E. LUPFER L. A. KANE
(1985)
B. A. JENSEN
B. A. JENSEN, B. G. LIPTÁK
V
(1970) (1995)
TR
D
R or L
(2005) Ri or Li
F Q V
LF
V Q
LF
B
Flow sheet symbol
INTRODUCTION Distillation is the most common class of separation processes and one of the better understood unit operations. It is an energy-separating-agent equilibrium process that uses the difference in relative volatility, or differences in boiling points, of the components to be separated. It is the most widely used method of separation in the process industries. The distillation process will most often be the choice of separation unless the following conditions exist: • • • •
Thermal damage can occur to the product. A separation factor is too close to unity. Extreme conditions of temperature or pressure are needed. Economic value of products is low relative to energy costs.
Control involves the manipulation of the material and energy balances in the distillation equipment to affect product composition and purity. Difficulties arise because of the multitude of potential variable interactions and disturbances that can exist in single-column fractionators and in the process that the column is a part of. Even seemingly identical columns will exhibit great diversity of operation in the field. Therefore, this section will not attempt to provide control strategies that can be applied 1820 © 2006 by Béla Lipták
to columns in a “cookbook” fashion. Instead, discussion will begin with a basic description of the distillation process and equipment, followed by techniques used to derive a mathematical column model. The presentation in this section will then describe methods to evaluate interactions and alternative control strategies; control models used for some product quality, pressure, and feed flow control strategies; and finally some common feedforward advanced regulatory control strategies commonly used in the regulation of fractionators. The goal of this section is to provide the process control engineer with the tools necessary to design unique control strategies that will match the specific requirements of distillation columns. General Considerations Distillation separates a mixture by taking advantage of the difference in the composition of a liquid and that of the vapor formed from that liquid. In the processing industries, distillation is widely used to isolate and purify volatile materials. Thus, good process control of the distillation process is vital to maximize the production of satisfactory purity end products. Although engineers often speak of controlling a distillation tower, many of the instruments actually are used to control the auxiliary equipment associated with the tower. For this reason, the equipment used in distillation will be discussed.
8.19 Distillation: Basic Controls
DISTILLATION EQUIPMENT
Condenser
There are some basic variations to the distillation process. One such basic difference is between continuous and batch distillation. The main difference between these processes is that in continuous distillation the feed concentration is relatively constant, while in batch distillation it is rich in light components at the beginning and lean in light components at the end. While batch distillation is also described in this section, the emphasis is on the continuous processes. Another basic difference is in the way the condenser heat is handled. The more common approach is to reject that heat into the cooling water and thereby waste it. This necessitates the use of “pay heat” at the reboiler, which usually is a large part of the total operating cost of the column. An alternate approach, also discussed in this section, is “vapor recompression” (Figure 8.19a), in which the heat taken out by the condenser is reused at the reboiler after a heat pump (compressor) elevates its temperature. While vapor recompression controls are also discussed in this section, the emphasis is on the traditional air- or water-cooled condenser designs. The Column The primary piece of distillation equipment is the main tower. Other terms for this piece of equipment are column and fractionator, and all three terms are used interchangeably. The tower, column, or fractionator has two purposes: First, it separates a feed into a vapor portion that ascends the column and a liquid portion that descends; second, it achieves intimate
D
Removed heat wasted
D M
F
F
B
Pay heat added
Compr.
Work
B
Recovered heat
FIG. 8.19a In contrast with conventional distillation, the vapor recompression system uses recovered heat.
© 2006 by Béla Lipták
1821
Column
Accumulator
Feed pump Reflux pump Preheater
Reboiler
FIG. 8.19b Distillation equipment.
mixing between the two countercurrent flowing phases. The purpose of the mixing is to get an effective transfer of the more volatile components into the ascending vapor and corresponding transfer of the less volatile components into the descending liquid. The other equipment associated with the column is shown schematically in Figure 8.19b. In continuous distillation, the feed is introduced continuously into the side of the distillation column. If the feed is all liquid, the temperature at which it first starts to boil is called the bubble point. If the feed is all vapor, the temperature at which it first starts to condense is called the dew point. The feed entering the column is normally operated in a temperature range that is intermediate to the two extremes of dew point and bubble point. However, some optimization strategies may call for designs where the feed is either superheated or subcooled. For effective separation of the feed, it is important that both vapor and liquid phases exist throughout the column. The separation of phases is accomplished by differences in vapor pressure, with the lighter vapor rising to the top of the column and the heavier liquid flowing to the bottom. The portion of the column above the feed is called the rectifying section and below the feed is called the stripping section. Packing and Trays The intimate mixing is obtained by one or more of several methods. A simple method is to fill the column with lumps of an inert material, or packing, that will provide surface for the contacting of vapor and liquid. Another effective way is to use a number of horizontal plates, or trays, which cause the ascending vapor to be bubbled through the descending liquid (Figure 8.19c). 1 Tray designs are numerous and varied. Tray designs include bubble cap plate unit, valve, sieve plate, tunnel, dual-flow, chimney, disc-and-donut, turbogrid trays, v-grid, Perform-Kontakt, Haselden baffle tray, Kittel trays, and other specialty-type units. Dualflo® trays, Flexitray®, Varioflex®, Bi-Frac®, Max-Frac®, NYE Trays®, Superfrac® trays, Super-Flux® trays, and Ultra-Frac® trays are specialty registered tray designs from different manufacturers that are variations of the aforementioned tray designs. Bubble caps
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Control and Optimization of Unit Operations
• L
•
• L
• L
FIG. 8.19c Intimate contact and therefore equilibrium is obtained as the vapor bubbles ascend through the liquid held up on each tray, as the liquid descends down the column.
and sieve trays are the most common designs used in distillation applications. 2 Many different types of packings are available. They are normally classified as random or stacked. Random packings are those that are dumped into the containing shell. Raschig rings, Berl saddles, Intalox saddles, and Pall rings are the most common random packings and come in various sizes from 1/2 to 31/2 in (1.25 to 9 cm). Stacked packings, also known as grid or stacked packing, include large-sized Raschig rings and Lessing rings. Packings generally give lower pressure drops at the cost of higher installation costs. They are made of ceramic, plastic, or metal, depending upon the type of packing and the intended application. Other packings such as Maspac®, HyPak®, Tellerette®, IMTP® FLEXIPAC® KATAMAX®: FLEXIGRID®-2, -3, and -4, and KOCH-GLITSCH GRID® EF-25A are specialty registered packings from different manufacturers that are just variations of the aforementioned packings. When deciding between the use of trays and packing, the 3 following factors should be considered: •
• • •
•
•
•
Because of liquid dispersion difficulties in packed towers, the design of plate towers is considerably more reliable and requires less safety factor when the ratio of liquid mass velocity to gas mass velocity is low. Towers using trays can be designed to handle wider ranges of liquid rates without flooding. Towers using trays are more accessible for cleaning. Towers using trays are preferred if interstage cooling or heating is needed because of lower installation costs of delivery piping. Towers using trays have a lower total dry weight, though total weight with liquid hold-up is probably equal. Towers using trays are preferred when large temperature changes are expected because of thermal expansion or when contraction may crush packing. Design information for towers using trays is generally more readily available and more reliable.
