Environ. Sci. Technol. 2000, 34, 4146-4151
Determination of Effluent Reduction and Capital Cost Targets through Pinch Technology DUNCAN M. FRASER* AND NICK HALLALE† Department of Chemical Engineering, University of Cape Town, Private Bag, Rondebosch, 7701, South Africa
This paper demonstrates how new techniques developed for the design of mass exchange networks may be applied to the reduction of waste in existing systems where pollutants are removed using processes such as absorption, stripping, adsorption, ion exchange, or solvent extraction. The paper applies recently developed Pinch Technology techniques for the design of systems to remove species from rich streams using mass exchange with lean streams (mass separating agents). These techniques are demonstrated by application to the retrofit of a gold solvent extraction process to reduce the effluent discharge by 40%. The result is an impact diagram that shows how much capital is required for a particular reduction in effluent. This is a significant diagram that shows the point of diminishing return on investment as well as the thermodynamic limit for effluent reduction (43% in this case). A design is presented that achieves the targeted effluent reduction at a capital cost within 6% of the target. The impact diagram developed is a significant new tool that may be used to determine the effluent reduction potential of existing processes as well as to evaluate alternative technologies for effluent reduction in both new and existing processes.
Introduction The purpose of this paper is to demonstrate the application of newly developed process synthesis techniques to the determination of effluent reduction targets for existing chemical processes. An integral part of these techniques is the determination of targets for the capital costs involved in the required process changes. The techniques to be applied are known collectively as Pinch Technology, which was originally developed for optimization of energy usage in chemical processes (1). Pinch Technology has recently been extended to optimization of mass recovery systems, which involve processes such as absorption, adsorption, liquid-liquid extraction, ion exchange, and stripping. In these processes a lean stream, known as a mass separating agent (MSA), removes certain species from a rich process stream. The units in which this mass transfer takes place are termed mass exchangers, and the systems are called mass exchange networks (MENs) (2). Most mass exchange occurs in systems with counter-current flow of the lean and rich streams, in tray or packed columns, or in a series of mixer-settlers. * Corresponding author phone: +27-21-650-2518; e-mail: dmf@ chemeng.uct.ac.za. † Present address: Department of Process Integration, UMIST, P.O. Box 88, Manchester, U.K. 4146
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The application of Pinch Technology to synthesis of MENs began with the setting of targets for the usage of MSAs (and hence operating costs) (2) and has only recently been extended to the setting of capital costs targets (using standard design techniques for mass transfer systems) (3-6) and the tradeoff between operating and capital costs (7, 8). The application of these techniques to reducing pollution when designing new “grassroots” process plants has also been demonstrated (9). Techniques that enable these targets to be met or closely approached with actual designs have also been developed (3, 4-8). This means that the targets are realistic and may be used at an early design stage for comparing alternative processes or alternative technologies within processes. These techniques have also been extended from their original application in the design of new plants to the retrofit of existing plants (10). In this application, the tradeoff between savings in operating costs and the capital investment required may also be determined ahead of detailed design. Retrofit of existing processes is normally undertaken for the purpose of saving operating costs, improving product yields or throughput, or reducing environmental impact. This paper is an extension of the application to the retrofit of existing processes, focusing on the usage with respect to effluent reduction and hence environmental impact. A simple case study is used to explain the details of the methodology clearly, although this will not convey its full potential.
Case Study Problem The case study used in this paper is related to the production of gold from gold-bearing ore. The conventional process for producing gold from ore is shown schematically in Figure 1 (11). The ore first undergoes size reduction, by crushing and milling, to expose the gold. This is followed, where needed, by concentration of the ore using froth flotation. Next, the gold is leached into an aqueous solution to form a cyanide complex. The technology currently used to extract the gold from this solution is to adsorb it on activated carbon or on ion-exchange resin, after which it is stripped from the carbon or resin and then precipitated by electrowinning or cementation. Finally, the precipitate is refined to produce highpurity gold. In this case study, we examine the Minataur process, which is an alternative to the conventional gold-refining process (12). This is a proprietary process which involves leaching of the gold from the precipitate into an aqueous solution, followed by extraction using an organic solvent, then stripping of the gold from the solvent, and finally precipitation of highpurity gold. This avoids the separate refining step normally needed for producing high-purity gold. In this case study, we examine the possible application of the Minataur process to the re-treatment of mine dumps from which most of the gold has already been extracted. Here the Minatuar process would replace the conventional leaching, adsorption, stripping, precipitation, and refining steps for direct production of high-purity gold. Figure 2 shows the existing Minataur process design for this particular application in more detail. The solvent extraction step consists of three mixer-settlers in which the aqueous feed stream (G1) and the organic solvent (L1) are contacted in a counter-current flow arrangement. The aqueous raffinate stream is recycled to the start of the leaching process, while the organic solvent extract stream is scrubbed by clean water (G2) to remove impurities (in the course of which some gold is also transferred to it). After the scrubbing, the organic solvent is then stripped of its gold by an aqueous 10.1021/es981347t CCC: $19.00
2000 American Chemical Society Published on Web 08/19/2000
FIGURE 3. Grid diagram of existing gold solvent extraction process.
