970
Ind. Eng. Chem. Process Des. Dev. 1985, 2 4 ,
Nomenclature D = particle size, m g = acceleration due to gravity, m/s2 U = settling velocity, m/s X = distance from the top of the buoyant sediment, mm Subscripts f = refers to flocs p = refers to primary particles Superscript O = at infinite dilution Greek Letters (Y
p p
= fluid to solid volume ratio in the floc = fluid viscosity, kg/(m s)
970-976
4 = volume fraction solids Registry No. Calcium carbonate, 471-34-1. Literature Cited Fessas, Y. P. Ph.D. Thesis, Clarkson University, Potsdam, NY, 1983. Fessas, Y. P.; Weiland, R. H. AIChE J . 1981, 2 7 , 588. Fessas, Y. P.; Weiland, R. H. Resour. Conserv. 1982, 9 , 87. Fessas, Y. P.; Weiland, R. H. I n t . J. MuMphase Flow 1984, 10, 485. Michaels, A. S.;Bolger, J. C. Ind. Eng. Chem. Fundam. 1962, 1 , 24. Stagle, D. S.;Shah, Y. T.; Klinzing, G. E.; Waiters, J. G. Ind. Eng. Chem. Process D e s . Dev. 1978, 17, 500. Thomas, D. G. AIChE J . 1963, 9 , 310. Vilambi, N. R. K. M.S. Thesis, Clarkson University, Potsdam, NY, 1982. Weiland, R. H.;Fessas. Y. P.; Ramarao. B. V. J . Fluid Mech. 1984, 142, 383. Weiland, R. H.; McPherson, R. R. Ind. Eng. Chem. Fundam. 1979, 18, 45. Whitmore, R. L. Br. J . Appl. Phys. 1955, 6 , 239.
Received for reuiew May 31, 1984 Accepted November 29, 1984
= density (of fluid if not subscripted), kg/m3
Cost Dtagrams and the Quick Screening of Process Alternatives James M. Douglas' Chemical Engineerlng Department, Universm of Massachusetts, Amherst, Massachusetts 0 1003
Duncan C. Woodcock Imperial Chemical Industries, Runcorn. Cheshire WA 7 4QE. England
Cost diagrams provide a useful way of summarizing total processing cost information for preliminary process designs. I n addition, they are often useful for checking rules of thumb, for obtaining quick estimates of the economics of process alternatives, and for establishing a hierarchy of optimization variables. Thus, they help to establish priorities for more detailed design studies.
A t the initial stage of designing a new process, it is possible to generate more than 1 million flow sheets (Douglas, 1985) and there are about 10-20 optimizations of the design variables required for each flow sheet (Westerberg, 1981). Heuristics can often be used to eliminate some of the alternate flow sheets and to provide first estimates of some of the design variables, but there are still a very large number of process alternatives and optimizations that need to be considered. Since flow sheets normally are dropped from further consideration based on the total processing costs (safety, operability, and pollution may play a part), it is useful to have a simple and efficient way of summarizing cost information. Cost diagrams can be used for this purpose. In addition, cost diagrams sometimes are useful for checking rules of thumb, for obtaining quick estimates of the economics of process alternatives, and for identifying a hierarchy of optimization problems. Previous Work From an examination of published design case studies (Washington University Design Case Study Series; AIChE Student Problems; Stanford Research Institute Reports; Peters and Timmerhaus, 1980; Happel and Jordan, 1975; Baasel, 1977; Ulrich, 1984),it seems to be common practice to tabulate the manufacturing costs and the capital costs separately. The list of capital costs normally is itemized to correspond to names or tags shown on a flow sheet, but 0196-4305/85/1124-0970$01.50/0
all the steam or cooling water costs usually are added together and reported as a single item. Separate tables of manufacturing and capital costs would then be prepared for each process alternative. Cost Diagrams As an alternate approach to summarizing cost information at the preliminary stages of a process design, we can prepare a cost diagram. The annualized, installed capital cost of each piece of equipment is listed inside of the equipment box on a flow sheet, and the annual operating costs are attached to the stream arrows. Figure 1 shows a cost diagram for the production of acetone by the dehydrogenation of isopropyl alcohol, which is a modified version of the 1948 AIChE Student Contest Problem (McKetta, 1976). The values in Figure 1are reported in terms of thousands of dollars per year. Of course, we could also divide both the annualized capital costa and the annual operating costs by the annual production rate of the process. Then, the cost diagram would indicate the dollars per pound of product that each item on the flow sheet contributed to the final product price. This type of an approach is sometimes used in industry for the design of batch processes. Use of Cost Diagrams To Check Rules of T h u m b It is natural to assume that the reflux ratios for the two distillation columns shown in Figure 1 were fixed by the 0 1985 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985 971
t. HZ
I
PREHEATER 60
FEH E
58
*
REACT
CONDENSER
FLASH
49 7t 23 7 CAT
76
-0
V
c0 w7
I
t
COND 2 7
11.
