Design and Control of Condensate-throttling Reboilers

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Guillot, J. “Computer Simulation of Emulsion Processes for Mono- mers of Different Water Solubility”. In Polymer Reaction En- gineering; Reichert, K., Ed.; Huthig and Wepf Verlag: Heidel- berg, Fed. Rep. of Germany, 1986.

Harris, B.; Hamielec, A. E.; Marten, L. Emulsion Polymerization Kinetics, Chain Entanglements and Glassy State Transition; Hamielec, A. E., Bassett, D., Eds.; ACS Symposium Series 165; American Chemical Society: Washington, DC, 1981; pp 315-326.

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1982,20,1993-2006.

Received for review March 14, 1988 Accepted August 22, 1988

PROCESS ENGINEERING AND DESIGN

Design and Control of Condensate-Throttling Reboilers

Heleni S. Papastathopoulou a n d William L. Luyben* Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015

Two reboiler designs, vapor throttling and condensate throttling, were studied to (1) quantify the conditions under which the condensate-throttling scheme is superior in terms of smaller area requirements and (2) compare the dynamic performance of the two alternatives when used on a distillation column. A design procedure which incorporates the process requirements at the maximum and minimum specifications is proposed. The following factors that affect the design were explored: heating medium, pressure level, turndown requirements, and heat-transfer coefficient. The condensate-throttling design saves heat-transfer area when the turndown ratio is quite large or when the pressure level of the heating medium approaches the critical pressure. The dynamic performance of the condensate-throttling reboiler is shown to be inferior to the vapor-throttling reboiler. Dis- tillation column control is significantly degraded if the distillation time constant is less than about 4 times the reboiler time constant. Several control system changes and process modifications are presented that improve the dynamics of the condensate-throttling design.

Introduction The main energy input to a distillation column is sup-

plied either by steam at an appropriate pressure or by some process vapor in a heat-integrated scheme. In both cases, it is necessary to tightly control the energy input to the distillation column.

The purpose of this paper is to investigate how two different reboiler configurations (vapor throttling and

condensate throttling) affect the design and control of distillation columns. Different energy input sources (steam at several pressures and several hydrocarbons) were considered so that the results are also applicable for heat-integrated systems.

A. Description of the Two Alternative Systems. 1. Vapor-Throttling Design. In the vapor-throttling scheme, the control valve is placed in the vapor supply line

0888-5885/88/2627-2293$01.50/0 0 1988 American Chemical Socidty

2294 Ind. Eng. Chem. Res., Vol. 27, No. 12, 1988

I &

Figure 1. Vapor-throttling scheme.

(Figure 1). A trap or condensate tank must be provided. A pump may also be required to get the condensate into a storage tank.

The rate of heat transfer is varied by changing the pressure of the vapor in the reboiler. At the maximum heat input, the control valve is fully open. Under these conditions, the pressure drop across the valve is at its minimum. A t any other heat input, the control valve is partially closed and the pressure drop is bigger.

Because of the pressure drop across the valve, the saturation temperature of the heating medium downstream of the valve is lower than that at the supply pressure. This means that part of the driving force potential for heat transfer is lost. To compensate for this and to satisfy the energy input requirements, more heat-transfer area in the reboiler must be provided, and this increases the capital cost of the equipment. A large control valve is required.

In the vapor-throttling design, the reboiler shell exhibits almost instantaneous dynamics. The big volumetric flow rate of the heating medium vapor inside the shell results in a very small residence time. Since the design is based on the assumption that the chest is drained under all conditions, the entire heat-transfer area is available for vapor condensation. Therefore, a change in the heat-input requirements of the process can almost instantaneously be satisfied.

The cascade control scheme (Buckley et al., 1985) was chosen because it compensates for the heating medium disturbances coming into the system. In both the primary and the secondary loops, a PI controller was implemented. The tuning procedure was that of the maximum closed- loop log-modulus specification (Luyben, 1973). The settings of the vapor flow controller are typical of most flow controllers: a wide proportional band and a fast reset time (Shinskey, 1979).

2. Condensate-Throttling Design. In the condensate-throttling design, the control valve is placed in the liquid outlet line (Figure 2). No trap is required in this case. The pressure in the reboiler is always equal to that of the supply pressure. The heat-transfer rate is varied by flooding the reboiler shell with condensate.

The vapor flow is equal to the rate of condensation. The maximum heat flow will occur when the vapor chest is completely drained. If the condensate level is lowered too far, vapor will begin blowing through the valve. This condition can occur when the valve can carry more condensate than the reboiler can condense. The flow at which this limit is reached will decrease as the heat-transfer area fouls (Shinskey, 1984). If a low-level override is used, the system will be protected against such instances.

As the condensate outflow is reduced, the level of condensate in the shell will rise, exposing less surface to the

Figure 2. Condensate-throttling scheme.

vapor. The higher the liquid level, the lower the heat- transfer rate. The condensate leaves with some subcooling.

Since full supply pressure is available in the reboiler, the condensate-throttling design requires less heat-transfer area than the vapor-throttling design. The control valve is much smaller because it handles liquid. The capital cost of the condensate-throttling design is lower than that of the vapor-throttling design.

In the condensate-throttling scheme, depending on the relative size of the process time constant and the reboiler time constant, the reboiler dynamics may or may not be important to the overall system performance. Any change in the process requirements will cause a change in the opening of the condensate valve. This will affect gradually the height of the condensate in the reboiler and thus the fraction of the heat-transfer area that is available for vapor condensation. This finally changes the heat-transfer rate. But these changes take time to occur. This is what makes the dynamics of the condensate-throttling reboiler design significant in some systems.

In this case, the cascade system will not filter out the effect of variations in the supply pressure of the heating medium. This is one of the dynamic disadvantages of the condensate-throttling system. For the sake of making consistent comparisons, the same controller type (PI) and tuning procedure are employed in this design as were used in the vapor-throttling scheme. Use of a PID controller is discussed later in the paper.

In both the vapor-throttling and the condensate-throttling designs, a vertical thermosyphon reboiler was used with the heating medium on the shell side. The results of this study are, however, not limited to thermosyphon reboilers. They apply to kettle and stab-in (internal) reboilers as well, since the only thing that is assumed is a constant overall heat-transfer coefficient.

Steady-State Design The steady-state designs of the two systems used the

same heat-input requirements and the same heating medium.

