The interaction between separation system synthesis and process synthesis

Compuren and Chemical Printed m Great

EngmxringVol 9. No 5. pp. 44-462. 1935

0098-1354/X51300 + .cQ 0

Bnrain.

THE INTERACTION SYNTHESIS

BETWEEN SEPARATION SYSTEM AND PROCESS SYNTHESIS

J. M.DouGLAs,M.F.MALoNE~~~ Chemical

Engineering

Department,

1985 Pergamon Press Ltd

University

M.F.DOHERTY

of Massachusetts,

Amherst,

MA 01003, U.S.A.

(Received 23 February 1984; revision received 15 April 1985; received for publication 29 May 1985) Abstract-The problem of selecting a separation system for a process cannot be uncoupled from the problem of determining the optimum process flow rates, since the optimum flows normally involve a tradeoff between raw materials costs and recycle (which includes separations) costs. An efficient way of obtaining a first solution of the coupled problem is to use shortcut procedures to get into the neighborhood of the optimum design conditions and to eliminate undesirable alternatives. Some of the available shortcut procedures and design heuristics are reviewed. Scope-The previous work on the synthesis of separation systems has assumed that this synthesis problem can be considered independently from the remainder of the process. However, the optimum process flows (which fix the load on the separation system) normally depend on recycle costs, which depend on the separation system selected. Hence, the interactions between the separation system synthesis problem and the remainder of the flowsheet are almost always significant. In the separation synthesis procedure described by Douglas [l], the separation system is decomposed into a vapor and a liquid recovery system, depending on the phase condition of the reactor effluent over the range of process flows of interest. There are a number of alternatives that we could use for a vapor recovery system (absorption, condensation, membranes, adsorption), but there are no widely accepted heuristics for selecting the cheapest alternative. Thus, shortcut design procedures can be used to make a preliminary decision. The available heuristics and shortcut design procedures for vapor recovery systems are reviewed. The published heuristics for selecting liquid separation systems are limited to single feed streams, sharp splits, simple columns, and constant volatility mixtures. Procedures for removing these limitations are also reviewed. Again, the emphasis is focused on the interaction between synthesizing a liquid separation system and estimating the optimum process flow rates.

1. For preliminary designs, where the synthesis problem is most important, the flow rate is never fixed; i.e. all of the process flows depend on the choices of conversion, the reactant composition of any gas-phase purge stream, the molar ratio of reactants at the reactor inlet and possibly the reactor temperature and pressure. All of those design variables represent optimization problems, where the recycle costs (including the separation system and the heat exchanger network) are involved in the optimization. Thus, the problem of specifying the process flow rates and the synthesis of the separation system are coupled, and there are no rules of thumb available to fix any of the process flows. 2. Numerous process flowsheets have multiple liquid feed streams that enter the train of distillation columns. It is never advantageous to mix these feeds together, and yet the available heuristics for column sequencing are valid only for a single feed stream. 3. The requirement of obtaining pure products seems to imply that unconverted reactants need to be purified to a high level before they are recycled back to a reactor. However, it is not apparent that this assumption is always valid. 4. Since the optimum conversion in most processes involves an economic trade-off between large reactor costs and large selectivity losses at high conversions balanced against large recycle costs at low conversions, it seems reasonable that we should attempt to minimize

INTRODUCHON The capital and operating costs associated with the separation system for many processes is a large fraction of the total processing cost. Thus, it is not surprising that the synthesis of separation systems has been the subject of an intensive research effort for the past decade. An excellent review of this literature was presented by Nishida et al. [2], and an update of this review has been presented recently by Westerberg [3].

Limitations

of previous work

Virtually all of the previous research results have been based on the problem definition [4]: Given a feed stream of known conditions (composition, flow rate, temperature and pressure), synthesize systematically a process that can isolate the desired (specified) products from the feed at minimum venture cost. Thus, the separation system synthesis problem has been abstracted from the flowsheet synthesis problem and treated independently. Despite the fact that many useful results have been obtained in these studies and that many new, interesting design procedures have been developed, it seems as if the basic problem definition has some serious limitations:

447

448

J. M. DOUGLAS etal

the number of distillation columns in a liquid recycle loop. The conventional problem definition does not consider any recycle effects. 5. For single-product plants, there is only one specification on product purity, but often there are two to four distillation columns required. Since two specifications are required for each column, all of the missing specifications correspond to optimization problems. These optimizations include trade-offs between incremental trays in the rectifying or stripping sections, as well as reflux ratios, balanced against the loss of valuable materials or incremental recycle costs. Thus, for a rigorous analysis, the connections between the separation system and the process must be considered. However, for preliminary calculations, the rule of thumb of greater than 99% recovery of all valuable materials usually leads to reasonable designs. 6. The conventional problem definition precludes a consideration of energy integration of the separation system with the remainder of the process. If a hotprocess stream can be used to drive a reboiler, then the optimum reflux ratio for the column will increase above the normal rule-of-thumb value of 1.2 times the minimum, and the number of plates required for a specified separation will decrease. 7. Some of the heuristics for selecting sequences of distillation columns include (1) lightest first, (2) most plentiful first, (3) difficult last, (4) favor equimolar splits. Since the first and third heuristics depend on volatility, whereas the second and fourth depend on feed composition, it is not surprising that these heuristics can be contradictory. Most of the research results have also been limited to systems having constant relative volatilities. Obviously, there are a large number of processes where the assumptions discussed above are not valid. Thus, a considerable research effort is still required in order to develop an efficient separation system synthesis procedure.

Design heuristics With the great success of artificial intelligence (AI) techniques in the development of expert systems, there is a growing interest in finding heuristics (rules of thumb) for design problems. Originally, heuristics were developed by experienced designers who had solved a large number of similar problems and then found a way of generalizing the results. However, design heuristics are currently being generated in universities [5,6] by generalizing the results of a large number of computer case studies. As an alternative to these approaches, it is possible to use order-of-magnitude arguments (i.e. the scaling arguments from boundary-layer theory) to simplify the normal design equations. Then, in many cases, these simplified design models can be used to derive the design heuristics algebraically. This approach is based on the observation that most design heuristics represent the solution of optimization problems for cases where the optimum solution is very insensitive to al-

most all of the design and cost parameters. The great advantage of this algebraic approach is that it is possible to identify the limitations of the heuristics. Several examples of this approach are presented.

Synthesis of separation systems with variable process jlo ws In this paper we review the design heuristics and shortcut design procedures that seem to be the most useful for solving the coupled problems of synthesizing a separation system and estimating the optimum process flow rates. The analysis is not complete, because it does not proceed as far as energy integration. Also, cases where shortcut design procedures are not available or where there is a significant interaction between the separation system and the remainder of the flowsheet that have not been previously discussed in the literature are noted.