!,
COND
cw
12 5
33 ACET
WASTE WATER
Figure 1. Cost diagram for acetone process.
rule of thumb of 20% in excess of the minimum reflux ratio. However, a t the optimum design conditions according to Happel and Jordan (1975), the distribution of annual costs should be 30% for the column, 35% for the condenser and reboiler, and 35% for the steam and cooling water. In a similar study, but using a 6.7 yr vs. a 2 yr time factor, Peters and Timmerhaus (1980) obtain 15% for the column, 10% for the condenser and reboiler, and 75% for steam and cooling water. Even though there is a significant difference in the treatment of the capital and operating costs between the studies of Happel and Jordan and Peters and Timmerhaus, both of these studies seem to indicate that there is something wrong with the column designs shown in Figure 1;i.e., the column cost appears to be much too large. Thus, the cost diagram indicates that some additional column design studies should be considered, where higher reflux ratios would decrease the column cost but would increase the annualized costa of the condenser and reboiler, as well as the annual cost of the steam and the cooling water.
Use of Cost Diagrams To Infer Structural Modifications The cost diagram shown in Figure 1 also makes it apparent that only $5800/yr is being spent for energy integration on the feed effluent heat exchanger around the reactor, but that a total of SO00 + 27 500 for the preheater, plus 29 300 18300 for the furnace (although some of this energy supplies the endothermic heat of reaction), plus 7600 3900 for the condenser and cooling water is allocated for reactor heating and cooling. Thus, it seems as if we should spend more for energy integration. Of course, it might be difficult to recover more of the heat from the hot reactor products because the temperature of this stream will eventually approach the temperature of the preheater outlet. However, we can avoid this difficulty and recover more of the heat if we simply eliminate the preheater. In actual fact, rather than just eliminating the preheater
+
+
from the flow sheet, it would be much better to undertake an energy integration analysis of the flow sheet (Linnhoff et al., 1982). Recent experience indicates that 30-50% energy savings are usually possible even in retrofit situations (Boland and Hindmarsh, 1984; Linnhoff and Vredeveld, 1984).
Use of Cost Diagrams To Identify the Significant Design Variables For the flow sheet shown in Figure 1,some of the design variables of interest are as follows: the conversion, the approach temperature between the Dowtherm furnace and the reactor inlet, the approach temperature between the preheater exit temperature and the temperature of the reactor products leaving the feed-effluent heat exchanger, the fractional recovery of acetone in the compressor, the reflux ratios in both distillation columns, the fractional recovery of acetone overhead in the product column (we assume that the product composition is specified), and the fractional recoveries of isopropyl alcohol-water azeotrope and water in the IPA still. Almost all of these optimizations involve only local tradeoffs, Le., the column reflux ratio involves a tradeoff between the number of plates and the costs of the condenser, reboiler, steam, cooling water, and column diameter. However, the optimum reactor conversion involves a tradeoff between an unbounded reactor cost as the conversion approaches unity and unbounded recycle costs as the conversion approaches zero. Thus, the optimum conversion depends on all the costs in the recycle loop in Figure 1,and it is apparent that it is much more important to get the conversion close to the optimum than any of the other design variables. Cost Diagrams for Complex Processes The new synthesis procedures for heat-exchanger networks (Linnhoff et al., 1982) lead to highly coupled processes. Figure 2 shows a flow sheet for the production of benzene by the hydrodealkylation of toluene (McKetta, 1977) before energy integration, and Figure 3 shows a cost
972
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985 PURGE
4
an inverse proportion to their heat-transfer coefficients (where the heat-transfer coefficient includes both the film coefficient and the appropriate fouling coefficient) (eq 1). cost allocated to stream l/heat-transfer coefficient of stream (1)
-
-.