B. Design Procedure. 1. Vapor-Throttling Design. A design procedure was developed that is not based on rules of thumb but on the basis that the maximum and minimum energy input requirements of the process must be attainable. The problem is to design both the control valve and the reboiler. This problem is similar to the simultaneous design of the control valve and the pump in a typical liquid flow loop. A perceptive discussion of the latter problem was recently presented by J. R. Connell (1987).

At the maximum conditions, the control valve is wide open. At the minimum conditions, the valve is designed to be no less than 10% open, so as to prevent mechanical

Ind. Eng. Chem. Res., Vol. 27, No. 12, 1988 2295

the valve flow coefficient, the shell-side pressure, temperature, flow rate, and liquid enthalpy at the maximum and minimum conditions.

First a value for the pressure inside the reboiler at the maximum conditions was guessed (Papastathopoulou, 1987). Equations 1-3 were used to get a value for the valve flow coefficient (evl). Equations 7-9 yielded another value for the valve flow coefficient (evz). If CV1 and Cv2 were not equal, another value for P,, was guessed.

There is an upper limit and a lower limit in the values used for the reboiler pressure. P,, must be less than the supply pressure (P,) because of the pressure drop across the valve. The lower limit is imposed by heat-transfer limitations. The shell-side (heating medium) temperature must be higher than the tube-side (process fluid) temperature. For the solution, the initial guess for P,, was some value near the upper limit. Then Pmax was changed by using the bisection method.

2. Condensate-Throttling Design. The design was again based on the fact that the maximum and minimum energy input requirements of the process must be attainable. For all operating conditions, the pressure downstream from the condensate valve was considered constant and specified by the process requirements. At the maximum conditions, the control valve was wide open.

At the maximum energy input condition, the equations describing the system are

(12)

(13)

(14)

h, = h(P,,T,) (15)

where f(x,) = 1, h, is the enthalpy of the saturated liquid heating medium at the supply conditions, Pout is the pressure downstream from the control valve, and AZ' is the hydrostatic head of the condensate in the reboiler shell.

I t is assumed in eq 12 and 13 that the chest is drained at the maximum conditions, so AP is zero.

The more accurate relations from the Masoneilan Handbook (1977) were used for flow of liquids through the control valve.

The system of eq 12-15 can be solved sequentially (without requiring any iteration) to find the area, the valve size, the flow rate, and the liquid enthalpy at the maximum conditions.

At the design and the minimum energy input conditions, the reboiler will be partially flooded. For these two cases, the characteristics of the system are determined by solving the following system of equations at the proper conditions: total heat balance

Qmax = UmaxA(Tv - TB)

Qmax = F m a x ( H v - hv)

Fmax = Cvf(xmax)(f'v + AI' -

Q = Qi + Qz (16)

where Q is the total heat input to the distillation column at the design or the minimum conditions, Q1 is the heat transferred in the vapor condensation region, and Qz is the heat transferred in the liquid subcooling region.

The total heat-transfer area (A) in the reboiler has been determined from the maximum conditions, and

A = A1 + A2 (17)

where Ai is the area available for vapor condensation and Az is the area available for liquid subcooling.

The heat-transfer equation in the vapor condensation region is

(18) Q1 = UiAi(T, - TB)

flow instabilities. The heat-transfer equations are com- bined with the control valve design equations to form the steady-state model of the system.

At the maximum energy input condition, the heat- transfer equation is

The vapor-side energy balance is

Qmax = F m a x ( H v - hmax)

F m a x = f ( x m a x ) C v ( P v - P m a ) 1 ' 2

(2)

The control valve design equation is

(3)

The following thermodynamic relations are also used: where f(x,,) = 1.

hmax = h(Pm,) (4)

H, = H(P,,T,) ( 5 )

T m a x T P m a x ) (6)

At the minimum energy input condition, the equations

(7)

(8)

(9)

hmin = h(Pmin) (10)

P m i n = P ( T m i n ) (11)

are

Qmin = UminA(Tmin - TB) Qmin = F m i n ( H v - hmin)

F m i n = f (xmin)Cv(Pv - Pmin)"'

where f(xmin) = 0.1, and the symbols in eq 1-11 are as follows: A is the heat-transfer area, Cv is the valve flow coefficient, Fm, and Fmh are the flow rates of the heating medium at the maximum/minimum conditions, f(x,) and f(xmin) are the valve opening fractions at the maximum/ minimum conditions, H, is the enthalpy of the vapor heating medium at the supply conditions, h,, and hmin are the enthalpies of the saturated liquid heating medium inside the reboiler at the maximum/minimum conditions, P, is the supply pressure of the heating medium, P,, and Pmin are the pressures of the heating medium inside the reboiler a t the maximum/minimum conditions, Q,, and Q- are the maximum/minimum heat-input requirements of the process, TB is the saturation temperature of the process fluid, T,, and Tmin are the saturation tempera- tures of the heating medium inside the reboiler a t the maximum/minimum conditions, Tv is the temperature of the heating medium at the supply conditions, and U,, and Umin are the heat-transfer coefficients a t the maximum/minimum conditions.

Actually the more accurate relations for vapor flow through a valve, taken from the Masoneilan Handbook for Control Valves Sizing (1977), were used in place of eq 3 and 9. These take into account the critical flow situation.

The system of eq 1-11 is based on the assumptions of constant heat-transfer coefficient, isothermal boiling in the tube side of the reboiler, isenthalpic flashing in the control valve, and isobaric condensation in the shell side of the reboiler.

The known parameters were U,,, Umh, Q,, Qmh, and the supply pressure and temperature of the heating medium. The overall heat-transfer coefficients were selected from the literature and from actual plant data from several industrial sources. By use of an iterative procedure, the system of 10 equations (eq 1-4 and eq 6-11) was solved numerically for the 10 unknowns: the heat-transfer area,


Table I. Design Seecifications Process Data

process temp, "C 100 max heat input, GJ/h 47.0 design heat input, GJ/h 39.1 min heat input, GJ/h 19.6 vapor heat-transfer coeff, kJ/(h m2 "C) liquid heat-transfer coeff, kJ/(h m2 "C)

3066.1 613.2

Supply Conditions of the Heating Medium medium steam heptane supply temp, "C 147.9 148.0 supply pressure, atm 4.4 3.5

The heat-transfer equation in the liquid subcooling region is

Q2 = u2A2ATh (19) where

(20)

where Tout is the temperature of the heating medium at the exit of the reboiler.