FIRST ESTIMATE OF THE RANGE OF PROCESS FLOWS A hierarchical decision procedure for synthesizing process flowsheets for single-product plants with specified feed streams and a specified reaction path has been presented by Douglas [l]. For a continuous process, the earliest decision level focuses on the decisions required to fix the feed and product streams (i.e. Should the raw material streams be purified before processing? Is a gas recycle and purge stream desirable? Should reversible by-products be recycled or recovered?, How many product streams will there be?). The next decision level is concerned with the recycle structure of the process (i.e. How many reactors are required? How many recycle streams should there be? Is it desirable to use an excess of one reactant at the reactor inlet? Should the reactor be operated adiabatically, with direct heating or cooling, or is a diluent or heat carrier needed? Is it desirable to shift the equilibrium conversion and what is the best way to do this?). In some cases heuristics are available to answer these questions, but otherwise we generate process alternatives that must be evaluated. For each process alternative, the design variables that have the greatest economic impact on the process economics are those that affect the feed and product flow rates and the recycle flows (conversion, purge composition of reactants, molar ratio of reactants at the reactor inlet, reactor temperature and pressure). The design variables of interest (from the list above) are identified at these early decision levels, and an economic analysis that computes the economic potential of the process in terms of these design variables is undertaken. The economic potential for the recycle structure of the process is defined as economic potential

product = value

- annualized reactor cost -

-

cost of raw value of + materials by-products

annualized capital and power cost of compressors

(1)

Interaction between separation system and process synthesis

449

TOLUENE

Fig. 1. Recycle structure of flowsheet.

For example, for a process that produces benzene by the hydrodealkylation of toluene (see [l]), the reactions of interest are

toluene

+ H, - benzene

Zbenzene

zz diphenyl

+ CH4,

(2)

+ H2.

For a case where the desired production rate of benzene is 265 moles/h, where pure toluene and a hydrogen stream containing 96% H, and 4% CH,, are used as feed streams, where we do not purify the H, feed stream, where we use a gas recycle and purge stream, where we recover the diphenyl, where the product distribution is independent of the reactor temperature and pressure, where the molar ratio of HZ/aromatics at the reactor inlet is fixed at 5 to prevent coking and where an adiabatic reactor is used, the recycle flowsheet is shown in Fig. 1 and the economic potential is shown in Fig. 2 as functions of purge composition and conversion. For this case the raw material costs include the toluene and the makeup H,, and the byproduct values include the fuel values of both the purge and the diphenyl streams. Figure 2 shows that there is a trade-off between selectivity losses to diphenyl at high reactor conversions, x, balanced against large recycle costs at low conversion of toluene. Also, there is a trade-off be-

Fig. 2. Economic

potential

vs conversion

tween H, raw material costs at high purge composition of H,, yHZ, balanced against high gas recycle costs at low purge compositions. The optimum values of x and yHI shown on the graph are not the true optimum values because not all of the recycle costs have been included in the analysis. However, it is interesting to note how much the range of conversions and purge compositions that correspond to potentially profitable operation (i.e. economic potential >O) have been narrowed.

SEPARATION SYSTEM SYNTHESISGENERAL STRUCTURE The next step in Douglas’ decision procedure [1] is to select a separation system. The general structure for the separation system for vapor-liquid processes is based on two heuristics: 1. A phase split always provides the cheapest separation. 2. Whenever a component is recovered from a gas stream, it is almost always necessary in addition to use a liquid separation to obtain the component in a pure state. Thus, liquid separations are preferred over vapor recovery systems. (Membrane separation of gases is an exception to this rule, i.e. a process alternative.)

with purge composition

as a parameter

J. M. DOUGLAS et al.

450

LIOUID FEED

-

REACTOR c

STREAMS

-

-

PRODUCT

------w

BYPRODUCTS

SEPARATION

SYSTEM

SYSTEM

4 i v

Fig. 3. Separation system options: reactor exit is liquid.

Based on these heuristics, a flash calculation the reactor effluent in Fig. 1 leads us to consider three possibilities:

for the

1. If the reactor effluent stream is a liquid, we assume that we can normally accomplish the separation using only liquid recovery units (see Fig. 3). 2. If the reactor effluent consists of two phases, the liquid phase is sent to a liquid separation system, and we cool the vapor phase to cooling water temperature and then flash it again. If the liquid leaving this lowtemperature flash is primarily a reactant, we recirculate it to the reactor (so that we have a reflux condenser), whereas if the liquid is primarily a product, we send it to the liquid separation system. The flash vapor is sent to a vapor recovery system (see Fig. 4). 3. If the reactor effluent is all vapor, we cool the stream to cooling water temperature and attempt a phase split. If a phase split does not occur, we consider pressurizing the reactor effluent and using refrigeration to accomplish a phase split (ethylene plants require both). In cases where high pressure is needed, we consider pressurizing the reactor, if the high pressure can be obtained with a pump. The flash liquid is sent to the liquid recovery system, and the flash vapor is sent to the vapor recovery system (see Fig. 5).

Flash calculations It is sometimes possible to obtain an explicit approximate solution of the flash equations, i.e. if the K, values for the light key and lighter components are greater than 10 and if the K, values for the heavy key and heavier components are less than 0.1. The analysis is based on the superposition of the equilibrium relationship on the conditions for a perfect split, and then a readjustment of the material balances. The errors in the predicted flows are within a few percent. The equations and an example for the hydrodealkylation process are given in the Appendix. These results are particularly useful for preliminary optimization studies and for estimating a reasonable operating pressure for a flash drum.

VAPOR RECOVERY SYSTEM After specifying the general structure of the separation system, the design of the vapor recovery system is considered before the liquid recovery system, because normally the liquid streams leaving the vapor recovery system have a more significant effect on the design of the liquid recovery system than vice versa. The decisions that must be made about the vapor recovery system are 1. the stream location of the vapor system, 2. the type of vapor recovery system.

Effect of process flows From Fig. 2 we can find the range of the design variables and then determine the range of reactor exit flows that correspond to potentially profitable operation. We want to ensure that the general structure of the separation system does not change over this complete range of flows. Hence, we must undertake a series of flash calculations that cover this range.

-

Location of vapor recovery system There are four possibilities: 1. If the flash vapor stream in Figs. 4 or 5 contains a significant amount of a valuable component (as com-

c

FLASH

VAPOR RECOVERY

-

PURGE

SYSTEM I * 1

2, . FEED

-

LIOUID

REACTOR I

STREAMS

-

*

SYSTEM

Fig. 4. Separation

I

-

PRODUCT

-

BYPRODUCTS

SEPARATION

SYSTEM

I

I

I

I

1 system options:

recovery

reactor

exit is vapor and liquid.

Interaction

between

separation

system and process

451

synthesis

VAPOR RECOVERY

--c

PURGE

SYSTEM

FEED STREAMS

Fig. 5. Separation

system options:

with the economic potential at level 3) that would be lost in a purge stream, put the vapor recovery system on the purge stream (normally it has the smallest flow rate). 2. If the flash vapor contains components that foul the catalyst in the reactor or are otherwise deleterious to the reactor operation, put the vapor recovery system on the gas recycle stream (it normally has the second smallest flow rate). 3. If both 1 and 2 occur, put the vapor recovery system on the flash vapor stream. 4. If neither 1 nor 2 is significant, do not include a vapor recovery system. pared

It should be noted that unless 3 above is chosen and the vapor recovery system is designed to achieve a high recovery, the overall and recycle material balances will change somewhat. Therefore, an iteration might be required.