39' K
r-
*
Figure 3, we see that there are five stream-stream --1heatFrom exchangers in a row on the reactor effluent stream.
Figure 2. Hydrodealkylation of toluene.
The f i t exchanger (cost = 63 X lo3 dollars/yr) is a gas-gas exchanger; we assume that the heat-transfer coefficients of the two streams are identical, and therefore we split the cost evenly. The toluene column reboiler (cost = 14 X lo3 dollars/yr) contacts a gas and a boiling liquid, and we allocate a smaller cost (4 X lo3 dollars/yr) to the toluene reboiler because the heat-transfer coefficient is higher. The allocation for the five exchangers is given in Table I.
diagram of the result for one alternative after an energy integration analysis. There are so many connections on Figure 3 that it is difficult to use the cost diagram in the same way as we did Figure 1. Thus, we need to find a way to simplify the information presented. In particular, we would like to be able to evaluate that fraction of the total processing costs that is associated with the gas and liquid recycle loops, as compared to the costs for processing the raw material streams. In order to simplify the cost diagram, we proceed through three stages: (1)allocate heat exchanger costs to process streams; (2) lump costs associated with neighboring processing operations; and (3) allocate costs to the gas recycle loop, liquid recycle loop, and fresh feed rate of the raw materials. We discuss each of these steps below. Allocate Heat Exchanger Costs to Process Streams Following a suggestion of Townsend and Linnhoff (1984),we allocate the cost of a heat exchanger, where two process streams exchange heat, to the process streams in
Lump Costs Associated with Processing Operations We lump the capital and operating costs of units: the compressor capital cost of 49 X lo3 dollars/yr and the operating cost of 60 X lo3 dollars/yr; the toluene column shell cost of 52 X lo3dollars/yr, the allocated reboiler cost of 4 X lo3 dollars/yr, and the condenser and cooling water costs of (12 + 8) X lo3 dollars/yr; and similarly for the stabilizer and benzene columns. Also, we lump neighboring heat-exchanger costs on the same stream (reactor product cooling allocated costs of (31.5 10 10 10 29) X lo3 dollars/yr, see Table I, plus the condenser 22 X lo3 dollars/yr and cooling water 43 X lo3 dollars/yr = 155 X lo3 dollars/yr; feed and recycle heating allocated costs of (12 + 31.5) X lo3 dollars/yr, see Table I, plus the furnace 66 x lo3 dollars/yr and fuel 262 X 103dollan/yr = 371 X lo3 dollars/ yr). With this lumping, we obtain the results shown in Figure 4. Allocate Costs to Gas Recycle, Liquid Recycle, and Fresh Feed We allocate the reactor cost between the three categories based on the molar flow rates of the streams, see Table
TOLUENE RECYCLE
DIPHENYL
c
Figure 3. Cost diagram for energy-integrated HDA process.
+ + + +
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985 973 Table I. Allocation of Heat-Exchanger Costs 63 orig cost (X103dollars/yr) reactor feed stream 0.69 hi,kw/(m2K) l / h i allocated cost 31.5 stream reactor effluent hi, kw/(m2K) 0.69 l / h i allocated cost 31.5
14 toluene reboiler 1.57 4 reactor effluent 0.69 10
RECYCLE COMPRESSOR
I-
1
(09
REACTOR
198
PRODUCT COOLING 453
I
PURGE
6W
iI
1
14 benzene reboiler 1.57 4 reactor effluent 0.69 10
41 reactor feed 1.57 12 reactor effluent 0.69 29
Table 11. Reactor Cost Allocation molar flow rate, kg stream mol/h gas recycle 3371 liquid recycle 91 toluene feed 273 769 H2 feed 496
cost (xi03 dollars/ yr) 158 4
14 stabilizer reboiler 1.57 4 reactor effluent 0.69 10
total DIPH‘NYL
36
4231
198
BENZENE
Figure 4. L u m p d cost diagram for HDA process.