© 2006 by Béla Lipták
•
Packed towers are cheaper and easier to construct than plate towers if highly corrosive fluid must be handled. Diameters of packed towers are generally designed to be less than 4 ft, while plate tower diameters are designed to be more than 2ft. Packed towers are preferred if the liquids have a large tendency to foam. The amount of liquid hold-up is considerably less in packed towers. The pressure drop through packed towers may be less than for plate towers performing the same service, making packed towers desirable for vacuum distillation.
Thus, generally, trays work better in applications requiring high flow, such as those encountered in high-pressure distillation columns, such as depropanizers, debutanizers, xylene purification columns, and the like. Packing works best at lower flow parameters, as the low-pressure drop of structured packing makes it very attractive for use in vacuum columns or ethylbenzene recycle columns of styrene plants. The contacting between the vapor and liquid in a singlestage contacting device will not produce total equilibrium. The relationship between ideal and actual performance is the efficiency that translates the number of ideal separation stages into actual finite stages that must be used to accomplish the desired final separation. Efficiency varies, not only with the type of mixing method used (e.g., packing or trays), but also with fluid rates, fluid properties, column diameter, and operating pressure. The influence of plate efficiency in the operation of the distillation tower becomes important in the control of the overhead composition. Because plate efficiencies increase with increased vapor velocities, the influence of the refluxto-feed ratio on overhead composition becomes a nonlinear relationship. Dynamics Dynamic considerations due to liquid hold-up on the trays comes into play when discussing distillation control. Because the liquid on each tray must overflow its weir and work its way down the column due to tray or packing hydraulics, this change will not be seen at the bottoms of the tower until some time has passed. The exact dynamics depend on column size, type of tray, number of trays, and tray spacing. The hold-up at each tray as shown in Figure 8.19c can be modeled by the LaPlace transform of the form KG ( s ) = where KG(s) K T1 S
= = = =
K (T1 s + 1)
transfer function system gain time constant LaPlace transfer operator
8.19(1)
8.19 Distillation: Basic Controls
X(t) Y1
Y
4
Y2
Y 1(t)
Y1
Y40
0
X(t)
Y 2(t) Y4(t) Y10(t) Y40(t) Y1 Y2 Y4 Y10 Y40
= = = = =
1 Lag 2 Lags 4 Lags 10 Lags 40 Lags
Sum of the time constants are equal. Time
These lags are cumulative as the liquid passes each tray on its way down the column. Thus, a 30-tray column could be approximated by 30 first-order exponential lags in series of approximately the same time constant. K (T1s + 1)n
In that case, the condensers are called partial condensers. In this instance, a vapor product is normally withdrawn as well as a liquid product. A total condenser is usually designed for accumulator pressures up to 215 psia (1.48 MPa) at an operating temper4 ature of 120°F (49°C). A partial condenser is used from 215 psia to 365 psia (1.48 to 2.52 MPa), and a refrigerant coolant is used for the overhead condenser if the pressure is greater than 365 psia (2.52 MPa). Common condensers include fin fans and water coolers. However, in order to improve efficiency of heat recovery, heat exchange with another process stream is often performed. Propane is the most common refrigerant used. A pressure drop of 5 psia (34.4 KPa) across the condenser is often assumed if no measurements are available. The condenser and accumulator are the key pieces of equipment with respect to controlling pressure in the column. Reboilers
FIG. 8.19d Response of nth-order lags to unit step change.
KG (s) =
8.19(2)
The liquid leaving the bottom of the column is reheated in a reboiler. A reboiler is a special heat exchanger that provides the heat necessary for distillation. Part of the column bottoms liquid is vaporized and the vapors are injected back into the column as boil-up. The remaining liquid is withdrawn as a bottom product or as residue. As shown in Figure 8.19e, reboilers come in widely varying designs. They can be internal, but most are external to the column. They can use natural or forced circulation.
where n = 30 for a 30-tray column Figure 8.19d shows the response of nth order lags to a unit step change. The effect of increasing the number of lags in series is to increase the apparent dead time and increase the response curve slope. Thus, the liquid traffic within the distillation process is often approximated by using a secondorder lag plus dead time as modeled by the LaPlace transform: KG (s) =
Ke − t s (T1s + 1)(T2s + 1)
e = e of log to the base e φ = dead time T1, T2 = time constants Condensers The overhead vapor leaving the column is sent to a condenser and is collected as a liquid in a receiver, or accumulator. A part of the accumulated liquid is returned to the column as reflux. The remainder is withdrawn as overhead product or distillate. In many cases, complete condensation is not accomplished.
V
Q
Q
L B
B
Internal
8.19(3)
where
© 2006 by Béla Lipták
1823
External kettle
V
V Q
Q
B Vertical thermosyphon
B Horizontal thermosyphon
FIG. 8.19e Reboiler design variations. External kettle reboilers often use forced circulation (pump), while the thermosyphon designs depend on natural circulation. The horizontal thermosyphon reboiler takes its liquid from the bottom tray, while the others take it from the column bottoms.
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Control and Optimization of Unit Operations
The kettle reboiler is the most common external forced circulation design. Vertical and horizontal thermosiphon reboilers operate by natural circulation. In these, flow is induced by the hydrostatic pressure imbalance between the liquid inside the tower and the two-phase mixture in the reboiler tubes. In forced circulation reboilers, a pump is used to ensure circulation of the liquid past the heat transfer surface. Reboilers may be designed so that boiling occurs inside vertical tubes, inside horizontal tubes, or on the shell side. A newer development in reboiler design is the concept self-cleaning shell-and-tube heat exchangers for applications where heat exchange surfaces are prone to fouling by the process fluid. Common heat sources include hot oil, steam, or fuel gas (fired reboilers). Cases where simple heat exchange with another process stream is used for efficiency of heat recovery are common. Thus, the choice of instrumentation to control heat addition to the tower depends upon the type of reboiler used. Interheaters/Intercoolers In some cases, additional vapor or liquid is withdrawn from the column at points above or below the point at which the feed enters. All or a portion of this sidestream can be used as intermediate product. Sometimes, economical column design dictates that the sidestream be cooled and returned to the column to furnish localized reflux. The equipment that does this is called a sidestream cooler, or intercooler. Multiproduct fractionators often have these intercoolers in a pumparound stream. At other times, localized heat is required. Then, some of the liquid in the column is removed and passed through a sidestream reboiler, or interheater, before being returned to the column. Interheaters are usually utilized in cryogenic demethanizers. Often the feed is preheated before entering the column. Common preheat mediums include the bottoms product or low-pressure steam. Preheating is often a convenient method to recover heat that would otherwise be wasted. Column Variables Controlling a fractionator requires the identifying of the controlled, manipulated, and load variables (Figure 8.19f). Controlled variables are those variables that must be maintained at a precise value to satisfy column objectives. These normally include product compositions, column temperatures, column pressure, and tower and accumulator levels. Manipulated variables are those variables that can be changed in order to maintain the controlled variables at their desired values. Common examples include reflux flow, coolant flow, heating medium flow, and product flows. Load variables are those variables that provide disturbances to the column. Common examples include feed flow rate and feed
© 2006 by Béla Lipták
L
Overhead product (D)
Feed Steam
(V)
Bottom product (B) Apparent variables: C1 C2 C3 C4 u1 u2 u3 u4 u5 u6 u7 u8 u9 m
= = = = = = = = = = = = = =
Independent variables
overhead temperature overhead pressure overhead composition overhead flow rate bottom temperature bottom pressure bottom composition bottom flow rate feed temperature feed pressure feed composition feed per cent vapor feed flow rate steam flow rate (heat input)
2 1 2 1 2 1 1 1 11
FIG. 8.19f In a binary distillation process the number of independent variables is eleven (11) and the number of defining equations is two (2). Therefore, the number of degrees of freedom is nine (9), which is the maximum number of automatic controllers that can be used on such a process.