The energy balance in the condensation region is (21)

The energy balance in the liquid subcooling region is (22)

where Cp is the specific heat of the liquid heating medium. At steady state, the shell-side mass balance yields

F1 = Fz (23) Equations 16-23 can be solved iteratively for the values

of the unknowns Q1, Q2, Al, A2, Tout, Fl , and F2. The solution has physical meaning only if it also satisfies the following relations:

Qi > 0 (24) Q2 > 0 (25)

Tout > T B (26) A value for the heating medium temperature leaving the

reboiler (Tout) was guessed (Papastathopoulou, 1987). Equations 16-22 were used to calculate F1 and F2. If Fl was not equal to F,, the procedure was repeated assuming another value for To,,. When the iterations converged, the percent valve openings at the design and at the minimum heat-input conditions were determined by using the control-valve sizing equation.

Note that in the condensate-throttling design Pout is fixed and the percent valve opening is the variable. To avoid flow instability problems with the valve at the minimum conditions, the valve should be at least 10% open. The pressure downstream from the condensate valve can be adjusted, if necessary, to keep f(x& greater than 10% *

C. Results. A methanol/water distillation column was used as a typical industrial example. The flow rates inside the column were such that a 10-ft column diameter was required. The reboiler heat duty was 39.1 GJ/h at design conditions. The temperature in the base of the column was 100 "C.

1. Base Case. The base-case steam and condensate- throttling design is presented in Table 11. The design specifications are summarized in Table I. The steam supply pressure is 4.4 atm (the corresponding saturation temperature is 147.9 "C). A total temperature difference

Qi = F i W , - h,)

Q2 = F z C P ( T ~ - Tout)

Table 11. Vapor- and Condensate-Throttling Design for Steam and Heptane

steam heptane VTQ CT" VT CT

A , m2 323.7 319.8 327.4 319.0 c v 2050.0 50.0 5240.0 430.0 F,,, kg/ h 22 150.0 22 180.0 165 800.0 168 400.0

F,,, kg/h 8754.0 8467.0 51 850.0 56 600.0 T,,, "C 147.3 147.9 146.8 148.0 Tdeelgn, "c 139.4 128.5 139.0 141.6 T-, "C 119.7 101.6 119.5 116.0

FdeSlgn, kg/h 18290.0 17 800.0 125 800.0 133 900.0

P,,, atm 4.33 4.4 3.41 3.5 PdWlgn, atm 3.54 4.4 2.86 3.5 Pmm, atm 1.96 4.4 1.78 3.5 f(Xm-1 1.00 1.00 1.00 1.00 f(xdeSlgn) 0.26 0.61 0.32 0.72 f ( X m n ) 0.10 0.25 0.10 0.26

* VT = vapor throttling; CT = condensate throttling.

of 48 "C is available as the driving force for heat transfer. The turndown ratio is defined as the ratio of the heat-

input requirements at the maximum conditions to the heat-input requirements at the minimum conditions. The base-case turndown ratio was 1.2/0.5 = 2.4 since Q, was 20% greater than Qdesign and Qmin was 50% of the Qdesign.

Note (Table 11) that there is only a slight decrease in the required area when changing the design from steam to condensate throttling because the heat-transfer area is primarily determined by the maximum conditions. In the steam-throttling design, at the maximum specifications, the pressure drop across the valve is only 4.4-4.33 = 0.07 atm which causes a 147.9-147.3 = 0.6 "C loss in the saturation temperature of the heating medium. This small loss does not result in big savings in the heat-transfer area: 323.73/319.8 = 1.01 (1% area savings). The control valve is much bigger in the vapor-throttling design.

In Table 11, the vapor- and condensate-throttling designs for heptane are also presented. The supply pressure was 3.5 atm (Table I) and was chosen so that the same 48 "C temperature difference was available for heat transfer. The savings in the heat-transfer area because of the condensate-throttling reboiler design was only 3% (327.4/319.0 = 1.03).

2. Effect of the Heating Medium. Six different heating media were investigated steam, heptane, cyclo- hexane, methanol, isobutane, and benzene. One of the reasons for exploring different heating media was to see if the reduction in area of condensate-throttling design over vapor-throttling design was increased as the slope of the vapor pressure curve increased. We found that this was not the case. Even for the best feasible case, the savings in the heat-transfer area was less than 8%. The larger savings occur when the reboiler is operating at higher pressures (where dT/dP is smaller) and for the heating medium that has the lowest critical conditions (in this case heptane). Isobutane was tested at supply pressures near its critical so that this trend could be checked.

The significant parameter seems to be the reduced pressure. As shown in Figure 3, the higher the reduced pressure the bigger the area savings become. For all the cases, the difference T, - TB was constant, 48 "C.

3. Effect of the Turndown Ratio. The previous conclusions are valid for a turndown ratio of 2.4. The design of the vapor- and the condensate-throttling schemes for other turndown ratios indicates that the condensate- throttling scheme becomes more favorable in terms of the savings in the heat-transfer area as the turndown ratio becomes larger. In Figure 4, this trend is presented. The heating medium is steam.


12 5 I I I ' I ' I / 0 Omax-l andesign 0 Omin-0 5 Q d e s ~ o n -

12 5 L

2 t

D steam o Hepcane b Benzer'le v netnanol 0 I s o b u t s n e E C y c l o h e x a n e

r

l o o L i 1

4

2 ' 5 t I , I , l ,

0 0 2 0 4 0 6 0 8 0 1 0 0 0 0

Turndown R a t i o

Figure 4. Effect of the turndown ratio on the heat-transfer area savings.

In the vapor-throttling scheme, when designing for larger turndown ratios, the heat-transfer area increases, whereas the valve flow coefficient decreases (Table 111). The size of the valve is determined by the minimum heat-input specifications. Notice that a smaller valve will result in higher pressure drops, which implies bigger losses in the available temperature differences for heat transfer. This is an intrinsic characteristic of the vapor-throttling design. I t implies that the savings in the area because of the condensate-throttling design become larger as the turndown ratio increases.