11, since the reactor volume will be proportional to the flow rate. We allocate the heating/cooling costs in proportion to the heat loads, see Table 111, for the product cooler and the feed and recycle heating, and we allocate the distillation costs proportional to the flow rates. Discussion of Complex Cost Diagram With the allocation assumption described above, we obtain the cost diagram shown in Figure 5. Obviously, the results are only approximate, but a t this stage of a design (when we are screening process alternatives), a more careful analysis might not be justified. It should also be noted that Figure 5 makes it appear as if the costs associated with the gas recycle stream, the liquid recycle stream, and the fresh feed streams are completely uncoupled, which is not actually the case because the material balances are coupled. However, when we use the cost diagram to make first estimates of the economic incentive corresponding to various process alternatives, we use the process material balances to change the costs associated with the relevant flows.
Stream Costs We can also include the stream costs and the material losses on the cost diagram. However, the most “reasonable”representation is to include only the amounts of the feed streams that correspond to the excess above the stoichiometricrequirements of the specified production rate, since these are the losses that might be avoidable by some other process alternative; see Figure 5. Our goal is to use the cost diagram to help us develop a better process. Use of Cost Diagrams To Evaluate Process Alternatives As was mentioned earlier, there are numerous process alternatives, and in a very large number of cases, there are no heuristics available for selecting the best alternative. One of the great advantages of cost diagrams is the help they often provide in obtaining a quick estimate of the economics associated with process alternatives without having to completely redesign the process. Some examples of this type are discussed below for the benzene process. Listing of Process Alternatives A list of decisions that were required to develop a process flow sheet (for a limited class of processes) was presented
Table 111. Heating/Cooling Cost Allocation prod cooler cost react feed heaters 103 103 heat load, dollars/ heat load, dollars/ stream GJIh vr GJ/h vr 86 53.3 172 gas recycle 39.2 liquid recycle 6.1 13 12.1 39 fresh feed 25.5 56 49.6 160 total
70.8
155
115.0
371
by Douglas (1985). In some cases, heuristics are available to help in making these decisions, but in other cases, there are no guidelines available. Hence, the choice made to develop a basecase design merely represents a guess. Of course, if we change this choice, we are led to a process alternative. Since the choices a t early decision levels depend on those made a t later levels, very different looking flow sheets might be obtained. Thus, in order to determine what process alternatives should be considered, we merely have to review a process flow sheet in light of the decision procedure proposed by Douglas (1985) and to recognize which choices were arbitrary or were based on qualitative heuristics. These choices are reviewed in Table IV. Example-Hydrodealkylation of Toluene. If we again refer to the process for the production of benzene by the hydrodealkylation of toluene, where the reactions are toluene
-
+ H2
2benzene
benzene
diphenyl
+ CH., + H2
(2) (3)
The level 2 decisions used to develop the base-case design (Douglas, 1985) were (1)do not purify the hydrogen feed stream, (2) recover the diphenyl, rather than recycling this reversible byproduct, and (3) use a gas recycle and purge stream. It would be desirable to estimate the economic incentive for changing these decisions and evaluating the process alternatives, without completely redesigning the process. The decision not to purify the hydrogen-methane feed stream seems to be sound, since methane is produced by the reactions. The other two decisions are discussed below.
Recycle of Diphenyl In order to evaluate the possible incentive for recycling
974
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985 GAS RECYC
GAS RECYC
f I
109
FEED HEAT TOL Hp
REACTOR
PROD COOL
1691 2463
LR
LR
GR
86
NFF LR
56
1
155
-
i3
r
160
198
r--
:1 ;:i ~~~
LR
39
LR
39
NFF
76
I
PURGE
c BEN2 8 TOL 600 (FEEDSTOCK)
( 5 mole/hr TOL) 95% H2 685 fuel
or
129
43
76
172
DIPHENYL 200
BENZENE PRODUCT
(8mole/hr TOL)
Figure 5. Cost allocation diagram for HDA process.