Type of vapor recovery system There are four major possibilities: 1. condensation--high pressure and/or low temperature; 2. absorption-use an existing component as a solvent, if possible; 3. adsorption-regeneration is required; 4. membrane separation. Each of these, except the membrane system, has a stream that would be fed to the liquid recovery system. In addition, absorption (and usually adsorption) requires a solvent stream to be recirculated from the liquid separation system; i.e. an additional recycle loop is introduced into the process. Fair [7] published a heuristic that adsorption is usually the cheapest alternative if the solute concentration is less than 5%. However, adsorption units are seldom used in the petroleum industry, so that there is a trade-off between design uncertainty and actual cost. Since all four types of processes are used in a variety of situations, there do not seem to be any

reactor

exit is vapor.

heuristics that provide alternatives.

a clear choice between

these

Effect of process _/lows on the design of the vapor recovery system Again, we have narrowed the range of vapor flows that would enter a vapor recovery system, but we still do not know the optimum flow. Normally, we would justify including a vapor recovery system based on the worst-case design condition in this range. Similarly, the location of the vapor recovery system would be based on this worst-case condition. However, in order to choose the type of vapor recovery system (if we decide to include one), we must compare the costs of the various alternatives. Moreover, we would like to determine whether or not one alternative is cheapest over the whole range of flow rates and feed compositions (since we still do not know the optimum flows). Thus, it would be very desirable to have a set of shortcut design procedures available that would aid us in determining the cheapest alternative (as a function of the flow and solute composition). Shortcut design procedures are available for gas absorbers and refrigeration systems. Also, the size of a membrane process can be estimated quickly, but a cost correlation does not seem to be available. On the other hand, the adsorption process design procedure described by Fair [7] is much more lengthy. The shortcut procedures and design heuristics are briefly reviewed below. Shortcut design procedures for gas absorbers The simplest way of understanding the design heuristics for a gas absorber is to consider the case of an isothermal dilute system. For this case we can solve the design equations for a plate column analytically (high-capacity, and therefore expensive, absorbers are normally plate columns), and the result is the Kremser equation:

N-t l=

ln((LImG - 1) [(v,, (YO”1- mx,Jl + ln(L /mG)

mx,,)/

1I

,

(31

J. M. DOUGLAS

452

where for low-pressure

et al.

towers

m=yPo

pr

A plot of this equation X I”

--

is shown in Fig. 6 for the case

XI,

Xl,

GUT

x

0.

Heuristic for the choice of liquid rate. From Fig. 6 we see that we would never choose L such that LI mG < 1, because with this choice we can never obtain high recoveries even with an infinite number of plates (and therefore infinite tower cost). Similarly, from Fig. 6 we see that it is not reasonable to choose L so that L / mG > 2, because we would obtain almost complete recoveries with only three or four plates (a very inexpensive absorber), but we would have to recover a large amount of the solvent and recirculate it to the absorber (large distillation column costs). Since we have found that I < L ImG < 2, we might use L = 1.4. mG

(5)

-

This is the rule of thumb cited in many places in the literature for selecting liquid rates for gas absorbers. Limitations of the L/mG = 1.4 heuristic. It is apparent from our rather trivia1 analysis that the design heuristic for the choice of the liquid rate, i.e. Ll mG = 1.4, is based on dilute isothermal systems. If we consider the design of an adiabatic absorber, the equilibrium line normally is sharply curved upward [see Fig. 7(a)], because as the solute is absorbed in the liquid phase it gives up its heat of vaporization, which increases the temperature of the liquid and also the value of the distribution coefficient m [see Eqn (4)]. If we mistakenly assume that the absorber will operate isothermally at the conditions at the top of the absorber where the solvent is fed, and if we choose a liquid rate so that L IG = 1.4 m, [see Fig. 7(b)], it could easily happen that the operating and equilibrium lines will cross and our design will be inoperable. In fact, the minimum liquid rate for an adiabatic absorber may be 10 times greater than that predicted by the design heuristic for isothermal systems. However, from Fig. 7(a) we see that an adiabatic

ADIABATIC

ISOTHERMAL

MORE

MORE

LIQUID ?a

XOUT

X

PLATES 7b

Fig. 7. Adiabatic

vs isothermal

absorbers.

absorber will require only a few trays, but large liquid rates. We have already noted that this is not a very desirable situation because we are obtaining a small absorber cost by paying the penalty of having a large distillation column cost, required to recover and recirculate the solvent. Thus, it is common practice to put cooling coils or pump-around loops on the bottom one or two trays of a gas absorber in an attempt to achieve near isothermal behavior.

Shortcut design procedure- back-of-the-envelope design of a gas absorber. As an illustration of the use of order-of-magnitude arguments to simplify design equations [8], let us consider the Kremser equation for the case of an essentially pure solvent, i.e. x,, = 0. At the preliminary design stage, we are only concerned about obtaining reasonably accurate costs for the expensive pieces of equipment. A fairly expensive absorber would be expected to have 10 or 20 theoretical trays, and therefore we shall make less than a 10% error if we let N+l=N

(6)

For an isothermal dilute system we expect that L I mG = 1.4, and therefore we can use a Taylor series to write, approximately, ln$GE$G-

1 = 1.4 -

1 = 0.4.

(7)

Since for 99%, or so, recoveries, yin/y,,, N 100, and since (L /mG - 1) (y,./yO,,) N 40, we can also write 10

& 8 Y

08

Thus, we can write the Kremser

E 2 06 5

F

N = 2.3 04

as

1og[o.4(Yin/Yout)l 0.4

2 E

equation

02 0 0

04

08

12

16

20

24

28

32

Now, if we are willing to do arithmetic so that the answers, instead of being rigorous, are easy to remember, we find that

L mG

Fig. 6. Choice of liquid flow rate from the Kremser

equation.

N-t

2 = 6logk.

(10)

453

Interaction between separation system and process synthesis (Again, we are doing an order-of-magnitude calculation.) With this expression we find that N = 10 for a 99% recovery, vs the exact solution of 10.1, and that N = 16 for a 99.9% recovery, vs the exact solution of 16.6. Thus, our back-of-the-envelope approximation gives quite good estimates. Design heuristic for fractional recoveries in gas absorbers. If we let LImG = 1.4, we can increase the fractional recovery of the solute (and thereby decrease the solute loss) by adding more trays (which increases the capital cost of the column). Thus, there is an economic trade-off, and there must be an optimum recovery. In order to get some “feeling” for the nature of this trade-off, we can write a simple model: TAC = 81 SOC,Gy,,, + C,N,

(11)

where a capital charge factor of l/l yr has been included in the capital cost coefficient C, to put the cost on an annualized basis, and C:, includes the plate efficiency. Now, if we substitute our simplified version of the Kremser equation, Eqn (lo), into Eqn (11) and solve for the optimum, we obtain YOM

-=

Y,"

G 815OC,Gy,,’

(12)

Substituting some typical values, i.e. Gy,, = 10 moles/ h, C, = $lU/mole, C,,, = $850/plate yr, we find that You1

6(850)

Ym

8150(15.5)(10)

= “Oo4’

(13)

which corresponds to a 99.6% recovery. The value of this elementary analysis is not to find the optimum fractional recovery, but to recognize that if we double any of the values that appear either in the numerator or denominator of Eqn (13), we only change the recovery from 99.2 to 99.8%. Thus, the optimum is essentially totally insensitive to any of the design or cost parameters, which is why we obtain a rule of thumb. In addition, the result indicates that there are some design problems where there is essentially no incentive to obtain accurate estimates of design parameters or to undertake rigorous solutions.