composition. Other common disturbances are steam header pressure, feed enthalpy, environmental conditions (e.g., rain, barometric pressure, and ambient temperature), and coolant temperature. To handle these disturbances, column controls can be so designed as to make the column insensitive to these disturbances, or secondary controls can be designed to eliminate the disturbances. It is also important to evaluate the expected magnitude and duration of the likely disturbances, so that proper control system scaling and tuning can be achieved. Feedforward controls are designed to compensate for these disturbance variables and are discussed later in this section. There are other advanced control or optimization methods that can be designed to compensate for these disturbance variables. They are discussed in Section 8.21. Pairing of Variables The variables that should be controlled are usually obvious. They are normally identified when process objectives are defined and understood. Load variables are also easily identified. But identification of the manipulated variables can be more difficult. The general guidelines for identifying which manipulated variables to associate with which controlled variables are
8.19 Distillation: Basic Controls
• • • • •
Manipulate the stream that has the greatest influence on the associated controlled variable. Manipulate the smaller stream if two streams have the same effect on the controlled variable. Manipulate the stream that has the most nearly linear correlation with the controlled variable. Manipulate the stream that is least sensitive to ambient conditions. Manipulate the stream least likely to cause interaction problems.
Unfortunately, the decision on pairing controlled and manipulated variables is complicated by the fact that the above rules may sometimes result in conflicting recommendations. Section 8.20 provides information on relative gain calculations, which can help to optimize the pairing of controlled and manipulated variables. Once the pairings are completed, the equations are then solved for the manipulated variables in terms of the controlled and load variables. In that form, the equations are the mathematical representations of the control systems.
MODELING AND CONTROL EQUATIONS The primary application of instruments in distillation is to control the product purity, and secondarily, to minimize upsets to the unit caused by a change in process inputs. The instruments calculate the effects of the input changes and determine the corrective action needed to counteract them. The control actions are implemented by direct manipulation of the final control elements or by alteration of the set points of lower level controllers. A careful analysis of limits and operating constraints is essential to the successful control of distillation columns. If the system is not designed to provide limit checks and overrides to handle operating limits, frequent operator intervention will be required during upsets. This is likely to result in a lack of confidence in the control system and will cause the operators to remove the column from automatic control more often than necessary, thereby not only reducing the effectiveness of the system, but also reducing safety. The first step in the design of a good control system is the derivation of a process model. Knowing the defining equations, the manipulated variables can be selected, and the operating equations for the control system can be developed. The instrumentation is then selected for the correct solution of these equations. The final control system can be relatively simple or can be a complex, interacting, multicomponent, computer-based system. In the discussion that follows, the procedures for designing distillation controls is followed by examples of the more common applications in distillation column control. A more detailed discussion of alternative strategies and advanced distillation column controls will be presented in Section 8.21.
© 2006 by Béla Lipták
1825
Steady-State Model The first step in the design of a control system must be the development of a process model. Frequently omitted in simple distillation columns, this step is essential to minimize the need for field reconfiguration of control strategies. Even with easily reconfigurable process automation systems (PASs), the development of the model is essential to fully understanding the process. The model defines the process with equations developed from the material and energy balances of the unit. A common simplifying assumption is that all components of the feed have equal heats of vaporization, which leads to the assumption of equimolal overflow. Most shortcut fractionation calculations are based upon this underlying assumption. The model is kept simple by the use of one basic rule: The degrees of freedom limit the number of controlled variables (product compositions) specified in the equations, as was illustrated in connection with Figure 8.19f. Some of the variables that can be manipulated to control a column are shown in Figure 8.19g. Material Balance For example, for a given feed rate only one degree of freedom is available for material balance control. If overhead product (distillate) is a manipulated variable (controlled directly to maintain composition), then the bottom product cannot be independent but must be manipulated to close the overall material balance according to the following equations: F=D+B Accumulation = Inflow − Outflow Accumulation = F − (D + B)
8.19(4) 8.19(5) 8.19(6)
Because accumulation is zero at steady state, B is dependent upon F and D, as expressed by Equation 8.19(4): B=F−D
8.19(7)
V Heat removed Pressure
Reflux rate (L)
Feed temperature,
Distillate rate (D) Composition (Y)
Composition (Z) and rate (F) Heat added (boilup) Bottom rate (B) Composition (X)
FIG. 8.19g Variables that fix the distillation operation.
1826
Control and Optimization of Unit Operations
or if the bottoms product is the manipulated variable: D=F−B
Di = V − Li
8.19(8)
Li = L[1 + (Cp/∆H) × (To − Tr)]
If the compositions of the feed, distillate product, and bottoms product are known, then the component material balance can be solved: 8.19(9) 8.19(10) 8.19(11)
V = VB + VF × F
F (z)
where: %LLKF = lighter than light key in the feed (mol%) %LKF = light key in the feed (mol%) %LLKD = lighter than light key in the distillate product
VB = QB/∆H
(mol%) %LKD = light key in the distillate product (mol%) %HKD = heavy key in the distillate product (mol%) %LKB = light key in the bottoms product (mol%) In the most general case, the feed might have four components, having the concentrations of LLKF , LKF , HKF , and HHKF . Three of these components appear in each of the bottom and overhead products. The separation of the column is fixed by specifying the heavy key component in the overhead product HKD and the concentration of the light key component in the bottom product LKB. Equations 8.19(9) to 8.19(11) assume no heavier than heavy key is found in the distillate and that no lighter than light key is found in the bottoms. Rearranging Equation 8.19(11) gives %LKD = (F • %LKF − B • %LKB)/D
8.19(12)
Substituting Equation 8.19(8) into Equations 8.19(10) and 8.19(12) gives %LLKD = (F • %LLKF)/(F − Β) 8.19(13) %LKD = (F • %LKF − B • %LKB)/(F − B) 8.19(14) Substituting Equations 8.19(13) and 8.19(14) into Equation 8.19(9) to eliminate %LLKD and %LKD:
B/F =
(100 − %HK D − %LLK F − %LK F ) (100 − %HK D − %LK B )
8.19(15)
For a given feed composition and desired product compositions, only one bottoms-to-feed ratio, B/F (product split), will satisfy the overall and component material balances. By fixing the bottoms flow, the distillate flow will be fixed.
© 2006 by Béla Lipták
D(y)
L @ Tr
where: F = feed rate (the inflow) D = overhead rate (an outflow) B = bottoms rate (an outflow)
100 = %LLKD + %LKD + %HKD D × %LLKD = F × %LLKF F × %LKF = D × %LKD + B × %LKB
QT
To
B
=
D
=
L − Lf − Li − QB − QT − VB − VF − ∆H − ∆HD − ∆HL − ∆HLi −
Bi if no accumulation occurs in the column bottoms. Di if no accumulation occurs in the accumulator External reflux Liquid flow below feed tray Internal reflux Heat addition at bottom Heat removal at top Vapor boilup rate Vapor fraction in feed Heat of vaporization in reboiler Heat of condensation of distillate Heat of vaporization of reflux Heat of condensation of internal reflux
Lf = Li + (1 − VF) × F QB
Bi = Lf − VB B(x) Material balance: F = D + B separation is the energy/feed ratio of a column. For binary y(1 − x) process: S = x(1 − y) Separation should be controlled by the more pure product.