the diphenyl, we can use the cost diagram to obtain most of the information we need. (a) We save the 8 mol/h toluene that get converted to diphenyl (we still lose the equivalent of 5 mol/h toluene, some as benzene, out the purge stream), but we lose the fuel value credit of the diphenyl. Thus, from the cost diagram, Figure 5, we can write savings in raw material = 1691 - - 200 = (P3) 840 (X103dollars/yr) (b) We can eliminate the toluene column savings = 76 (X103dollars/yr) On the other hand, the diphenyl flow in the liquid recycle recycle loop builds up to an equilibrium level, and all the equipment in this loop must be oversized to accomodate this flow. (c) From an equilibrium calculation, see Hougen and Watson (1974))the equilibrium diphenyl flow a t the reactor exit is 12 mol/h, so that the total liquid recycle flow becomes 12 91 = 103 mol/h. We assume that the costs associated with the liquid recycle streams are proportional to the flow, and therefore the increased cost for the items that depend on the liquid recycle flow in the cost diagram, Figure 5, would be
+
12 -(4 91
+ 13 + 7 + 43 + 39) = 14 (X103dollars/yr)
In fact, this cost should be an upper bound, because the capital costs only increase with the flow raised to the 0.6 power, or some similar fractional exponent. However, at this point in the analysis, we are willing to sacrifice accuracy for speed in the first screening of alternatives. (d) The increased liquid recycle of aromatics will require that the gas recycle flow is also increased, since there is
a requirement of a 5/1 H2/aromatics ratio a t the reactor inlet in order to prevent coking. Thus, an extra 12 mol/h aromatics recycle will require an extra 12(5) = 60 mol/h hydrogen recycle, but since the hydrogen recycle stream is only 40% H2,the gas recycle flow must be increased by 150 mol/h. The costs associated with this increased gas recycle flow in the cost diagram, Figure 5, are, approximately, 150 -(158 86 + 109 + 172) = 24 (X103dollars/yr) 3371 (e) Combining the expressions above, we estimate the order of magnitude of the saving as
+
savings = 840
+ 76 - 14 - 24 = 878 (X103dollars/yr)
Obviously, the calculations are only rough approximations. However, they indicate that there H a large incentive for evaluating this alternative more rigorously. Purification of the Gas Recycle Stream In our original decision to use a gas recycle and a purge stream with a purge composition of 40% H2,our increment raw material cost is 2163 X lo3 dollars/yr, while the fuel value of this hydrogen is only 685 X lo3 dollars/yr. (a) Thus, the incentive for recovering and recycling the hydrogen is very large, i.e., raw material savings = 2163 - 685 = 1478 (X103dollars/yr) With the use of a hydrogen recovery system, such as a membrane process, the revised material balances are shown in Figure 6. (b) The gas recycle flow is reduced from 3371 to 1628 mol/h; so the cost savings associated with a decreased gas recycle flow from the cost diagram, Figure 5, are
(1-3371) 1628
(172 + 109 + 158 + 86) = 271 (X103dollars/yr)
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985
Table IV. Decisions level 1: batch vs. continuous-we consider only continuous processes level 2: input-output structure of flow sheet (1)‘should we purify the raw material streams before they are fed to the reactor?”; if the impurities are inert, there are no quantitative heuristics (2) “how many product streams will there be?”; reasonable heuristics seem to be available, except for the case of a reversible byproduct (3) “should a reversible byproduct be recovered or recycled to extinction?”; no quantitative heuristic is available (4) “do we need a gas recycle and a purge stream?”; a quantitative heuristic seemed to be available before the recent invention of membrane separation processes to separate gaseous mixtures. level 3: recycle structure (1)“how many reactor systems are required?”; the heuristics seem to be reasonable; “is there any separation between the reactors?”; usually a decision can be made based on the chemist’s data (2) “how many recycle streams are there?“; heuristics are available (3) “should we use an excess of one reactant?”; normally, chemist’s data will indicate the answer (4) “is a gas recycle compressor required?”; a heuristic is available (5) “should the reactor be operated adiabatically, with direct heating (or cooling), or is a diluent (heat carrier) needed?”; some calculations are needed to use the heuristic (6) “do we want to shift the equilibrium conversion?”; calculations and judgment are required level 4: separation system (1) “what is the structure of the vapor and liquid recovery system?”; heuristics are available level 4a: vapor recovery system (1)“what is the best location of the vapor recovery system?”; a heuristic is available (2) “what is the best type of vapor recovery system to use?”; no heuristics are available level 4b: liquid separation system (1)“what separations can be made by distillation?”; a heuristic that usually works is available (2) “what sequence of distillation columns should be used?”; the published heuristics are limited to sharp splits of ideal mixtures for a single feed, but in many cases they do not lead to the best sequence (3) “how should the light ends be removed?”; calculations and judgment are required (4) ”should the light ends be vented, sent to fuel, or recycled to the vapor recovery system?”; calculations and judgment are required (5) “how should we accomplish the other Separations?”; no heuristics are available level 5: heat exchanger network-a design procedure is available (Linnhoff et al., 1982) for developing alternative designs for heat-exchanger networks; also, a procedure described by Androkovich and Westerberg can be used for energy integrating distillation columns
(c) The reduction in the hydrogen feed rate from 496 to 287.4 mol/h also reduces the costs associated with the fresh feed processing costs on the cost diagram, Figure 5, to (1 - 2
~
~
+
+
~ (160 + + 36 ~ ) 56) =
68 (X103 dollars/yr)
(note that we do not include the stabilizer and benzene column fresh feed costs in this calculation because they are not affected by the hydrogen flow.) (d) The total potential savings of the hydrogen purification process is total savings = 1478 + 271 + 68 = 1817 (X103 dollars/yr)
95 % H2
9 5 % H2 RECYCLE
-
95% H2/CH4 SEP
t REACTOR
TOL RECYCLE TO L
91
SEP
975
C“4 2074
-B
I
273
Figure 6. Material balances for alternate HDA process.