Choices of absorber pressure, temperature, and solvent. We can easily evaluate the effect of changing the operating pressure or temperature for an isothermal absorber, or the effect of choosing a solvent having a different activity coefficient, on the distribution coefficient m from Eqn (4). However, if we always choose L so that L ImG = 1.4 and choose a 99.5% recovery, we see from Eqn (3) that for the case of an almost pure solvent, x,, = 0, the number of theoretical plates does not change as we change any of these variables. However, the liquid flow rate is exactly proportional to m, according to Eqn (5), so that we will change the cost of the distillation column required to recover and recirculate the solvent. Thus, the changes in the design conditions of the absorber are reflected primarily in the cost of the solvent recovery column (actually, changes in the absorber operating pressure will change

the column diameter). Thus, a systems viewpoint, rather than a unit operations viewpoint, is needed to understand a design. Shortcut procedure for condensation processes We can condense valuable materials from a vapor stream either by increasing the pressure or by lowering the temperature below the cooling water temperature level. Both methods require a compressor and, therefore, are expensive. If the flash vapor stream is at high pressure, then a low-temperature condensation is the only option, but if the flash vapor stream is at a moderate pressure, then we may choose both the temperature and the pressure of the condenser exit. In this last case we obtain an additional degree of freedom for the design, because we trade off the cost of the compressor to obtain a high pressure against (primarily) the cost of the refrigeration compressor required to obtain a low temperature. There do not seem to be any heuristics published for the optimum fractional recovery in a condensation process. We might expect the optimum value to be less than 99%, because we are trading off solute loss against incremental compressor costs (which is different than a plate gas absorber or distillation column, where we trade off solute loss against incremental trays). Nevertheless, we might base a first design on a 99% recovery in order to compare the condensation process with a gas absorber. Once we have selected a fractional recovery and either a temperature or pressure for the flash drum after the condenser (the other quantity can be calculated), we can calculate the load and cost of the feed compressor required to achieve the high pressure, the load on the refrigeration system, and the size and the cost of the heat exchanger used as the partial condenser. Then, the results of Shelton and Grossmann [9] can be used to select a refrigerant. Also, the required flow of refrigerant, the refrigeration compressor size, and the water-cooled condenser duty can be estimated using Shelton and Grossmann’s [9] equations: process fluid condenser Q, = [AH compressor

water-cooled

C,,(T,

-

T,)]wR,

power

condenser

Qz = Q, + W,,.

(16)

The refrigeration compressor size is based on the approximation that the curves of constant entropy are almost linear on a Mollier diagram showing the log of pressure vs enthalpy. With this approximation the design equations above are simple to calculate, and cost correlations are readily available. Hence, it is also a simple matter to estimate the optimum design conditions.

J. M.

454

DOUGLAS et

Shortcut design of a membrane recovery process A shortcut design procedure for a membrane separation process has also been developed by Grossmann [lo]. However, a cost correlation has not been published. Thus, there does not seem to be a simple way of comparing the cost of a membrane separation process with other vapor recovery systems.

LIQUID

SEPARATION

SYSTEM

We specify the vapor recovery system before the liquid recovery system because normally there will be a liquid stream leaving the vapor recovery system that must be purified (and recycled to the vapor recovery system if a gas absorber is used). However, in some cases there will be light ends dissolved in a flash liquid stream that enters the liquid separation system, which may be recovered and returned to the vapor recovery system. Thus, an additional recycle loop may be introduced into the process. In many cases there will be multiple feed streams entering the liquid separation system (see Figs. 4 and 5). However, all of the published techniques for selecting a sequence of distillation columns are limited to a single feed stream of known composition (see Ref [2] for a review). With our approach, we also consider the synthesis of the liquid separation system for the complete range of process flows that correspond to potentially profitable operation (instead of considering only a single set of flows). The decisions that need to be made to select a liquid separation system include: 1. How many of the separations can be accomplished by distillation? 2. What arrangement of distillation columns should be used? 3. How should the light ends be removed? 4. Should the light ends be vented to the atmosphere, used as fuel, or recycled to the vapor recovery system? 5. How should we accomplish the other separations?

Heuristics for using distillation We order the components by their normal boiling points (or the boiling points of azeotropes), and we determine the relative volatilities. Whenever the relative volatilities of neighboring components in this list are less than 1.1, we lump these components and treat them as a new compound. Then we look for a distillation sequence to separate the components in our revised list. After we have established this sequence, we look for a way to separate the lumped components into the desired products. The alternatives available are a. b. c. d. e.

azeotropic distillation, extractive distillation, reactive distillation, extraction, crystallization.

al.

The first four alternatives require multiple distillation columns, rather than a single column. There do not seem to be simple heuristics available for selecting one of these alternatives. However, a shortcut design procedure for some of these systems is discussed later.

Light ends removal If light ends contaminate a product alternatives for their removal are to:

stream,

the

a. drop the pressure and phase split the stream, b. use a pasteurization section in the first column, c. use a stabilizer column. The choice normally depends on the amount of light ends present. We usually send the light ends to a fuel supply, but if significant amounts of valuable materials leave with the light ends stream, we recycle this stream through the vapor recovery system. The flow of light ends leaving the liquid recovery system and being returned to the vapor recovery system obviously introduces another recycle loop into the process.

Heuristics for the sequencing of distillation columns The specification of a sequence of distillation columns has been the focus of a major research effort in recent years. The most useful results for preliminary process designs have been summarized in the form of design heuristics (see Refs [5], [6] and [l l] and the paper by Nishida et al. [2] for a complete review). It should be noted that the heuristics are based on a single feed stream and the assumption that pure products are required. The limitations of these assumptions were discussed earlier in this paper. Some of the most commonly quoted heuristics are a. b. c. d.

recover the lightest component first, remove the most plentiful first, save difficult separations until last, favor equimolar splits.

It is not surprising that these heuristics can be contradictory, since the first and third depend on relative volatility, whereas the second and fourth depend on feed composition. Lu and Motard [12] have proposed an empirical form for a quantitative heuristic that includes both volatility and composition effects. Our approach is similar, except that we use order-of-magnitude arguments and sensitivity analyses to simplify the design and cost equations to a point where we can obtain approximate analytical expressions for the heuristics. Some examples of this approach are presented below.

Deriving a quantitative heuristic for the direct vs indirect column sequence Most of the literature, and the heuristics listed above, consider the problem of selecting the direct (lightest first) vs the indirect (heaviest first) column sequence for constant volatility, ternary mixtures and sharp splits in simple columns.