FIG. 8.19h Energy balance equations can be used to describe the steady-state heat flow model of a distillation column.
However, fixing a value of product split does not fix either the distillate or bottoms composition because many combinations of %LLKF , %LKF , %LKB, and %HKD could yield the same value of B/F. Energy Balance The energy balance and the separation obtained are closely related. Conceptually, product composition control can be thought of as a problem of the rate of heat addition QB at the bottom of the fractionator and the rate of heat removal QT at the top of the column. A series of energy balances produces additional equations. Figure 8.19h shows a steady5 state internal model of these equations. The vapor boil-up rate VB equals the heat QB added by the reboiler divided by the heat of vaporization (∆H) of the bottoms product: VB = QB /∆H
8.19(16)
The vapor rate V above the feed tray equals the vapor boil-up rate plus the vapor entering with the feed (feed rate
8.19 Distillation: Basic Controls
F times vapor fraction VF , provided the feed is neither subcooled nor superheated): V = VB + F × VF
8.19(17)
The internal reflux rate, that is, the liquid at the top tray of the column is derived by a heat balance around the top of the tower. Assuming a steady-state heat balance where the heat into the tower equals the heat out: D × ( ∆ H D + C pD × Tt ) + LI × ( ∆ H LI + C pR × Tt )
being used by the control equation. Also, C pL and ∆HL should be calculated near the existing pressure and temperature of the external reflux. The liquid rate, LF , below the feed tray equals the internal reflux plus the liquid in the feed: LF = LI + (1 − VF) × F
D = V − LI 8.19(18)
+ L × ( ∆ H L + C pL × To ) + LI × (C pL × Tt ) I
where Cp = specific heat To = overhead vapor temperature (vapor at its dew point) L = external reflux Tr = external reflux temperature LI = internal reflux Tt = top tray temperature (liquid at its bubble point) Equation 8.19(18) reduces to: D × C pD × (Tt − To ) + LI × ∆H LI − L × ∆H L + L × C pL × (Tr − To ) = 0
The bottoms rate, B, equals the liquid rate, L, minus the boil-up, VB : B = L − VB
Because the tower doesn’t always operate at steady state, it is essential to also account for the dynamics of the process. This necessitates extending the steady-state internal flow model and requires additional considerations. Figure 8.19i 6 shows the internal flow model that includes dynamics.
Di = V − Li DA= Di − D QT
or To
or
zI = L × [1 + K1 × ∆T]
V = VB + VF × F
8.19(22)
GT F
GT & GB are second order lags GB
8.19(23) VB = QB/∆H
8.19(24)
Note: This equation is valid for whatever units are used for C pL or ∆HL. Because specific heat and heat of vaporization are nearly always in mass units, care must be taken to account for density differences whenever volume units are
© 2006 by Béla Lipták
D
Li = L[1 + (Cp/∆H) × (To − TR)]
If a total condenser is employed, the composition of the internal reflux and external reflux are the same, i.e., ∆H LI = ∆H L , so the constant K2 = 1.0. Thus, LI [1 + K1 (TO − Tr )]
L @ Tr
8.19(21)
resulting in the equation
L=
8.19(27)
The criterion for separation is the ratio of reflux (L) to distillate (D) flows vs. the ratio of boil-up (V) to bottoms (B) flow rates. Manipulating reflux affects separation equally as well as manipulating boil-up, albeit in opposite directions. Consequently, only one degree of freedom exists to control separation. Thus, for a two-product tower, two equations define the process. One is an equation describing separation, and the other is an equation for material balance.
LI × ∆H LI = L × ∆H L + L × C pL × (To − Tr ) 8.19(20)
LpI /L = K2 × [1 + K1 × (Tpo − Tpr)]
8.19(26)
Dynamic Model 8.19(19)
Making a simplifying assumption that the tray temperature equals overhead vapor temperature (i.e., the dew point of the vapor equals the bubble point of the liquid; Tt = To) produces:
C pL Li ∆H L = ⋅ 1.0 + ⋅ (To − Tr ) L ∆H Li ∆H L
8.19(25)
The distillate rate, D, equals the vapor rate, V, above the feed tray minus the internal reflux:
I
+ L × (C pL × Tr ) = D × ( ∆ H D + C pD × To )
1827
QB
FIG. 8.19i Dynamic internal flow model.
DA & BA represent accumulations in the accumulator and the column bottoms respectively. Li = GB[GT Li + (1 − VF) × F) Bi = Li − VB BA = Bi − B
B
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Control and Optimization of Unit Operations
Because a change in the reflux rate must work its way down the column due to tray or packing hydraulics, this change will not be seen at the reboiler until some time has passed. The holdup at each tray has previously been modeled by the LaPlace transform of Equation 8.19(1). This Laplace transform can be converted to a simple first-order exponential lag equation of the form, which describes the response to a step change in input: −t
Llag = L (1 − e )
8.19(29)
where − t1 −t 2 GB = φ1 (1 − e ) (1 − e ) −t3 −t 4 GT = φ2 (1 − e ) (1 − e ) φ1 and φ2 are the dead times
while the orientation of separation for a given degree of separation is defined as Orientation of Separation =
%HK D %LK B
S=
y(1 − x ) x (1 − y)
8.19(33)
8.19(34)
where x = mole fraction of the key light component the distillate (%LKD) y = mole fraction of the key light component in the bottoms, (LKB) The relationship between separation (S) and the ratio of boil-up to feed (V/F) over a reasonable operating range is V/F = a + bS
8.19(35)
where a and b are functions of the relative volatility, the number of trays, the feed composition, and the minimum V/F. The control system therefore computes V based on the equation:
GB and GT are the solution to the LaPlace transform of Equation 8.19(3). Changes in boil-up rates are observed at the condenser in a matter of seconds. Normally, no dynamic terms are necessary for vapor streams, as the value of use of computing resources to that of the benefits by compensating for the dynamics is negligible. The liquid inventory in the condenser or associated accumulator will change during unsteady-state actions. In the unsteady state, the difference DI − D is the rate of accumulation of material in the accumulator. Similarly for the liquid inventory at the bottom of the tower (the kettle), the difference BI − B is the rate of accumulation: 8.19(30) 8.19(31)
where DA is the accumulation in the overhead accumulator BA is the accumulation in the tower bottoms Separation Equations The control of product compositions for a fractionator is primarily a matter of control of the internal flows. In considering
© 2006 by Béla Lipták
(%LK D × %HK B ) 8.19(32) KB ) (%HK D × %LK
The relationship between x (the light key component) and 7 the energy balance was developed by Shinskey as a function of separation S:
These lags are cumulative as the liquid passes each tray on its way down the column. However, implementation of multiple first-order lags is impractical. Fortunately, it can be shown that multiple lags in series can be approximated by a dead time and a second-order exponential lag as shown by the LaPlace transform of Equation 8.19(3). For this reason, two dynamic terms (GT and GB) are included in Figure 8.19i. Equation 8.19(25) is then rewritten as
DA = DII − D BA = BI − B
Degree of Separation = ln e
8.19(28)
where L is the liquid incoming to the tray Llag is the liquid leaving the tray t is the time constant
L = GB[GT LI + (1 − VF) × F]
product separation, the degree of separation and the orientation of separation are important. The degree of separation is
y(1 − x ) V = F a + b x (1 − y)
8.19(36)
Because y is held constant, the bottom composition controller adjusts the value of the parenthetical expression if an error should appear in x. Let V/F = y(1 − x)/(1 − y), and the control equation becomes: V = F(a + b[V/F])/x
8.19(37)
where [V/F] = the desired ratio of boil-up to feed. Figure 8.19j illustrates four of the most common basic controls for the flows and levels of a two-product fractionator, where it is assumed that feed flow and tower pressure are held constant. A different set of the above control equations for controlling internal product flow rates will apply, depending upon the configuration of instrumentation used. Scaling The form of the control system equations influences the computing functions required. Boolean operands, such as high and low selectors, and dynamic functions, such as dead times, lead, and lag function, are also used. Most process automation systems have these basic computing function blocks. Implementation in a distributed control system (DCS), programmable
8.19 Distillation: Basic Controls
PSP
PC
PSP
PC
LC
LC D
L
FC
D
L
FC
FC
FC
DSP F
1829
DSP F
LSP
LSP
QSP FC
FC
QSP
BSP
BSP
LC
LC
FC
FC
Q
Q B
B
Case 1
Case 2 PSP
PC
LC
LC D
L
FC F
D
L
FC
FC
FC
LSP
DSP
F
LSP
DSP
QSP
QSP FC
FC
LC
BSP
LC
FC
BSP FC
Q
Q B Case 3
FIG. 8.19j Four cases of conventional distillation control configurations.