These savings must be greater than the annualized installed cost of a membrane process for this alternative to be attractive. However, it should also be noted that the large recycle flow of methane acts as a heat carrier (diluent) and limits the adiabatic temperature rise in the reactor to less than 1300 O F . Thus, eliminating the methane in the recycle might cause this constaint to be violated. If this is the case, we would design the hydrogen purification unit so that enough methane could be recycled to satisfy the constraint, and we would need to adjust our estimates of the savings.
Other Decision Levels We can estimate the economic incentives for changing the decisions made a t other levels in a similar way. The other decisions are listed in Table V, and changing these decisions will lead to other process alternatives (in most cases). We can also use the cost diagram to assess the economic incentive for changing design constraints, such as the 5 / 1 hydrogen/aromatics ratio a t the reactor inlet. Reducing the Hydrogen/Aromatics Ratio The specification of a 5/ 1hydrogen/aromatics ratio at the reactor inlet in order to prevent coking is probably an uncertain constraint; it seems unlikely that a chemist would undertake experiments to find the exact coking limitations for a significant range of design variablesreactor temperature, pressure, conversion, etc. Instead, a chemist would set the ratio to a sufficiently high value so that coking was never encountered (which is perfectly reasonable). However, it is desirable to estimate the economic incentive for reducing this ratio very early in the development of a project, so that a chemist can make additional experiments in the range of the optimum design conditions. The cost diagram can be used for this purpose. (a) If we evaluate the effect of a 311 rato (Rase (1977) suggests a 2/1 ratio), the gas recycle flow is approximately cut in half, and the savings would be 0.5 (158 85 109 + 172) = 260 (X103 dollars/yr). (b) However, a decrease in the partial pressure of hydrogen in the reactor will affect the rate of the reverse reaction given by eq 3 and, therefore, might affect the amount of diphenyl formed; i.e., the correlation of selectivity vs. conversion used for the initial design might change. It is essential to verify experimentally that operation with a 3 / 1 H,/aromatics ratio is possible before any detailed design studies are undertaken. However, the information obtained from the cost diagram does provide a rough measure of the economic incentive for carrying out these experiments. Energy Integration Alternatives The cost diagram clearly indicates that the heating and cooling costs are significant. Therefore, we want to consider other energy integration alternatives. For example, we could pressure-shift the toluene column, so that part of the benzene reboiler heat load could be supplied by the toluene condenser. Similarly, we could use multiple levels
+ +
976
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985
Table
V.
Process A l t e r n a t i v e s f o r t h e
HDA P r o c e s s
structure level 2: decisions-input-output (1) d o n o t purify t h e hydrogen feed stream (2) recover, r a t h e r t h a n recycle, d i p h e n y l so t h a t there are three p r o d u c t streams (purge, benzene product, d i p h e n y l byproduct) (3) use a gas recycle a n d purge stream level 3: decisions-recycle structure (1) use a single reactor (2) use a gas (H, a n d CH,) a n d a liquid (toluene) recycle stream (3) Use a 5 / 1 H2/aromatics r a t i o t o prevent coking-assuming t h i s t o b e a design constraint (although it could b e formulated as a n o p t i m i z a t i o n problem) (4) a gas recycle compressor is needed (5) operate t h e reactor adiabatically (6) d o n ' t consider e q u i l i b r i u m effects level 4a: decisions-vapor recovery system (1) if a vapor recovery system is used, place it o n t h e purge stream (2) don't use a vapor recovery system level 4b: decisions-liquid separation system (1)a l l separations by d i s t i l l a t i o n (2) direct sequence o f simple columns-probably complex columns should b e used (3) remove l i g h t ends in stabilizer (4) l i g h t ends t o fuel-no vapor recovery system level 5: decisions-energy integration-there are numerous alternatives
of utilities (e.g., LP steam instead of fuel).