455

Interaction between separation system and process synthesis We begin our analysis of this problem by considering the factors that influence the column cost, i.e. the capital cost of the column, condenser and reboiler, and the operating costs for the steam and cooling water. For the case of a saturated liquid feed, where the vapor rate is constant throughout the column, it is easy to show that both the condenser and reboiler areas are directly proportional to the vapor rate. Similarly, energy balances indicate that steam and cooling water flows are directly proportional to the vapor rate. Guthrie’s correlations [13] can be written so that the column cost depends on the column height raised to the 0.8 power multiplied by the column diameter. We assume that the height is proportional to the number of theoretical trays, and we use the flooding correlation to show that the diameter depends on the square root of the vapor rate. Thus, based on Guthrie’s correlations, our cost model for a column takes the form

TAC = C,,NO-*Vos + C,Vo65 + C,V,

This result, that the total vapor load has the dominant effect on the separation sequence cost, is well known in industry. However, our elementary analysis clearly indicates that this result is suspect whenever the column cost for either the A/B or the B/C split is not the same in both configurations. Thus, if A is a corrosive component or if the A/B split requires a significantly higher pressure than the B/C split, the column cost term in Eqn (19) should be retained in the analysis. Keeping in mind this limitation, we look for simple expressions for the vapor rate.

Minimum reflux ratios-sloppy splits of ternary mixtures with constant volatility. The vapor rates are normally determined from the reflux ratios, and the operating reflux ratio is often taken as 20% (this value assumes no energy integration of the column) larger than the minimum values obtained from Underwood’s equations:

(17) aAXAF

where Co represents the annualized cost of the column, C, represents the annualized cost of both the condenser and reboiler, and C, is the sum of the annual steam and cooling water costs. For the sake of simplicity, we use a Taylor series expansion to linearize this cost model to obtain TAC = K,N + K,V.

(18)

Direct vs. indirect sequence for constant volatility systems. If we consider a ternary mixture, A, B, C, with A being the lightest component, we can use Eqn (18) to write an expression for the difference in the costs of the direct sequence, lightest first configuration D, and the indirect sequence, heaviest first configuration I: A = TAC,

a A-

XCF 1-e

aBXBF

-

e+aB-e+

=

1 -

q = 0,

(21)

(22)

R,+l=

The simplest approximate solution of Underwood’s equations, which involves a quadratic, was published by Cerda and Westerberg [14]. However, we prefer to have an explicit expression for the vapor rate that can be substituted directly into Eqn (19). A solution of this type was recently developed by Glinos and Malone

[la If we write that Xc-D

=

1 - XAD - XBD

and use this result to eliminate we can show that

(23)

xcD from Eqns (22),

- TAC,

= K,(N,D, + KI(V&

N:B + N& -

NlgC)

(19)

(24)

ViB + I’& - V;,).

-

or However, if we estimate the number of trays required for a fractional recovery of the light key overhead and the fractional recovery of the heavy key in the bottom by using the well-accepted approximation of twice the number of trays at total reflux, as predicted by Fenske’s equation, i.e.

(25) where N

N

N

_ 2 ln([r,i(l

AB-

= 2 ln{[r,l(l

BC

-

r.dl[r,l(l - r,)]) In aAB

- rdl[rJ(l

- rc)ll

CT= X

(20)

In aBC

and if the cost coefficient K,, for a column in both sequences is the same [see Eqn (19)], then substituting Eqns (20) into (19) indicates that the least expensive sequence only depends on the vapor rate.

atx#F.

(26)

I=,

Thus, R, is exactly a linear function of each distillate composition. Since R, > 0 and xiD > 0, we cannot arbitrarily choose values for the distillate compositions. A plot of xAD vs R, and the fractional recoveries of A and B overhead is shown in Fig. 8. The ordinate corresponds to a flash of the feed mixture, and we see

J. M. DOUGLAS

f 1

er al.

AB/C split:

R, =

1

1) + (x9, + xcF)/(aB - 1). (XAF+ xBF)(l + XAFXCF)

xAF/bA -

(29)

These expressions can be generalized to any number of components. The results of about 600 case studies, with a ranging from 1.2 to 10 and x,~ ranging from 0 to 1, indicated about a 4% average error, which is adequate for screening purposes. Also, fortunately, the errors were smallest when the reflux ratios were largest (expensive columns). Quantitative heuristic for constant volatility. When we use these simplified expressions to determine the vapor rates, and then substitute the results into Pqn (19), we find that the difference in the vapor rates between the direct and indirect sequences is given by

_AV =

l,2

xB

+-

-

Fig. 8. Sloppy splits. Distillate or bottoms composition fixes minimum reflux and reboil ratio and ratio of fractional recoveries. Dark circles indicate the critical condition for a sharp split.

that there is a discontinuity when we achieve a sharp ABlBC split, x cD = 0. The curve then terminates when x AD = 1.0. We obtain a similar linear result when we plot xcw vs the reboil ratio S,,,, which is also shown in Fig. 8, along with the fractional recoveries for B and C. From Fig. 8 we see that we can predict the reflux ratio for any value of xAD (or xcw) if we can predict the locations of the reflux ratios for the sharp splits AB/BC, AIBC, ABIC, and a flash. Hence, we need to find simple expressions for the reflux ratios for sharp splits. Minimum rejkx ratios-sharp splits with constant vo/ati/ity. If we consider the ABIBC sharp split, i.e. xca = 0, then Underwood’s equations give the exact result 1

R, = UAXAF

+

aBxBF + XCF -

Glinos and Malone [ 151 also developed equations for the other sharp splits:

(27)

1’

semiempirical

AIBC split:

R, =

aB(xAF + xBF) (aA - a9

XA~

XCF

I+ x,,F(a~

-

1)

xC

+

aB -

F

XAXC

1 1 + XAXc xc - fxA + XAX.$

1 a A-

l

aB(xA

+

x&f

aA -

aB

f(l

+ x,x,) -

1

f I

(30)

- XA,

where f = 1 + cl/ 100x,) and the compositions refer to the feed mixture. This algebraic expression can replace the qualitative heuristics (i.e. lightest first, most plentiful first, etc.) that were discussed earlier. Moreover, it is a simple matter to evaluate this function as the process flows change. Complex columns Tedder and Rudd [5] showed that sharp splits in either the direct or indirect sequence seldom gave the cheapest separation. Their results indicate that sidestream columns were preferred if the amount of the lightest or heaviest component was small (less than 5%) and there was a large amount of the intermediate. Similarly, sidestream rectifiers were preferred for small amounts of B and with A = C, whereas Petlyuk columns were best for large B and A + C > 20%. It should be possible to develop algebraic heuristics that are similar to Eqn (30) for these more complex configurations. In order to accomplish this task, it is necessary to develop a shortcut procedure for the design of complex columns. A start on this problem has been developed by Glinos and Malone [16]. Sidestream columns In order to illustrate a procedure for the approximate design of sidestream columns, we only consider here the case of a sidestream above the feed. For this case we assume that our primary goal is to split B and C, and we hope to take advantage of the vapor required for this B/C split to also accomplish an A/B split at only a small additional cost. If our primary goal was