© 2006 by Béla Lipták
PSP
PC
B Case 4
Control and Optimization of Unit Operations
Process values
Normalized values
Analog signals
1
2
3
4
Volts 50 mA dc 20 mA dc
10
20
30
40
4
8
12
16
1
2
3
4
3
6
9
12
mA dc 15 PSIG
0.2
0.4
0.6
0.8
1.0 bar
0
0.25
0.50
0.75
1.0
0
25%
50%
75%
100%
93
116
138
160
182°C
200
360°F
0
240 280 320 Temperature transmitter 0.85 1.7 2.93
0
225
5
100% L′ = 100%
75 L′ = 75%
50 L′ = 50%
25 L′ = 25%
3.4 m3/h
450 775 Linear flow transmitter 1.7 2.4 2.95
900 GPH
0
450 636 779 Differential pressure flow transmitter
900 GPH
0
2.50 3.75 1.25 Chromatograph output
0
1.143 L′
5
Multiplier output, normalized manipulated variable (M′)
1830
3/h
3.4 m
0%
50 100% 25 75 Multiplier input, normalized ratio (R′)
FIG. 8.19l Multiplier output for the solution of Equation 8.19 (39).
% 5.0
FIG. 8.19k Common analog signals and their relationship to process variables.
logic controller (PLC), or multivariable digital controllers is vendor-specific. The terms of the equations are sometimes scaled because most analog instruments and some PAS systems act on normalized numbers (0–100%) rather than on actual process values. With digital instrumentation and today’s process automation systems, those occurrences are rare. The calculations become easier for those systems operating in engineering units. Analog, and many digital, transmitters also operate on normalized values of the process variables. That is, the measurement signal will vary from 0 to 100% as the process variable shifts from 0 to its maximum value. Figure 8.19k illustrates the relationship among the various forms of analog signals and some typical process measurements. The actual value of a process measurement is found by multiplying the analog signal by the calibrated full-scale value (meter factor) of the process variable. In the examples of Figure 8.19k, the temperature, represented by a 75% analog signal, is 320°F (160°C), the linear flow is 775 gph 3 (2.93 m /h), the output of the differential pressure transmitter 3 (flow squared) is 779 gph (2.95 m /h), and the composition is 3.75%. Example As an example, let us review a flow ratio system in which the load stream, L, has the range of 0 to 1000 gpm 3 (0 to 3.79 m /h); the manipulated stream, M, has a range of
© 2006 by Béla Lipták
3
0 to 700 gpm (0 to 2.65 m /h); and the ratio range, R, is 0 to 0.8 (R = M/L). 700M′ = (1000L′)(0.80R′)
8.19(38)
Reducing to the lowest form, M′ = 1.143(L′)(R′)
8.19(39)
The number 1.143 is the scaling factor. M′ is plotted as a function of L′ and R′ in Figure 8.19l. In applications such as the constant separation system, exact scaling is not critical. Exact scaling is when scaling constants must be used as calculated from instrument spans. The alternative is flexible scaling, where exact ranges are not needed but some arbitrary range is used to allow internal calculations to remain within range. The flexible scaling cannot be used (1) when compensation for feed composition is part of the model, (2) when narrow spans must be used for reasons of stability, and (3) when transmitter calibrations are inconsistent with material balance ratios. Exact scaling techniques must be used for these cases.
MULTIPLE COMPONENT DISTILLATION With binary mixtures, only two products are removed in the distillation column. However, most separations involve multiple components. Even then, most distillations remove only two liquid products. In other applications a vapor product is removed, or multiple liquid products are drawn from the tower. Sometimes only one product is withdrawn at a time.
8.19 Distillation: Basic Controls
1831
Columns with Sidedraw Having a sidestream product in addition to the overhead and bottom products adds a degree of freedom to a control system. The source of this extra degree of freedom can be seen from the overall material balance equation: F=D+C+B
8.19(40)
where C is the sidestream flow rate. Two of the product streams can be manipulated for control purposes, and the material balance can still be closed by the third product stream. The presence of this added degree of freedom makes the careful analysis of the process even more essential to avoid mismatching of the manipulated and controlled variables. As in the case of the previously discussed columns, the development of a control system for sidedraw applications also involves developing the process model and determining the relationship among the several controlled and manipulated variables. In this case, for a constant feed rate and column pressure, five degrees of freedom exist: three composition specifications and two levels that can manipulate three product flows, and two heat balances (V and L). Several possible combinations of variables are available and should be explored. The possible combinations of manipulated variables for the column in which the bottom composition and the sidestream composition must be controlled are Distillate and sidestream flows Distillate and bottom flows Distillate flow and heat input Sidestream and bottom flows Sidestream flow and heat input Bottom flow and heat input Similarly, the possible combinations of manipulated variables for the column in which the distillate composition and the sidestream composition must be controlled are: Distillate and sidestream flows Distillate and bottom flows Distillate flow and heat input Sidestream and bottom flows Sidestream flow and reflux Bottom flow and reflux
LT X FY
FIC V
Dynamics FY
FT
FT
FIC
L Dynamics FY F, z1, z2
D, y1, y2
FT ARC
AT
C, c1, c2
Ratio RIC controller FT
LT
FT FIC LIC
FY
X
ARC
AT
B, x1, x2
FIG. 8.19m Control of composition in two product streams with a sidedraw.