Optimization Variables The cost diagram also helps us to identify which are the most significant design variables. For the flow sheet shown in Figure 3, the factors that affect the raw material costs (reactor conversion as it affects the selectivity and the purge composition of hydrogen) are the most important. Factors that affect the gas and liquid recycle flows (again, the purge composition of hydrogen as well as the 5/1 H,/aromatics ratio constraint and reactor conversion for toluene recycle) are the next most important. The pressure of the flash drum, which affects the purge loss of aromatics balanced against the incremental cost of using higher pressure equipment in the gas recycle loop, might be next. Note that there are no rules of thumb available to fix any of these variables. The fractional recoveries in the distillation columns, the reflux ratios in these columns, the approach temperature in the heat-exchanger network, the pressure levels of the intermediate stages of the gas compressor, etc., involve local tradeoffs. Also, rules of thumb are available for
obtaining a first guess of these design variables. However, it should be noted that the rule of thumb for choosing the reflux ratio in a distillation column of 20% greater than the minimum is not valid for energy integrated columns, so that an optimization analysis might be useful. Evaluating Alternatives vs. Optimization Experience seems to indicate that greater savings normally are possible by evaluating a new process alternative rather than optimizing a process. However, since there are no rules of thumb available for selecting the reactor conversion (which usually fixes the product distribution, raw material costs, and recycle costs) or the purge composition of reactants (which usually fixes raw material costs and gas recycle costs), some case studies or an optimization analysis is needed for these variables.
Conclusions It should be apparent that the use of cost diagrams to evaluate process alternatives does not give results that are sufficiently accurate for final designs. Instead, we use this approach to get some "feeling" for the economic incentive for evaluating various alternatives in more detail. Thus, cost diagrams provide a useful tool for establishing priorities for additional design studies. Literature Cited Baasel, W. D. "Preliminary Chemical Engineering Plant Design"; Eisevier: New York, 1977. Bobnd, D.; Hindmarsh, E. Chem. Eng. Prog. 1984, 80(7), 47. Douglas, J. M. AIChE J . lg85, 3 1 , 353. Happel, J.; Jordan, D. G. "Chemical Process Economics", 2nd ed.: Marcel Dekker: New York, 1975. Hougen, 0. A.; Watson, K. M. "Chemical Process Principles"; Wiley: New York, 1947; Vol. 111, p 875. Linnhoff, B.; Townsend, D. W.; Boland, D.; Hewitt, G. F.; Thomas, 8. E. A.; Guy, A. R.; Marsland, R. H. "A User Guide on Process Integration for the Efficient Use of Energy"; Institution of Chemical Engineers: Rugby, 1982. Linnhoff, B.; Vredeveld, D. Chem. Eng. Prog. 1984, 80(7), 33. McKetta, J. J. "Encyclopedia of Chemlcal Processing and Design"; Marcel Dekker: New York, 1976; Vol. 1, p 314. McKetta, J. J. "Encyclopedia of Chemical Processing and Design"; Marcel Dekker: New York, 1977; Vol. 4, p 182. Peters, M. S.; Timmerhaus, K. D. "Plant Design and Economics for Chemical Engineers", 3rd ed.; McGraw-Hill: New York, 1980. Rase, H. F. "Chemlcal Reactor Deslgn for Process Plant", Wiiey: New York, 1977; Vol. 2. Townsend, D. W.; Linnhoff, 8. Paper presented at the Annual Research Meeting of the Institute of Chemlcal Engineerings, Bath, U.K., April 1984. Ulrich, G. D. "A Guide to Chemical Engineering Process Design and Economics", Why: New York, 1984. Westerberg, A. W. "Foundations of Computer Aided Chemical Process Design"; Mah, R. S. H., Seider, W. D., Eds.; Engineering Foundation: Henniker, NH, 1981; Vol. 1, p 149.
Received f o r review May 29, 1984 Accepted D e c e m b e r 17, 1984