(28)

Interaction

an A/B split, we would put the sidestream below the feed. Thus, we base the minimum reflux ratio on the primary separation, and from the previous work of Glinos and Malone [lS] for an AB/C split we can write

R, =

x,,/(a,

1) + (x,, + xc,)/(a,

(x,,

+ x,,)(l

-

1)

1

xAS.mln=

r-t

1’

1) = r(a,,

1)’

(33)

(34)

w,

(35)

W = Fx,,

(36) ff’)x,, X A.9 -

-

Fx,F

(37)

XAS

to obtain

XLrnl” -

1

XBF

’ + R(x,,

+ xBF) + R(aAB -

1)

1

(38)

xx

AS.rnm

+

x.4,/(1- XCF)= R(a

Aa

-

-

1)

+ xcf)(aAB -

1, a high purity

(40) 1)’

in the sidestream

is

Sidestream below the feed. Glinos and Malone [16] have developed analogous expressions for both vapor and liquid sidestreams below the feed. Even though a vapor sidestream will be less contaminated with component C, the reboiler load will be higher than if a liquid sidestream is taken. Thus, both cases need to be evaluated. Heuristics for sidestream columns. The minimum vapor rate for a sidestream column, with the sidestream above the feed is V

m = CR,+ F

1)(x,,

+ xap)r se-

V

-

(r + 1)D = (R + l)(D + S),

s = (F -

x&a, Lx,,

(39)

where R, is given by Eqn (31). For the indirect quence we find that

Equation (33) must be solved simultaneously with the material balances (R is the reflux ratio at the feed tray, whereas r is the reflux ratio at the top of the column)

F=D+Si-

For aAB > > possible.

(32)

1

XAD

r(a AB -

aBxsF + xcF + XCF, a 8-1

(31)

And if we let N = 00, we find that

V=

V _=ml” F

1ln -aAd

OxAD -

da,, - 1)x,, -

xASml” =

Pasteurization columns. If aA > > ag, which is often the case with a pasteurization column, the expressions above simplify dramatically to

+ XAFXCF)

As specifications for the column design we can choose xAD (or the fractional recovery of A overhead), x*w = 0, XcD = 0, xcw (the fractional recovery of C in the bottom) and xAs (the sidestream composition of A). However, xAs must be above some minimum value for a solution to exist. In order to estimate this minimum composition, we consider the case where the number of trays between the top of the column and the sidestream approaches infinity. An approximate solution of Smoker’s equation [ 171 gives

r(a AB -

457

between separation system and process synthesis

-E = (R, + F +

1)(x,,

1 P-t---a AB -

+ xBF) xAF

1

(1 -

1 - XCFI

xcF_),

(42)

where R, is also given by Eqn 31. Thus, the single sidestream column always has a smaller vapor rate, but the sidestream might contain significant amounts of A. The contamination of the sidestream might not be important if we do not have tight product specifications or if the sidestream is recycled back to the reactor. Effect of sidestream impurities on recycle flows. When we recycle reactants back to the reactor from a liquid separation system, we are not usually concerned with the purity of the stream. By using a sidestream column to recover the reactant, we can eliminate one column. However, since the recycle stream will now contain a contaminant, the recycle flows will change. As a simple example of this behavior, consider the disproportionation reaction

o,

1)

If we estimate R, from Eqn (31), let R = 1.2R,; then we can solve Eqn (38) for .x~~,~,~.Of course, we must choose our column specifications so that x,,~ > xAS,,,,,” in order to obtain a finite number of plates in the section of the column between the top tray and the sidestream.

2 toluene (T)

- benzene (B)

+ xylene. 00

(43)

For the sake of illustration, we suppose that we feed 20 moles/h of toluene and that we produce 10 moles/ h of both benzene and xylene. If the reactor conversion is 25%, then the recycle flow of toluene will be approximately 60 moles/h.

458

J. M. DOUGLAS

a. Direct sequence-use

two columns. For

this case the feed to the separation train will be B = 10, X = 10, T = 60 where all flows are in moles/ per hour. If R = 1.2R,, we find that V, = 63, V, = 120, so that VT, = V, + V, = 183 and the recycle flow is RR = 60. b. Liquid sidestream below the feed. If we guess xcs = 0.25, then the recycle flow of xylene is 20. Thus, the total recycle flow is R, = 60T + 20X = 80. Then, the feed to the separation system is B = 10, T = 60, X = 30; the vapor rate required for the sidestream column is V = 74.6 and ~c~,~,” = 0.23. Hence, there is a new trade-off between separation costs and recycle costs; i.e. the total vapor load in the separation system is decreased significantly (74.6 vs 183), but the recycle flow to the reactor increases (80 vs 60). c. Vapor sidestream below the feed. If we guess xcS = 0.14, the recycle flow of xylene becomes 10 moles/h, the feed to the separation system is B = 10, T = 60, X = 20, the minimum vapor load at the feed tray is 72.7, and the vapor load in the reboiler for the vapor sidestream (T = 60, X = 10) is V = 142.7. Thus, the vapor load in the separation system is significantly higher than with a liquid sidestream (142.7 vs 74.6), but the recycle flow to the reactor is lower (70 vs 80) because of the higher purity obtained. Comments on complex columns. It is apparent that a considerable amount of work remains to be done in order to develop quantitative criteria that can be used to screen complex column configurations. As we mentioned earlier, we really do not know the feed rate to the liquid separation system (the optimum conversion involves a trade-off between reactor costs and selectivity losses balanced against recycle costs). If we consider the possibility of using sidestream columns, we add an additional degree of complexity to this problem. Furthermore, the energy integration, which we have not considered as yet, is affected by these changes. Thus, the methodology required to integrate the separation sequence with the rest of the process is not a trivial problem, and design heuristics that ignore this interaction might not lead to the best process alternatives.

et al.

Benzene

Binary

Acetone

Chloroform

azeotrope

Fig. 9. Residue curve map showing

a distillation

boundary.

the distillation train depend on the reactor conversion and the other process flows, which have not been fixed yet. Thus, there may be cases where the best separation sequence changes dramatically as the design variables that fix the process flows are varied. In cases of this type, a simple procedure for the design of azeotropic and extractive distillation columns will be much more efficient than a trial-and-error simulation approach. The feasible separations can be determined from residue curve maps, like those shown in Figs 9 and 10. It is easy to sketch the residue curve map for a given mixture, knowing only the boiling temperatures of each pure component and azeotrope (see Ref [18]). The most important feature of a residue curve map is the internal boundaries (see Figs 9 and 10). These boundaries cannot be crossed by the liquid-phase tra-

Azeotropic distillations The problem of selecting a separation sequence when azeotropes are present is much more difficult because the separations that are possible depend on the feed composition. For example, if the feed mixture corresponding to xF, in Fig. 9 is placed in a simple still, the liquid composition at the end of the distillation will approach pure acetone, whereas a feed mixture at xFz will yield a final liquid product of pure chloroform. In Fig. 10 we see that the final liquid composition in the still will be pure hexane, methyl acetate or methanol, depending on the initial feed composition. Thus, for azeotropic mixtures, only certain separations are possible. It is particularly important to establish the regions of feasible separations since the feed compositions to

Methyl

Acetate

Methanol

Fig. 10. Residue curve map for the system methanollhexanei methyl acetate at 1-atm total pressure. Arrows point in the direction of increasing time (or temperature).