In the condensate-throttling scheme, the design of the reboiler for larger turndown ratios results in larger heat- transfer areas and bigger valves (Table 111). In this design, the area and C, are determined by the maximum heat- input requirements. The increased heat-transfer area makes possible the transfer of the required amount of heat a t the minimum and the design conditions, while using smaller flow rates and higher liquid heights.

There can be a rangeability problem in the condensate-throttling design. Table I11 shows that for a turndown ratio of 1.510.3 = 5 the valve opening at the minimum conditions is less than lo%, which for control purposes is undesirable. Redesign of this system for a higher pressure downstream of the condensate valve (that is, for a smaller pressure drop across the valve) cures this problem and gives a percent valve opening at the minimum conditions bigger than 10%. In most cases, the pressure downstream from the condensate valve is determined by the operating

Table 111. Effect of the Turndown Ratio (Heating Medium: Heotane) _ _ _ _ _ _ _ _ ~ ~

condensate vapor throttling throttling

turndown ratio 1.2/0.5 1.5/0.3 1.2/0.5 1.5/0.3 A , m2 327.4 464.3 319.0 398.7 C" 5240.0 2820.0 430.0 540.0 Fmam kg/h 165 800.0 193 700.0 168450.0 210 600.0

Fmim k / h 51 850.0 28370.0 56610.0 31 310.0 T,,, "C 146.8 141.2 148.0 148.0

139.0 127.5 141.6 133.1 Tdeslgnr OC

Tmint "C 119.5 108.3 116.0 102.0

Fdesign, kg/h 125800.0 111 600.0 133 900.0 126 300.0

Pmam atm 3.41 3.01 3.5 3.5 pdesign, atm 2.86 2.17 3.5 3.5 Pmin, atm 1.78 1.32 3.5 3.5 Yma, m 0.0 0.0 0.0 0.0 ydesign, 0.0 0.0 1.0 2.0

f (xmin) 0.1 0.1 0.26 0.09 Ymin, m 0.0 0.0 3.2 4.2

1 ' I ' I ' 1-1

sol 1 0 Qmax/Qmln 1 2 / 0 5 0 omax/omin 1 2/0 3 A Osax/omln i 4/0 5

0 0 2 s s o 7 5 1 0 0 125 0 0

// 0 0 2 s s o 7 5 1 0 0 125

0 0

FIXMINI ( % 1

Figure 5. Effect of the minimum valve opening on the heat-transfer area savings.

pressure of the condensate tank, and it may or may not be possible to change it to a new level of operation. A split range control valve system (one big and one small valve in parallel) can be used with the condensate-throttling scheme to overcome this problem. At normal operating conditions, the small valve remains wide open and the flow rate is adjusted by changing the opening of the large valve. When the opening of the large valve drops below lo%, the control of the flow rate is maintained through manipula- tion of the opening of the small valve. The flow rate becomes zero when both valves are entirely closed.

Figure 5 shows how the percent valve opening at the minimum conditions affects both the vapor-throttling and the condensate-throttling designs. The heating medium is steam. As the percent valve opening at the minimum conditions decreases, the savings in the heat-transfer area reduce toward zero. When a split range control valve is used, the minimum valve opening is not a limitation. In such cases, there is less incentive for choosing the condensate-throttling reboiler design.

4. An Industrial Application. Table IV gives specifications for an actual commercial reboiler that was designed for a very large turndown ratio. The reboiler of this tower was designed for a heat-transfer rate of 55 X lo6 Btu/h and a turndown ratio of 1.2710.18 = 7.1. The heating medium was steam at a supply pressure of 2.36 atm. The discharge pressure was 2.02 atm. The saturation temperature of the process fluid was 110 "C. Since the design was for a big turndown ratio, the condensate-


Table IV. Design Specifications of the Industrial Application

Process Data process temp, "C 110 max heat input, GJ/h 73.7 design heat input, GJ/h 58.0 min heat input, GJ/h 10.4 vapor heat-transfer coeff, kJ/ (h m2 "C) 3066.1 liquid heat-transfer coeff, kJ/(h m2 "C) 613.2

Supply Conditions of the Heating Medium medium steam supply temp, "C 126.1 supply pressure, atm 2.36

Table V. Vapor- and Condensate-Throttling Design for Industrial Application [Effect of f(xmin)]

VT C T VT 0.10 2070 2140 33 520 26 380 4660 121.6 119.2 111.6 2.06 1.93 1.51 1.00 0.75

0.06 1490 110 33 810 25 930 5330 126.1 126.1 126.1 2.36 2.36 2.36 1.00 0.38

0.06 1630 3600 33 720 26 470 4670 124.7 121.6 112.1 2.26 2.08 1.53 1.00 0.54

throttling design resulted in significant savings (28%) of the heat-transfer area (Table V).

The choice of the valve opening at the minimum conditions of the steam-throttling design has a large impact on the design. The steam-throttling scheme requires a heat-transfer area of 2070 m2 when the valve opening is 10% at the minimum conditions. The area reduces to 1630 m2 when the design is for a minimum valve opening of 6%. On the other hand, the size of the valve increases (C, increases from 2140 to 3600). Thus, it may be quite ben- eficial, in terms of the heat-transfer area, to use two vapor control valves (one large and one small) for large turndown designs with vapor throttling.

Conclusions of the Steady-State Design. The key point throughout the entire steady-state design is the consistent comparison of the two cases on a similar basis. Generally, the use of the condensate-throttling design is more effective when the heating medium is some hydrocarbon.

As far as the heat-transfer area is concerned, there are significant savings in the condensate-throttling design when the turndown ratio is big and/or the reboiler operating pressure is close to the critical pressure of the heating medium. The control valve in the condensate exit pipe is drastically smaller than the valve in the vapor line.

The vapor-throttling design requires a condensate trap and sometimes a condensate pump. There is no such need in the condensate-throttling design. However, there is need for a low-level override controller to prevent vapor blowing through the condensate valve.

Dynamics Dynamic simulations were used to explore how the de-

terioration in performance of the condensate-throttling case affects the composition control of the column and to develop methods (control schemes) that improve the dynamic response. Different distillation columns with a range of time constants and dead times were investigated. It was hoped that a relationship between the process time

reboller process

transminer Iransmmer

I

rtl wniroiier 1

6 1 ~

Figure 6. Block diagram representation of the system.