The symbols z1, y1, and c1 refer to the concentrations in the feed, distillate, and sidestream of the component under control in the sidestream. The concentrations of the key component in the bottom are respectively expressed by z2, x2, and c2 for the feed, the bottoms, and the sidestream. The resulting control system is shown in Figure 8.19m. Note that in this configuration the ratio of heat input to feed (and, therefore, boil-up to feed) is held constant. Separate dynamic elements are used for the distillate loop and for the heat input and sidestream loops. Multiproduct Fractionators
The equations are
© 2006 by Béla Lipták
LIC
z −c D= F 1 1 y1 − c1
8.19(41)
z − x2 C = F 2 c2 − x2
8.19(42)
Multiproduct fractionators are most common in the refining industry where multicomponent streams are separated into many fractions. Examples of multiproduct fractionators are crude towers, vacuum towers, and fluidized catalytic cracking unit (FCCU) main fractionators. Product quality controls are used to adjust local column temperatures and sidedraw flow rates to control distillate properties related to the product specifications. An example is true boiling point (TBP) cut points. TBP cut points approximate the composition of a hydrocarbon mixture and are numerically similar to the American Society for Testing and
1832
Control and Optimization of Unit Operations
SP FT
FRC D
PRC PT
Accumulator FRC
FT D
L Q
Q
FRC
FRC
FT
FT
FT
Main fractionation
Heat balance logic
FRC Boiling point calculation
C
FT
FRC C
F
B
FIG. 8.19n Control of product flows and pump-around refluxes.
Materials’ (ASTM’s) 95%. The ASTM laboratory distillate evaluation method is the standard used in the petroleum refining industry for determining the value (composition) of the distillation products. A computer is required to calculate the product boiling point specification, such as 95% boiling point or TBP cut point on the basis of local temperature, pressure, steam flow, and reflux data. Local reflux is derived from internal liquid and vapor flows, as discussed previously, and the remaining variables are measured. Boiling point analyzers can be used to provide the measurement signals. If there is no analyzer, the calculated boiling points can be used by themselves, or if there is one, they can be used as a fast inner loop with analyzer trim. Because of the volume of liquid/vapor loads within most multiproduct fractionators, the manipulated variables that provide the greatest sensitivity and the quickest response are generally the product flows. Adjustment of reflux flows, as shown in Figure 8.19n, is an example of a heat balance control. The goal is to 8 maximize heat exchange to feed, subject to certain limits (limits and constraints are discussed as part of the subject of the optimization of distillation towers in Section 8.21). The task of maximizing the heating of the feed often simplifies to recovering heat at the highest possible temperature, which means recovering it as low as possible in the column.
© 2006 by Béla Lipták
Superfractionators The term superfractionator is applied to towers that are physically large. These distillation units separate streams having their light and heavy key relative volatilities quite close to each other. Included in this classification are deisobutanizers, which separate isobutane from normal butane; propylene splitters, which separate propane from propylene; ethylbenzene towers, which separate ethylbenzene from xylene; and xylene splitters, which separate para- and ortho-xylene from meta-xylene. Sometimes, the number of trays and subsequent height make it necessary to physically divide these towers into two or even three sections. Superfractionators have tremendous internal vapor-liquid rates in order to achieve the separation. Reflux-to-distillate ratios are very high, as are vapor-to-bottoms ratios. A large pressure drop through the tower also exists. Long dead times and lag times are experienced before any response is seen to feed rate or reflux changes. Generally, distillate compositions of superfractionators have to be controlled with material balance equations due to the lack of sensitivity of response. Batch Distillation In batch distillation (see Figure 8.19o), an initial charge of liquid is fed to a vessel, and the distillation process is initiated
8.19 Distillation: Basic Controls
TC
HIC V + LqL
TT
FT
Yi
FY X & Σ mD + Yi
SP FC
ARC
1833
Y
AT
D FY Distillate D(y)
Reflux, L
FRC
D2 FT Distillate (D)
Receiver Wi - Initial batch quantity yi - Initial product concentration v
FC FT Steam, Q Wi( y2)
x
Figure 8.19p shows the control system that will accomplish this when the vapor rate from the batch column is maintained constant. The equation describing this operation is:
L − LqL
FIG. 8.19o Batch distillation.
Y = mD + yi
by turning on the heating and cooling systems. During the distillation process, the initial charge in the vessel continually depletes while building up the overhead product in the distillate receiver. Batch distillations are more common in smaller, multiproduct plants where the various products can only be manufactured at different times, and where a number of different mixtures may be handled in the same equipment. Equation 8.19(43) is the basic equation that describes this operation: W = Wi − Dt
8.19(43)
where W = amount remaining in the bottoms Wi = the initial charge D = distillate rate t = time period of operation The basic objective of the control system of this type of separation is to keep the composition of the distillate constant. Other goals include keeping the distillate flow constant or maximizing the total distillate production. The main goal of a batch distillation is to produce a product of specified composition at minimum cost. This often means that operating time must be reduced to some minimum while product purity or recovery is maintained within acceptable limits. If product removal is too fast, separation and the quantity of the product are reduced. Conversely, if the product is withdrawn to maintain separation, its withdrawal rate is reduced and operating time is increased. However, the set point to a composition controller can be programmed so that the average composition of the product will still be within 9 specifications while withdrawal rate is maximized.
© 2006 by Béla Lipták
FIG. 8.19p Control system for batch distillation.
8.19(44)
where y = the fraction of key component in the product m = the rate of change of y with respect to the distillate (D) yi = the initial concentration of the product The only adjustment required is the correct setting of m. The higher its value, the faster y will change and the smaller will be the quantity of material recovered.
CONTROL OBJECTIVES AND STRATEGIES Operating objectives include the composition specifications for the top and bottom product streams. Other objectives can include increasing throughput, enhancing column stability, and operating against equipment constraints. Yet other considerations include what product composition is considered most important to maintain during disturbances, what are acceptable variations in product specifications, and what are relative economic values of the product streams and cost of 10 energy used in the separation. The column operating objectives are ultimately governed by economic benefits that are measurable, significant, and 11 achievable. Economics of individual fractionators may continually change throughout the life of the plant. Prices and costs may determine that energy savings are important at one particular time but that recovery is more important at some other time. The economic benefits of fractionator control include shifting of less profitable components into more profitable products, energy conservation, and increased throughput. Other benefits arise, including minimum disturbances propagated to downstream units, minimum rework or recycle of off-spec products, and more consistent product quality. Thus, a given column’s operating economics and, therefore, its objectives may change with time.
1834
Control and Optimization of Unit Operations
When minimization of fractionator utilities is an objective, the following guidelines are recommended: • • • •
Implement control to achieve composition control on all products of the fractionator Operate the fractionator to produce minimum overseparation Ascertain that the reduction in energy usage is reflected in the energy inflow to the production complex Minimize energy waste from blending of overseparated products
Alternative Control Strategies Many choices confront the design engineer when selecting the control variables for a column. The first decision involves configuration of the top or bottom control loops, which directly determines product compositions. Once these strategies are tentatively determined, the control strategies for the remaining variables (e.g., pressure or levels) become easier to select. Pairings of controlled and manipulated variables are normally made according to the single-input single-output (SISO) method. Multivariable control, where multiple-input and multiple-output (MIMO) variables are paired, are discussed in Section 8.21. In these multivariable strategies, although a controlled variable can be affected by several manipulated variables, only one manipulated variable is used to directly affect the controlled variable. The minimum number of controlled variables for a fractionator tower is four. These include: Controlled Variables
Manipulated Variables
Overhead composition
Reflux flow
Bottoms composition
Reboiler heating media flow
Accumulator level
Distillate flow
Bottoms level
Bottoms flow
This allows for 24 possible configurations (4 factorial). Of course, most towers include pressure as a controlled variable, with condenser flow or vapor bypass as a manipulated variable. Additional manipulated variables can include feed flow and enthalpy. If a tower includes a sidedraw stream, another control pair is added to the possible combinations. In fact, additional control variables increase the number of possible control configurations factorially (e.g., six variables produce 720 possible configurations). The pairing of controlled and manipulated variables can follow three general control structures: energy balance con12 trol, material balance control, and ratio control. Energy balance control uses reflux and reboiler heating media flow to control compositions, thus fixing the energy inputs. Material balance control uses the distillate and bottoms product flows to control compositions, thus fixing the overall
© 2006 by Béla Lipták
material balance. Ratio control utilizes a ratio of any two flow rates at each end of the column. The two common examples of ratio control are the control of reflux-to-distillate ratio and the boil-up-to-bottoms ratio. These control configurations perform quite differently depending upon the fractionator characteristics.