Interaction

between

separation

jectories (i.e. residue curves) in a simple distillation, and, for all practical purposes, they cannot be crossed by the liquid composition profile in a distillation column. This has important consequences for the sequencing of azeotropic columns, as we see later. Minimum rejlux We still expect that the cost of any separation will depend primarily on the vapor rate, and therefore we want to develop the simplest possible procedure for estimating the minimum reflux ratio. The method derived by Levy, Van Dongen and Doherty [19] seems to be the simplest available. Their method is described below for a direct split and needs only minor modification for indirect splits. We begin by specifying the purity and recovery of the lightest component (i.e. yo,, and xa,,, taking component 1 as lightest and 3 as heaviest). The optimal value for the heaviest component in the distillate is yo,i = 0 and must be taken as lo-“’ or smaller in the calculations. Three of the terminal compositions being known, the fourth is calculated from an overall mass balance; i.e. x F,Z

-

XB.2

XF,Z -

YD.2

XF.,

-

xrl.1

XF.1 -

Y0.l

(44

For terminal compositions specified in the above way, it can be shown that the column has two active pinch zones (i.e. the equations defining a pinch give rise to multiple solutions, typically three in each section, but when it comes to calculating R, only two of them count). The stripping section displays a “feed pinch” at x, and the rectifying section a “saddle pinch” at x,, which are located by solving the equations saddle pinch: rx, -

(r + l)y, + y. = 0,

(45a)

feed pinch: sy, - (S + 1)x, + xa = 0.

(45b)

system and process

Mole

n

t

+

xB.l - xF.l

1)

Ym

[ XF.1 -

80tlomg

0 999

0 001

tieptone

03

0 001

0 428

NO”OW

04

10 I lo-”

0571

X2 0

04-

OZ-

ol/ 0

1

02

04

06

08

I

X,

Nonone

Hexone

Fig. 11. Shape of composition R,

profiles = 1.54.

at minimum

reflux:

Figure 11 shows the liquid composition profiles for a ternary ideal direct split under minimum reflux conditions. Note the collinearity between xF , x, and x,. The collinearity condition is not exact for nonideal or azeotropic mixtures. For these cases, Eqn (47) is replaced by a slightly more complex relation. However, extensive calculations indicate that the now approximate collinearity condition is so close to the exact condition that we recommend using Eqn (47) for all types of mixtures. If we consider the azeotropic system shown in Fig. 12, the continuous lines show the exact profiles under minimum reflux conditions (R,= 7.35). The dashed line shows the linear approximation involved in Eqn (471, and the resulting value of r,,, is 7.7, which is in error by less than 5%. This is the worst error ever recorded using Eqn (47) for nonideal and

(46)

1

m

03

\

IO

(r

w

He”O”e

OB

Benzene =

459

Heptone l0

The reflux and reboil ratios are related by an overall mass balance:

s

synthesis

Mole

Feed

Dlsflllate

Bottomr

Acetone

0120

0990

IO

k”EW

0 660

0003

0 749

Chloroform

0 220

0007

0 25,

Straight soddle

,,neconnec+l”g lo feed pm+

x 0’

Equations (45) and (46) are a simple system of equations in one parameter, r. It can be proved that minimum reflux occurs at the value of r that makes xF, x, and x, collinear. That is (x,,, -

x,.,)(x,,* -

CG,,

‘)

xF.2.

-

XF.2

k.,

-

XF,,)

=

0.

(47)

Equation (47) is one tquation in one unknown (r), and the value of r that satisfies it is R,.This method is exact for ideal mixtures with negligible heat effects, and it can be shown to be identical to Underwood’s method. The great advantage to this approach is that it can easily be modified to accommodate nonidealities, nonnegligible heat effects and multiple feeds.

Chloroform

Fig. 12. Minimum

Xl

reflux for an azeotropic 7.35.

Acetone

mixture:

R,

=

J. M. DOUGLAS et al.

460

azeotropic systems. More typical errors are “‘$5 to 1%. Systematic extensions of the method have been made for multifeed columns [20], single and multifeed columns with nonnegligible heat effects [21], columns with four or more components [20] and columns with two liquid phases [22].

Sequencing azeotropic systems Another illustration of the care that is needed in dealing with azeotropic systems has been presented by Doherty and Calderola [23]. In Fig. 13 it seems as if we can completely separate water and ethanol into pure components by introducing an entrainer that forms an azeotrope with water and by using the appropriate mixing and recycling of streams. Thus, the feed F is mixed with the overhead D3 of the last column to form a new feed Fl. This feed is split into an overhead Dl, which is near the distillation boundary, and pure water in the bottom. The overhead Dl is then mixed with a bottom stream 83, which is on the other side of the boundary, to form a new feed F2, which is in the other distillation region. This feed F2 is split into a bottoms stream which is pure ethanol and an overhead stream D2. Then D2 is split into the streams D3 and 133, which are recycled back to the process. Even though it appears as if this process is reasonable, it is possible to show that the material balance equations can be satisfied only if some of the flow rates

Entrolner

are negative. heuristics:

This

result

leads

to

some

design

To separate two components using recycle only, the feed and the pure components must be within the same distillation region. Use an entrainer that does not produce an internal distillation boundary between two components to be separated. If an entrainer that does produce an internal boundary is used, 1. shift the boundary by operating the columns at different pressures or by adding a salt to one column, 2. use an entrainer that forms a heterogeneous region that straddles the boundary. The normal extractive distillation process for separating ethanol and water using ethylene glycol as an entrainer, which is shown in gig. 14, is a case where only a single distillation region is obtained. This work on azeotropic systems represents an initial step in the development of a general approach for synthesizing separation systems. However, there are several other types of systems, such as heterogeneous azeotropes that need to be studied in much greater detail.

CONCLUSIONS

AND SIGNIFICANCE

The design heuristics and dures described above can be puter program that aids in the systems as a function of the

Entramer (e g ethylene glycol)

shortcut design procecombined into a comsynthesis of separation range of process flow

EntraIner 53

Ethanol

Water

Orlginal binary

EWWy ozeotrope

82 Ethanol * PUR ethanol

feed

Pure water

*

Note

mnory ozeotrop~composltlo”

Fig. 13. Distillation

sequence

not drawn to stole

with internal

l

recycle

L-LB3 Entramer

stream

!&nary aze0trope ccmpo*,+lO” “0, drOwn10 SC&

Fig. 14. Sequence

for classical

extractive

distillation.