Table VI. Transfer Functions

PI controller TIS + 1

B(s) = Kc- TIS

TIS + 1 r@ + 1 B(s) = Kc- ___ PID controller

TIS CYrDs + 1 1

temp transmitter GT1 = K T l r T I S + l

1 control valve G, = K,-

(TYS + 112 where 01 = 0.1, rT1 = 0.25 min, T T ~ = 0.083 min, ry = 0.167 min

Table VII. PID Controller Settings (T,, = 16 min, T~ = 1.6 min, rB = 5.83 min)

Z-N Tn oDtimum Tn

temp loop

flow loop

KC1 0.0602 0.0965 TI1 14.3 6.75

Kc, 0.46 10.5 712 1.20 1.20 TD 0.18 0.70

constant and the reboiler time constant could be found. A. Transfer Functions. The two control schemes,

vapor- and condensate-throttling design, can be represented by the same block diagram shown in Figure 6. Note that the only difference between the two configurations is in the G2 transfer function, the reboiler dynamics transfer function.

Transfer functions for transmitters, valves, and controllers are given in Table VI.

1. Process Transfer Function. The process transfer function is assumed to be of the form

where F, is the flow rate of the vapor heating medium, G1 is the process transfer function, K p is the steady-state gain of the process, T,, is the temperature on a tray of the distillation column, 7d is the process dead time, and T~ is the process time constant.

Several combinations of the process time constant and dead time were examined so that the dynamics of different types of columns could be approximated. Two cases for the process dead time were investigated:

Ind. Eng. Chem. Res., Vol. 27, No. 12,1988 2299

7d = 0.17, (28)

7d = 0.57, (29)

For each one of them, the process time constant was taken to be rP = 2, 4, 8, 16, 32, and 64 min.

The range of the process time constant was chosen so that it represented typical industrial applications: columns with fast, medium, or slow responses.

2. Transfer Function of the Reboiler. In the vapor-throttling scheme, because of the very big flow rates, the residence time of the heating medium in the reboiler shell was calculated to be 1 s or less. Since this value is small compared to the other time constants of the system, it was assumed that the shell dynamics are almost instantaneous.

G, = 1 for vapor-throttling (30) where G2 is the reboiler transfer function.

In the condensate-throttling scheme, the proper transfer function was found by using a simplified model of the system.

The mass balance for the liquid in the shell side of the reboiler yields

(31) where F, is the condensate flow rate, t is the time, V2 is the volume of the condensate in the shell, and p is the density of the condensate.

The heat transfer rate in the vapor-condensation region is

Q = F,AH = U,A,(T, - TB) (32) where AI is the heat-transfer area in the steam condensation region, Q is the heat input to the distillation, TB is the temperature of the process fluid, T, is the saturation temperature of the heating medium at the supply conditions, VI is the heat-transfer coefficient in the steam condensation region, and AH is the latent heat of vaporization.

Ai = A ( 1 - V,/V) (33)

p dV2/dt = Fa - F,

where V is the total volume of the reboiler shell and V , is the volume of the liquid in the reboiler shell.

If we define

(34) PVAH

UiA(Tv - TB)

7R dF,/dt + Fa = F,

7 R =

where 7R is the reboiler time constant, then (35)

Laplace transforming eq 35, we get the transfer function expression in perturbation variables:

(36)

Equation 36 gives the reboiler transfer function for the condensate-throttling scheme.

The previous derivation has been based on the assumptions that there is no accumulation of mass in the vapor phase, that the dynamics of the vapor phase are very fast so that the energy balance is represented by an alge- braic equation, and that the heat-transfer occurring in the condensate subcooling region is not significant (it was calculated to be less than 10%).

Equation 34 reveals that the time constant of the reboiler is affected by the density of the condensate, the heat of vaporization of the heating medium, the size of the reboiler, the heat-transfer coefficient, and the temperature difference that is available for heat transfer. Table VI11

Table VIII. Time Constants of the Condensate-Throttling Reboiler

heating medium Q, GJ/h turndown ratio U, kJ/(h m2 " C ) U, Btu/(h ft2 O F )

4, cm no. of tubes L, m D,, m V , m3 T R , min

steam 39.1 1.210.5 3066.1 150 2117.2 100 147.9 319.8 2.54 822 4.9 1.07 2.33 5.83

steam 39.1 1.210.5 5110.2 250 2117.2 100 147.9 191.9 2.54 657 3.7 0.89 1.05 2.63

heptane 39.1 1.210.5 3066.1 150 278.8 100 148 319.0 2.54 819 4.9 1.07 2.33 0.57

gives data for several reboilers under different conditions. Time constants can range from 1 to 10 min depending strongly on the heat-transfer coefficient.

As the heat-transfer coefficient decreases, the reboiler time constant increases by almost the same factor. In practice, the heat-transfer coefficient often decreases with time because of fouling. The subsequent change of the reboiler time constant could give control problems because it may require retuning of the controllers.

Changing the heating medium from steam to heptane results in a smaller reboiler time constant. There is a reduction by almost a factor of 10 for the same heat- transfer coefficient. Heptane has a much smaller heat of vaporization than steam. Therefore, higher flow rates are required in order to satisfy the heat-input requirements. The residence time of the heating medium in the shell is smaller, and the reboiler time constant is smaller. From this point of view, the condensate-throttling scheme could be more favorable in a heat-integrated environment where the heating medium is not steam. Actually, the U for organics is lower and thus the change in the reboiler time constant is not that big.

B. Tuning of the Controller. The tuning of the cascade control scheme started from the secondary (inner) loop. Once the settings of the secondary controller were determined, the master controller could be tuned. In this study, the maximum closed-loop log modulus tuning procedure was used for both loops. The resonant peak was chosen to be +2 db (db = decibel). This corresponds to a magnitude ratio of 1.3 and is approximately equivalent to a closed-loop damping coefficient of 0.4.

1. Tuning the PI Controller. The reset time was determined from the Ziegler-Nichols (Z-N) settings. Then the proportional gain was set so that the resonant peak of the closed-loop log-modulus Bode plot was +2 db.

2. Tuning of the PID Controller. In order to see if the system dynamics could be improved, a PID controller was used in the secondary loop of the condensate-throttling scheme in some cases. The reset time (q) was set equal to the Z-N value. Initially the derivative time (7D) was also set equal to the Z-N value. The proportional gain was adjusted to give +2-db maximum closed-loop log modulus. Then TD was varied over a wide range, finding the value of K, at each rD that gave L, = +2 db. The value of 7D that resulted in the biggest proportional gain (Kc, Table VII) was considered as the optimum (Cheung and Luyben, 1979).