CONTROL LOOP INTERACTION The selection of which product composition to control (or both, if control of both can be controlled) and the decision on which variables will give better control can be aided by calculation of a relative gain array. The concept of relative 13,14 provides a measure of the interaction that can be gain expected between control loops. This subject is covered in more detail in Chapter 2 in Section 2.12 and in Section 8.20. The concept may be used to find the control configurations that will have the least amount of interaction. Therefore, relative gain analysis should be considered the first step in evaluating alternative composition control strategies. In addition, some pairings can be made heuristically from operating experience and on the basis of a general understanding of column dynamics (Table 8.19q). The following are general rules used to reject some pos15,16 sible control pairings: 1. Overhead composition and bottoms composition should not both be controlled with material balance equations if the objective is to control product specifications at both ends of the fractionator. Because of lack of dynamic response the following loops should not be paired: 1. Accumulator level should not be controlled with reboiler heat if the reboiler is a furnace. 2. Bottoms level should not be controlled with reboiler heat if the reboiler is a furnace. 3. Bottoms level should not be controlled with distillate flow. 4. Accumulator level should not be controlled with bottoms product flow. 5. Overhead composition should not be controlled with bottoms product flow. 6. Bottoms composition should not be controlled with distillate flow. 7. Bottoms level should not be controlled with reflux flow. 8. Bottoms composition should not be controlled with reflux flow if the number of trays is greater than a minimum limit (approximately 20). 9. Bottoms level should not be controlled with reboiler heat if the diameter of the column is greater than a minimum limit (approximately 15–20 ft (4.5–6 m), indicating a high volume of liquid in the bottoms).
8.19 Distillation: Basic Controls
1835
TABLE 8.19q 4 Dynamic Response and Sensitivity Limitations on the Pairing of Distillation Control Variables (Both compositions should not be controlled by material balance (B,D) if both specifications are important) Manipulated Variable
Controlled Variable
Composition of Overhead Product (ACy)
Distillate Flow (D) OK if L/D 6 Note 3
Composition of Bottoms Product (ACx) Accumulator Level (LCa)
Note 3 OK if L/D 6
Bottoms Level (LCb)
Notes: 1. 2. 3. 4.
Bottoms Product Flow (B)
OK if V/B 3
Vaporization Rate (V) or Heat Input at Reboiler (O)
Reflux Flow Rate (L)
Notes 1 and 2
Note 2
Notes 1 and 2
OK if trays 20
Not good with furnace OK if V/B 3
OK if L/D 0.5
Not good if furnace is used OK if diameter at bottom 20 ft
Control that concentration (x or y) which has the shorter residence time by throttling vapor flow (v). More pure product should control separation (energy). Less pure product should control material balance. When controlling both x and y, the only choices for possible pairings are: a. Control y by D and x by V. b. Control y by D and x by L. c. Control y by L and x by V. d. Control y by B and x by L.
Of these, choice d is not recommended because a y/B combination is not responsive dynamically.
10. Accumulator level should not be controlled with reboiler heat if the control objective is to maintain overhead product specification and the V/B ratio is less than a minimum limit (approximately 3). Because of lack of sensitivity, these loops should not be paired: 1. Overhead composition should not be controlled with reflux flow if the reflux ratio (L/D) is less than a minimum value (approximately 6). 2. Accumulator level should not be controlled with distillate flow if the reflux ratio (L/D) is less than a maximum value (approximately 6). 3. Accumulator level should not be controlled with reflux flow if the reflux ratio (L/D) is less than a maximum value (approximately 0.5). 4. Bottoms composition should not be controlled with sidedraw flow if the sidedraw is a vapor phase. 5. Overhead composition should not be controlled with sidedraw flow if the sidedraw is a liquid phase. 6. Bottoms composition should not be controlled with sidedraw flow if the sidedraw is a liquid phase and the sidedraw tray number is greater than a minimum number (approximately 20). 7. Sidedraw composition should not be controlled with reflux or distillate flow if the difference between the total number of trays and the number of the sidestream tray is greater than a minimum value (approximately 20). 8. Bottoms level should not be controlled with sidedraw flow if the difference between the bottoms and the
© 2006 by Béla Lipták
number of the sidestream tray is greater than a minimum value (approximately 100). 9. Bottoms level should not be controlled with bottoms flow if the V/B ratio is greater than a minimum limit (approximately 3). Choices for controlling product compositions include (1) controlling top or bottom composition only (generally suitable for constant separation conditions, where specifications for one product are loose or where effective feedforward/ feedback systems can be designed to compensate for load changes) and (2) controlling of both product compositions (minimizes energy use and provides tight specification top and bottom products for columns in which the problems of interaction are small). These choices can be broken down further into considerations such as manipulation of distillate-boil-up, DV configuration (generally suitable for high reflux columns) or manipulation of reflux-boil-up, LV configuration (generally suitable for low reflux columns), and so forth. Further considerations include the use of decoupling control schemes (can present practical problems, such as insensitive control, operating problems, and high sensitivity to errors) and the use of temperature measurements to infer composition or analyzers to measure composition directly (generally an economic decision based on how well a temperature-sensitive control point can be determined and the costs of analyzer hardware and maintenance). These choices are based on operating objectives of the column, expected disturbance variables, and the degree of control loop interaction.
1836
Control and Optimization of Unit Operations
PRODUCT QUALITY CONTROL Water
Conceptually, product control is a problem of making precise adjustments to the rate of heat addition and the rate of heat removal from the tower. Heat removal determines the internal reflux flow rate, and the internal reflux as measured on the top tray is a direct reflection of the composition of the distillate. Heat added determines the internal vapor rate. These internal vapor and liquid flow rates determine the circulation rate, which in turn determines the degree of separation between two key components. Once interaction of the various variable pairings has been established, and the column’s operating objectives and disturbance variables are considered, the primary composition control loops of the column can be selected. Measurement of these control variables can be either direct or inferred.
PRC
PT TRC
Set TT
LT
FRC
LRC
Set
FT
FRC
FT
FIG. 8.19s If overhead composition is to be controlled, the reflux flow to the column is throttled by a temperature controller.
Inferring Composition from Temperature If the cost of on-line analyzer hardware and maintenance is prohibitive, or if backup is desired in case of analyzer failure or maintenance, and because the results of laboratory analysis take too long to be usable for effective control, temperature measurement often can be used to infer composition. Because distillation separates materials according to their difference in vapor pressures, and because vapor pressure is a temperature-controlled function, temperature measurement has historically been used to indicate composition. This presumes that the column pressure remains constant, or that the temperature measurement is compensated for pressure changes, and that feed composition is constant. Then, any change in composition within a column will be detected as a temperature change. The best point to locate the temperature sensor cannot be established from generalizations. The important consideration is to measure the temperature on a tray that strongly reflects the changes in composition. When composition of the bottom product is important, it is desirable to maintain a constant temperature in the lower section. This can be done by letting the temperature measurement manipulate the reboiler steam supply by resetting the steam flow controller set point (Figure 8.19r).