Interaction

between

separation

rates, where profitable operation is possible. However, it is apparent that improved procedures are needed for adsorption and membrane vapor recovery systems, as well as for condensation processes using mixed refrigerants. Similarly, improved procedures are needed for the recycling of sloppy splits or sidestreams back to the reactor, as well as for several nonideal distillation systems. Moreover, the effect of energy integration between the process and the separation system has not been considered in the analysis. AcknowledgementThe authors are grateful to the National Science Foundation for partial support of this work under grants NSF CPE 79-18041 and NSF CPE 81-05500, to the Department of Energy for partial support of the work under grant DE-AC02-81ER10938, to the Petroleum Research Fund administered by the American Chemical Society, and to the Eastman Kodak Company, Eastman Chemicals Division.

NOMENCLATURE A,B,C, B C0 C, C,

K, K,

Rlll s: s T T, T,,T, TAC AV v, V, W,, WR

components in ternary mixture benzene annualized cost coefficient for a distillation column annualized cost coefficient for a condenser plus a reboiler annualized cost coefficient for cooling water and steam cost per tray per year of a column heat capacity of liquid cost of solvent distillate flow 1 + (1/100x,) feed rate of light components feed rate of heavy components column feed rate gas rate heat of vaporization (at the lowest pressure for a refrigeration process) annualized cost coefficient for column trays annualized cost coefficient for all other separation costs equilibrium distribution coefficient liquid rate slope of equilibrium line; see Eqn 4 number of trays vapor pressure total pressure feed quality heat duty of process partial condenser heat duty of water-cooled condenser reflux ratio at the top of a column fractional recovery of component i gas constant, reflux ratio at the feed tray of a sidestream column minimum reflux ratio reboil ratio minimum reboil ratio sidestream flow toluene temperature low and high temperatures in a refrigeration system total annual cost difference in vapor rate bottoms flow compressor power refrigerant flow rate

system and process

synthesis

461

X

xylene inlet liquid composition mole fraction of component i in liquid Y?. inlet gas composition Y”“, outlet gas composition Y, mole fraction of component i in vapor Greek symbols 0, 8, root of Underwood’s equation y activity coefficient A difference in cost between direct and indirect separation sequences relative volatility a, (+ Za, X, Subscripts D distillate F feed N tray N S sidestream B bottoms Superscripts D direct sequence I indirect sequence x,, x,

REFERENCES J. M. Douglas, A hierarchical decision procedure for process synthesis. AIChE J.. 31, 353 (1985). N. Nishida. G. Stenhanopoulos & A. W. Westerberp- A review of process synthesis. AIChE J. 27, 321 (198$‘A. W. Westerberg, The synthesis of distillation based separation systems. Computers Chem. Engng 9, 421 (1985). synthesis of 4. R. Nath & R. L. Motard, Evolutionary separation processes. 85th National AIChE Meeting, Philadelphia, Pennsylvania, 1978. studies in 5. D. W. Tedder & D. F. Rudd, Parametric industrial distillation. Part I, design comparisons, AIChE J. 24, 303 (1978); Part II, Heuristic optimization, AIChE J. 24, 316 (1978). 6. R. W. Thompson & C. J. King, Systematic synthesis of separation schemes, AIChE J. 18, 941 (1972). in 7. I. R. Fair, Mixed solvent recovery and purification, Washington University Design Case Study No. 7 (Edited by B. D. Smith), p. I-1. Washington University, St. Louis, Missouri (1969). 8. J. M. Douglas, Quick estimates of the design of platetype gas absorbers. Indust. Engng Chem. Fundam. 16, 131 (1977). 9. M. R. Shelton & 1. E. Grossmann, A short-cut procedure for refrigeration systems. Computer Chem. Engng (1985), in press. Short-cut method for membrane sep10. 1. E. Grossmann, aration. Course Notes for ChE 06-302, Carnegie-Mellon University, Pittsburgh, Pennsylvania (1982). distillation of natural gas11. F. J. Lockhart, Multi-column oline. Petrol. Refiner 26, 104 (1947). 12. M. D. Lu & R. L. Motard, A strategy for the synthesis of separation sequences, Industrial Chemical Engineering Symposium Series, No. 74, p. 141 (March 1982). 13. K. M. Guthrie, Capital cost estimating. Chem Engng76, 114, (1969). 14. J. Cerda, & A. W. Westerberg, A shortcut design methodology for conventional and complex columns. Paper No. 13d presented at the 72nd AIChE Meeting, San Francisco, California (1979). 15. K. Glinos & M. F. Malone, Minimum reflux, product distribution, and lumping rules for multicomponent distillation. Indust. Engng Chem. Process Des. Dev. 23, 764 (1984). 16 K. Glinos & M. F. Malone, Design of sidestream distillation columns, Indust. Engng Chem. Process Des. Dev. (1985), in press.

J. M. DOUGLAS ef al.

462

17. A. Jafarey, J. M. Douglas & T. J. McAvoy, Short-cut techniques for distillation column design and control. 1. Column desien. Indust. Enann Chem. Process Des. Dev. 18, 197 (197%. 18. M. F. Doherty, The presynthesis problem for homogeneous azeotropic distillation has a unique explicit solution. Chem. Engng Sci. (19851, in press. 19. S. G. Levy, D. B. van Dongen & M. F. Doherty, Design and synthesis of azeotropic distillations, II. Minimum reflux calculations. Indust. Engng Chem. Fundom. (1985), in press. 20. S. G. Levy & M. F. Doherty, Design and synthesis of homogeneous azotropic distillations IV. Minimum reflux calculations for multiple feed columns. Indust. Engng Chem. Fundom. (1985), submitted. 21. J. R. Knight & M. F. Doherty, Design and synthesis of homogeneous azeotropic distillations V. Columns with non-negligible heat effects. Indust. Engng Chem. Fundam. (19851, submitted. 22. H. N. Pham & M. F. Doherty, Design and synthesis of heterogeneous azeotropic distillations I. Heterogeneous phase diagrams. Chem. Engng Sci. (19851, submitted. 23. M. F. Doherty & G. A. Caldarola, Design and synthesis of homogeneous azeotropic distillations III. The sequencing of columns for azeotropic and extractive distillations. Indust. Engng Chem. Fundom. (1985), in press.

Thus,

I_

V = TXJ for all components

where K, > 10

L = ,ZL for all components

where K, < 0.1

Superimpose

equilibrium

on perfect split x, = E K,

y, = $, equil

Thus,

Then,

v,=f;-

l,=f;

J!!L

l-

[

KZ

1

APPENDIX APPROXIMATE Total material Component

FLASH balance

balance

Equilibrium Combine

the above

F = V + L

APPROXIMATE

Y, = K,x,

Component H* CH,

XEl

Y, =

(K,-

EXACT

f;

K,

“,

1,

v,

1,

1547 2321

86.1 12.4

1545 2304

2 17

1545 2305

2 16

265 91 4

0.013 0.005 O.oool

37 5 0

228 86 4

34 5 0

231 86 4

-f)f XF,

x, =

l,Vy,=Fx,,=f,;lfK,<<

Example

Fx,, = Vy, + Lx,

;+(I

IfK,>>

j, if K, > 10, 4 if K, < 0.1

CALCULATIONS

l);+

1

l,Lx,=F~~,=f/

BENZ TOL DIPHENOL