C. The Dynamic Performance of the Two Schemes. The base case for all the following comparisons is a distillation column with a time constant (7,) of 16 min and a dead time (rd) of 1.6 min. The reboiler time constant for the condensate-throttling design was 5.83 min. The heating medium was steam.


1i2.0 7 t I

0 20 0 40 0 60 0 80 0

T I M E ( M I N I

I

1 1 i

3 20 0 40 0 60 3 80 0

T I M E ( M I N )

'7 303 0 '

- 5 296 0 I \ 0 Y -

292 0

I

1

i t \ W

27601 ' ' ' ' ' ' ' I

3 20 0 40 0 60 0 80 0

T I M E ( M I N I

Figure 7. Comparison of vapor (VT) and condensate (CT) throttling. Disturbance in the feed flow to the column ( T ~ = 16 min, 7 d = 1.6 min, Q = 5.83 min).

In Figure 7 the behavior of both the steam-throttling and the condensate-throttling designs is presented. The disturbance is a step change in feed flow coming into the column.

In the vapor-throttling design, the transition is handled easier and the system moves quickly to the new steady state. The deviation of the column temperature from its final value is smaller in absolute magnitude and the settling time is less. Thus, when the reboiler time constant

i

0 20 0 40 0 60 0 80 0

TIME ( M I N )

Figure 8. Temperature on a tray of the column. Disturbance in the supply pressure of the steam (T,, = 16 min, 7 d = 1.6 min, 7R = 5.83 min).

is 5.83 min and the process time constant is 16 min, a fairly significant deterioration in performance occurs.

In the vapor-throttling design, the steam flow rate is always equal to the condensate flow rate (the reboiler exhibits almost instantaneous dynamics). In the condensate-throttling design, the two flow rates change in a different fashion during the transient period but both finally reach the same steady-state value (the dynamics of this reboiler are important). The condensate flow rate changes first because the flow controller acts on the condensate valve. But it takes time to adjust the level in the shell side of the reboiler and thus the steam flow rate changes later.

The behavior of the system to a disturbance in the supply pressure of the heating medium is shown in Figure 8. In the vapor-throttling scheme, the system remains almost undisturbed from a change in the supply pressure of the heating medium. The secondary loop of the cascade configuration takes corrective actions before the disturbance is even sensed by the column. Although a cascade control configuration also exists in the condensate-throttling design, the reboiler dynamics prevent tight control of flow. The transition period is much longer and the overshoot bigger.

1. Effect of the Column Characteristics. Up to now, a certain distillation column design was considered with 7, = 16 min, 7 d = 1.6 min, and reboiler time constant of 7~ = 5.83 min.

An increase in the process dead time results in a slower and more sluggish response of the system. The overshoot becomes bigger and the settling time longer. The effect of the process dead time is the same for both reboiler designs (vapor and condensate throttling).

The effect of the process time constant on the overall performance of the system is presented in Figure 9. The process dead time satisfies the relation 7 d = 0.17,. The reboiler time constant is 5.83 min.

When the process time constant is 8 min, the effect of a 5.83-min reboiler time constant is very significant. The deterioration in the performance of the condensate- throttling design is large. The settling time becomes about 6 times longer and the overshoot more than twice that of the corresponding quantities for the vapor-throttling scheme. When the time constant is 32 min, the performance of the condensate-throttling scheme differs only slightly from that of the vapor-throttling scheme. In this case (7, = 32 min, rR = 5.83), either of these schemes can be used effectively.

The main point is that, when the reboiler time constant is in the order of magnitude of the process time constant, the performance of the condensate-throttling scheme is poor. But when T, becomes 4-5 times bigger than TR the


G' 1 0 8 . 0 If \ CT -

w H \

96.0

0 . 4 0 . 0 8 0 . 0 1 2 0 . 0 1 6 0 . 0

TIME (MINI

1 1 2 . 0

1 0 8 . 0 I

96.0

0 . 20 .0 4 0 . 0 6 0 . 0 80 0

T IME (MINI

'7d= 3.2 m'n

1 1 2 . 0

s 1 0 8 . 0 ..-.

96 0 o 40 o ao c 120 o 160 o

T IME (MINI

Figure 9. Effect of the process time constant. Disturbance in the feed flow to the column ( T R = 5.83 min).

behavior of the condensate-throttling scheme is compa- rable to that of the vapor-throttling design.

2. Effect of the Reboiler Design. The effect of the reboiler characteristics on the overall performance of the system is shown in Figure 10. When 7R = 2.63 (almost 6 times smaller than 7J, both reboiler designs behave very similarly and the dynamic performance is not a restriction in choosing either one of them for such an application.

A reboiler time constant of 2.63 min is calculated for the base steady-state reboiler design case (Table VIII) when the heat-transfer coefficient is 5110 kJ/(m2 h "C) (250 Btu/(ft2 h OF)). This big heat-transfer coefficient can be achieved in practice after a reboiler cleaning and start-up. However, after some time of the reboiler operation, the heat-transfer coefficient starts decreasing because of fouling. In Figure 11, the behavior of such a system is presented. The same base case distillation column is used. Three values for the reboiler time constant are considered. The 7R = 2.63 min describes the reboiler behavior during the start-up period and is the value used for the tuning of the controller. The 7R = 4.38 min represents the behavior of the reboiler after some time of operation when the heat-transfer coefficient has been reduced to the typical

112.0

1 0 8 . 0 I

9 6 . 0

0 2 0 . 0 4 0 . 0 60 0 8 0 . 0

TIME (MINI

1 1 2 . 0 I I l ) I I I

7~ = 5.83 min

108.0 1 A

96,O

0 . 2 0 . 0 4 0 . 0 6 0 . 0 8 0 . 0

TIME (MIN)

Figure 10. Effect of the reboiler time constant. Disturbance in the feed flow to the column (T,, = 16 min, Td = 1.6 min).