When composition of the distillate is more important, it is desirable to maintain a constant temperature in the upper section, as in Figure 8.19s. In this configuration the sensing point for column pressure control should be located near the temperature control point. Keeping the sensor locations close to each other helps to fix the relation between temperature and composition at this particular point. If column temperature profiles caused by small positive and negative changes in manipulated variables, such as a ±1% change in distillate flow (Figure 8.19t), can be generated, the
Stage
Sensor location for maximum sensitivity
18 16 14 1% decrease in D
1% increase in D 12 10
TRC
TT
8
Set FRC
6 FT 4
Steam LT
LIC
2 −0.3
FIG. 8.19r In this configuration the reboiler heat input is throttled by a temperature controller to keep the bottoms product composition constant.
© 2006 by Béla Lipták
−0.2 −0.1 0 0.1 0.2 0.3 Stage temperature change in °C
FIG. 8.19t Example of column temperature profiles resulting from a 1% increase and from a 1% decrease in distillate flow.
8.19 Distillation: Basic Controls
14
TT
6
TT
TDRC
FRC FT
SP 1
1837
FRC FT Steam AT
ARC
FIG. 8.19u Heat input controlled by temperature difference.
FIG. 8.119v Distillate withdrawal controlled by chromatograph.
following criteria may be helpful in selecting sensor loca17 tions: (1) The sensitivity of the temperature-manipulated variable pairing should be in the range of 0.1 to 0.5°C/% and (2) equal temperature changes should result when increasing and when decreasing the manipulated variable. For a two-product fractionator, distillation temperature is an indication of composition only when column pressure remains constant or if the temperature measurement is pressurecompensated. When separation by distillation is sought between two compounds having relatively close vapor pressures, temperature measurement, as an indication of composition, is not satisfactory. Fixing two temperatures in a column is equivalent to fixing one temperature and the pressure. Thus, by controlling two temperatures, or a temperature difference, the effect of pressure variations can be eliminated. The assumption used here is that the vapor pressure curves for the two components have constant slopes. Controlling two temperatures is not equivalent to controlling a temperature difference. A plot of temperature difference vs. bottom product composition exhibits a maximum. Thus, for some temperature differences below the maximum it is possible to get two different product compositions. Separation of normal butane and isobutane (in the absence of other components, such as pentanes and heavier substances) can be accomplished very well by using temperature difference control. Figure 8.19u illustrates how the heat input to such a column can be controlled by a temperature difference controller.
used. (For details, refer to Chapter 8 of Volume 1 of this handbook.) Once, the time required for a chromatographic analysis (several minutes) was a great barrier to its use for automatic control. Since then, the equipment has been enhanced so that analyses can now be made in less than 5 min, and in many cases for low-volatility hydrocarbons, the analysis can be made continuous. With careful handling, the under 5 min sampling rate will permit closed-loop distillate control. In fact, fractionators are successfully controlled with cycle times as long as 7–10 min by applying dead time compensation algorithms. Light ends fractionators have been satisfactorily controlled by the use of chromatography. Figure 8.19v illustrates the controls of a superfractionator designed to separate isobutane and normal butane. In this case, the chromatograph continuously analyzes a sample from one of the intermediate trays, and this measurement is used by the analyzer controller to modulate the product draw-off valve. Overhead and bottoms analyzers typically measure the loss of a valuable product or the presence of impurities. Impurity components are chosen because small concentration variations can be measured more precisely and with better repeatability, and can provide a more sensitive measure of separation. For example, the change of an impurity from 1.0 to 1.1% can be measured with greater precision than a change of the major component from 99 to 98.9%. When composition analyzers are used in feedback control, several configurations can be considered. These include 1) direct control of a manipulated variable, 2) cascade control adjusting the set point of a slave temperature controller, and 3) analysis control in parallel with temperature control in a selective control configuration. The configuration used depends on the control objective, sensitivity of control, and analysis dead time.
Control by Analyzers Analytical or composition control is a way to sidestep the problems of temperature control. Although additional investment is needed for the analytical equipment, savings from improved operation usually results. Several types of instruments are available for composition analysis. Of these, the gas chromatograph is the most versatile and most widely
© 2006 by Béla Lipták
Direct Control by Analyzers Analyzer controllers in a feedback configuration can be considered when the dead time of each analysis update is less than the response time of the
1838
Control and Optimization of Unit Operations
SP FT
SP
FRC
FT
Σ ARC
ARC
PRC
AT
PRC X
TT
SP FRC FT
Accumulator
Fractionation
FIG. 8.19w Direct control of overhead product composition by an analyzer controller (ARC) throttling the set point of a reflux flow controller (FRC).
process. Because it is the control of the composition of the product, which is often the objective, direct control by an analyzer controller would seem to be better than indirect control by temperature. The composition controller provides feedback correction in response to feed composition changes, pressure variations, and variations in tower efficiencies. Figure 8.19w shows the configuration of a control system, in which a chromatograph analyzes a liquid sample from the condenser rundown line. A sample probe gathers the liquid sample and the sampling system conditions and vaporizes the liquid sample to provide a representative vapor sample to the chromatograph. The analyzer controller (ARC) uses the chromatographic measurement to manipulate the reflux flow by adjusting the set point to the reflux flow controller (FRC). Smith Predictor Often the analyzer is so slow that it introduces a significant delay time that degrades the controllability of the process. In that case, some type of dead time compensation is used (see Section 2.19 in Chapter 2). A Smith predictor compensator can serve to model the process to predict what the analyzer measurement should be between analysis updates. When the actual measurement is completed, the model’s prediction is compared to the actual measurement and the input to the controller is biased by the difference.
SP FRC
AY FT
+
AY
+ −
AY
AY
Lag
Dead time
AT
Accumulator D
L
F
B
© 2006 by Béla Lipták
TT
D
L
F
PT
+∆
Fractionation
PT
AY
FRC
B
FIG. 8.19x Analyzer controller with dead-time compensation cascaded to reflux flow control.
Figure 8.19x shows the same configuration as did Figure 8.19w except that the analyzer controller is equipped with a first-order Smith predictor that provides dead time compensation. In Figure 8.19x, the multiplier, lag, and dead time calculations (AY) provide the predicted analysis. (The lag represents the first-order process.) This predicted response is subtracted from the actual measurement to give a differential of the actual process from its own model. This delta is added to the model without dead time to provide a modified pseudomeasurement to the analyzer controller. Thus, the analyzer measurement, which has a significant dead time due to sampling and cycle times, provides a trim to the predicted measurement of the model. Triple Cascade and Selective Control Analyzer control cascaded to temperature control can be used when stable temperature on a particular tray is desired and the tower operates at a constant, maintainable, and controllable pressure. An example is cascading the analyzer controller to the overhead temperature of a tower, which in turn is cascaded to the reflux flow rate. Because temperature is an indicator of composition at this pressure, the analyzer controller only serves as a trim correcting for variations in feed composition. Figure 8.19y shows this triple cascade configuration of an analyzer controller setting the temperature controller setting the reflux flow controller.
8.19 Distillation: Basic Controls
1839
SP FT
FRC
PRC PT
PRC PT
TT
ARC
SP FRC FT
AT
Accumulator D
L
FY