1 0 8 . 0 -

R - 296 0 z 13

ZI \ (II

Y 28a o W I- U a: g 280 0

W + m z W 0 z

u 2 7 2 . 0

8 2 6 4 . 0 t l l I 1 V.eR=5.83min 256 0 I I I I I I I I I ,

0 10 0 20 0 30 0 40 0 50 0 60 0

TIME (MINI

Figure 11. Effect of variable reboiler time constant. Disturbance in the feed flow to the column (iP = 16 min, Td = 1.6 min).

value of industrial applications, 3066 kJ/(m2 h "C) (150 Btu/(ft2 h OF)). The 7R = 5.83 min corresponds to an even


optimum ' 4

Figure 12. Condensate-throttling scheme with auxiliary vapor- throttling reboiler.

/ 1

I I

Figure 13. Valve position control of the condensate-throttling reboiler.

smaller value of the heat-transfer coefficient. As the heat-transfer coefficient decreases and the re-

boiler time constant increases, the performance of the system deteriorates and the response of the process becomes oscillatory. This implies that the system progres- sively becomes tightly tuned, and it may be a good practice to retune it.

D. Alternative Control Structures. In the next few paragraphs, alternative control structures are presented that improve the dynamic performance of the condensate-throttling scheme.

1. Split Range Valve Control. A split range control valve scheme may be used with either the vapor-throttling or the condensate-throttling design, as has already been discussed. It could also be used when only part of the heat-input requirements of the distillation column is supplied from the condensate-throttling reboiler, the rest being provided from an auxiliary steam/vapor-throttling reboiler (Figure 12). The second control valve handles the heating medium flow rate at the desired level when the condensate valve is saturated.

2. Valve Position Control. Valve position control (Shinskey, 1971; Yu and Luyben, 1986) can be used to improve the dynamic performance of the condensate- throttling reboiler (Figure 13).

During the transient periods, when the process is away from the steady state, the vapor-throttling valve controls the system. As it moves toward the steady state, the condensate-throttling valve starts controlling the process. Near the steady state, the vapor-throttling valve is nearly wide open and the control is maintained through the condensate-throttling valve.

3. PID Control. Use of a PID controller in the flow loop improved significantly the dynamic performance of the condensate-throttling system. Figure 14 compares the temperature response when PI and PID control is implemented. The derivative and the integral time of the PID controller were set equal to the Z-N values. The pro-

1 96 0 1 , I , . , , ,

0 2 0 0 40 0 60 0 E0 0 100 C 12J 0

T IME (MIN I

Figure 14. Comparison between the PI and the PID control of the condensate-throttling design. Disturbance in the feed flow to the column ( T ~ = 16 min, T~ = 1.6 min, T R = 5.83 min).

8 0 E a i ci i I \

* O t I -1

0 I I I I I ,

0 0 8 I C 2 4 3 2 4 0

D E R I V A T I V E T I M E

Figure 16. Variation of the proportional gain of the flow PID controller with the derivative time.

portional gain was set to give +2-db maximum closed-loop log modulus. With PID control, the overshoot and the settling time became smaller.

In addition to using the Z-N values for the derivative time, an optimum value of TD was determined. Figure 16 presents the dependence of the proportional gain of the flow controller on the value of the derivative time. For each TD, the proportional gain was determined by the +2-db specification.

Figure 15 compares responses using Z-N and optimum TD. The improvement over the PID with Z-N settings is significant. The overshoot and the settling time have been reduced by almost a factor of 2. Although derivative action can improve the performance of the system, in the presence


The condensate throttling is dynamically inferior, par- ticularly in rejecting disturbances of the heating medium. But if the column time constant is more than 4 times greater than the reboiler time constant, both schemes behave essentially the same.

Nomenclature A = heat-transfer area, m2 A, = heat-transfer area in the condensate-throttling design,

A, = heat-transfer area in the vapor-throttling design, m2 B(s) = controller transfer function B1, B2 = transfer function of the controller in the primary/

C p = specific heat of the liquid heating medium, kJ/(kg "C) C, = valve flow coefficient D, = inside diameter of the reboiler shell, m D, = outside diameter of the reboiler tubes, cm F = flow rate of the heating medium, kg/h F, = condensate flow rate, kg/min F, = flow rate of the vapor heating medium, kg/min f ( x ) = fraction valve opening Gd = transfer function of the heating medium disturbance

coming into the system Gf, G, = transfer function of a feed flow rate/composition

disturbance coming into the column GT1, G T ~ = transfer function of the transmitter in the pri-

mary/secondary loop G, = transfer function of the control valve GI = process transfer function G2 = reboiler transfer function H = enthalpy of the vapor heating medium, kJ/kg h = enthalpy of the liquid heating medium, kJ/kg K , = proportional gain of the controller Kp = steady-state gain of the process KT1 = steady-state gain of the temperature transmitter KT2 = steady-state gain of the flow transmitter K, = steady-state gain of the valve L = total height of the reboiler, m P = pressure of the heating medium, atm Q = desired heat input to the distillation column, kJ/h t = time, min T = saturation temperature of the heating medium, O C

TB = temperature of the process fluid, "C Ttr = temperature on a tray of the distillation column, O C

U = heat-transfer coefficient, kJ/(h m2 O C ) V = total volume of the reboiler shell, m3 Y = height of the condensate in the reboiler shell, m Greek Letters a = parameter of the PID controller A H = latent heat of vaporization, kJ/h AP = hydrostatic head of the condensate in the reboiler shell,

p = density of the condensate, kg/m3 TD = derivative time, min 7 d = process dead time, min T~ = reset time, min T~ = process time constant, min TR = reboiler time constant, min T~~ = time constant of the temperature transmitter, min T~~ = time constant of the flow transmitter, min 7, = time constant of the valve, min Subscripts B = of the process fluid design = at the design conditions max = at the maximum conditions min = at the minimum conditions out = downstream from the condensate-throttling control

v = at the supply conditions of the heating medium

m2

secondary loop

atm

valve

A I

Figure 17. Condensate feedback scheme.

of noisy control signals it deteriorates rapidly. In practice, the flow transmitter signals are often noisy and as a con- sequence the use of derivative action may not be effective. E. Alternative Process Structure . During normal

operating conditions, the condensate-throttling reboiler is partially flooded. If there is need for increased heat input to the process, the condensate valve opening increases and the condensate level in the reboiler shell drops. If a large condensate valve is used, area can be exposed quickly. So more heat can be provided rapidly. If the need is for decreased heat input to the process, the condensate valve can be completely shut, but it still takes time to accumu- late condensate in the reboiler shell and reduce the heat input. Thus, the condensate-throttling system could ex- hibit nonlinear dynamic responses: fast increases in heat input but slow decreases in heat input.

The condensate feedback strategy, shown in Figure 17, might be useful in some processes to permit more rapid covering of the tubes. The condensate level rises faster because additional make-up condensate is fed into the reboiler through the auxiliary valve from a feed water Pump.

Conclusions of Dynamic Study. The dynamics of the condensate-throttling scheme can be slow and result in poorer performance than the vapor-throttling design. The difference becomes even larger when the system is dis- turbed by a change in the supply pressure of the heating medium. The dynamics of the condensate-throttling reboiler become less and less important as the ratio TJTR reaches or exceeds the value of 4 or 5. Thus, the condensate-throttling scheme can be used effectively with slow columns. Several alternative control or process structures can be used to improve the dynamic performance of the condensate-throttling scheme.

Conclusions This study was concerned with the design and the con-

trol aspects of the condensate-throttling reboiler scheme. It was found that the condensate-throttling design results in significant savings of the heat-transfer area when turndown ratios are large or when pressures are near the critical pressure of the heating medium.

The valve opening a t the minimum conditions was critical for the overall design. If smaller values of f(xmin) can be used, the savings in the heat-transfer area of the condensate-throttling design become very small. In a split range control valve scheme, the minimum valve opening is not a limitation.

2304 Ind. Eng. Chem. Res. 1988, 27, 2304-2322

1 = in the stream/vapor condensation region 2 = in the condensate subcooling region

Literature Cited Buckley, P. S.; Luyben, W. L.; Shunta, J. P. Design of Distillation

Column Control Systems; Instrument Society of America: New York, 1985.

Cheung, T. F.; Luyben, W. L. "PD Control Improves Reactor Stability-. Hydrocarbon Process. 1979, Sept., 215-218.

Connell, J. R. "Realistic Control-Valve Pressure Drops". Chem. Eng. 1987, Sept, 123-127.

Luyben, W. L. Process Modeling, Simulation and Control for Chemical Engineers; McGraw-Hill: New York, 1973.

Masoneilan Handbook for Control Valves Sizing; Masoneilan In- ternational: New York, 1977.

Papastathopoulou, H. S. "Design and Control of Condensate- Throttling Reboilers". Master's Thesis, Department of Chemical Engineering, Lehigh University, 1987.

Shinskey, F. G. "When to Use Valve Positioners". Instrum. Control Syst. 1971, Sept, 11.

Shinskey, F. G. Distillation Control for Productivity and Energy Conservation, 2nd ed.; McGraw-Hill: New York, 1984.

Shinskey, F. G. Process Control Systems: Applications, Design, Adjustment; McGraw-Hill: New York, 1979.

Yu, C. C.; Luyben, W. L. "Analysis of Valve-Position Control for Dual-Input Processes". Ind. Eng. Chem. Fundam. 1986, 25,

Received for review March 15, 1988 Revised manuscript received July 13, 1988

Accepted July 31, 1988

344-350

Studies in Chemical Process Design and Synthesis. 8. A Simple Heuristic Method for the Synthesis of Initial Sequences for Sloppy Multicomponent Separations?

Shueh-Hen Chengj and Y. A. Liu* Department of Chemical Engineering, Virginia Polytechnic Institute and Sta te University, Blacksburg, Virginia 24061

A simple heuristic method for the synthesis of initial sequences for sloppy multicomponent separations is proposed. In this type of separation, some components being separated may simultaneously appear in two or more product streams. Included in the proposed method are (i) effective and flexible tools for representing the synthesis problem, called the component assignment diagram (CAD), and for analyzing the technical feasibility of separation tasks or product splits, called the separation specification table (SST); (ii) practical design guidelines for the shortcut feasibility analysis of product splits; and (iii) simple rank-ordered heuristics for the synthesis of initial separation sequences. Of particular significance in the method is the quantitative consideration of the feasibility of product splits. The proposed method has been applied to a number of industrial separation problems. The results show that the heuristic method offers a simple and effective means for design engineers to generate several good initial sequences for sloppy multicomponent separations prior to the final heat integration and separator optimization.

1. Introduction An important process-design problem in multicompo-

nent separations is separation sequencing, which is concerned with the selection of the best method and sequence for the separation system. This problem has been covered in textbooks by King (1980, pp 710-720) and Henley and Seader (1981, pp 527-555). Reviews of recent studies on the subject can be found in Westerberg (1985) and Liu (1987).

Most of the published work on multicomponent separation sequencing has been limited to high-recovery or sharp separations, in which each component being separated appears in one and only one product stream. In industrial practice, however, it is often useful to permit some components to simultaneously appear in two or more product streams. This type of separation is called non- sharp or sloppy separation. Figure 1 compares two alternative schemes (sharp and sloppy) for the separation of a three-component mixture. We see that one more separator is needed in the sharp scheme than in the sloppy sequence.

* To whom correspondence should be addressed. 'Par t I of this series appears in AIChE J. 1985, 31, 487. Present address: Glitsch, Inc., P. 0. Box 660053, Dallas, TX

72566.

0888-5885/88/2627-2304$01.50/0

A typical chemical process usually comprises a reaction system and a separation system. The separation system generally involves reactant recovery, product separation, and waste and byproduct separations. As was pointed out by Douglas et al. (19851, the problem of flow-sheet synthesis can be posed as an optimization problem in which the reaction conversion is a key parameter for the optimum flow sheet. Further, there is an economic trade-off between high reactor costs and significant selectivity losses asso- ciated with high reaction conversions, which are balanced against large separation costs a t low reaction conversions. This implies that it may not be necessary to purify un- converted reactants to a high level prior to recycling them back to the reactor system. In other words, sloppy separations may be sufficient for many processes. The ob- jective of this work is to present a simple heuristic method for the systematic development of initial sequences for sloppy multicomponent separations.

Section 2 introduces an effective and flexible framework for representing the problem of multicomponent separation sequencing. In particular, we propose a new representation, called component assignment diagram (CAD), to facilitate the identification of alternative separation tasks or product splits. In section 3, we analyze the technical feasibility of product splits based on component recovery specifications. Key developments in this section

1988 American Chemical Society

Documents

Design and Control of Condensate-throttling Reboilers