FIGURE 4. y-x plot of existing gold solvent extraction process.
FIGURE 1. Schematic flow sheet of gold recovery process.
FIGURE 2. Schematic flow sheet of existing gold solvent extraction process. solution (L2). The stripping water, after precipitation of the gold and neutralization, is the effluent stream leaving this process. The environmental impact of gold ore processing is discussed by Stewart and Petrie (13). It is clear that, while no systematic environmental impact study of gold processing has been published, the major environmental impact arises from the materials sent to dumps and slimes dams. The major source of pollution in this extraction process is therefore the stream going to the slimes dam. To reduce the environmental impact of this process, we need to reduce the amount of material leaving the neutralizer. Other sources of pollution would be in the solvent leaving in the raffinate and in fugitive emissions to the atmosphere from handling of the solvent. These will all be reduced if less solvent is being stored and
recirculated in the system. The only other significant source of pollution for the process as a whole would be the leach residue being returned to the dumps. The design of the scrubbing and stripping units was fixed. The design of the scrubber requires that the flow rate of the clean scrubbing water is the same as the flow rate of the organic solvent (i.e., G2 ) L1). The stripping water flow rate, on the other hand, is specified to be half of the solvent flow rate (i.e., L2 ) 0.5L1). A change in the organic solvent flow rate would therefore directly affect both the scrubbing water flow rate and the stripping water flow rate. The neutralizing stream is proportional to the stripping stream flow rate so the effluent flow to the slimes dam is also proportional to the stripping water flow. Therefore, given the proportionality between the effluent flow and the solvent flow, the flow of organic solvent will need to be reduced if the effluent is to be reduced. This will in turn affect the solvent extraction step because not only will the organic solvent flow change but also the aqueous flow (through the change in scrubbing water flow). The design of the solvent extraction step is thus central to the solution of this problem. Figure 3 shows the solvent extraction step drawn as a “grid diagram”, which includes the flow rates and concentrations of all the streams and the number of stages in the mass exchanger. Note that the rich process streams go from right to left on this diagram and that the lean MSA stream goes in the opposite direction. It is immediately clear that the mixing of the scrubbing water stream (at a concentration of 15 g/l) with the main feed stream (at a concentration of 5 g/l) leads to a loss of mass transfer driving force. Any retrofit design will clearly need to take this into account. It was felt that, to improve the existing design, a suitable target for the reduction of the effluent stream from this section of the process would be 40%. In this case study, the reduction in effluent is the major consideration rather than savings in operating costs, which were not considered, although they would clearly improve the economics of the process and make it more profitable. Figure 4 shows the situation on a y-x plot (14). The gold concentration in the aqueous stream is plotted against that in the solvent as an operating line. The slope of this line is VOL. 34, NO. 19, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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equal to the ratio of solvent flow rate to aqueous flow rate (L1/G ) 0.43/2.43 ) 0.177, with G ) G1 + G2). The equilibrium relation for gold extraction between the water and the solvent is also shown. The three extraction stages are indicated on this diagram, using the standard McCabe-Thiele stepping procedure (14).
Standard Approach Now, the usual approach would be to add extraction stages in order to reduce the solvent flow rate, expending capital in order to reduce the operating costs and/or the effluent produced. We will illustrate how this is limited by thermodynamics. Consider again the y-x plot for this system (Figure 4). As the solvent flow rate (L1) is reduced, the slope of the operating line ()L1/G) decreases in proportion. This moves the operating line closer to the equilibrium line, so the number of equilibrium stages required to reduce the concentration of gold to 0.1 g/t increases. The end of the operating line is the point (xp, yf), where xp is the concentration of gold in the solvent product stream (extract) and yf is the gold concentration in the aqueous feed stream. Noting that the scrub liquor flow rate (G2) is equal to the solvent flow rate (L1), the locus of the end of the operating line is given in terms of the solvent flow rate L1 as
yf ) (10 + 15L1)/(2 + L1)
(1)
xp ) ((2 + L1)/L1)(yf - 0.1) + 0.45
(2)
Given that the slope of the operating line is L1/G, the minimum solvent flow rate corresponds to the operating line with the lowest slope, which occurs when the locus of the end of the operating line intersects the equilibrium curve, as shown in Figure 4. At this flow rate, an infinite number of extraction stages would be required. For this process, the minimum solvent flow rate would be 0.305 l/min. Thus, the maximum achievable effluent reduction would be 29%. This is a thermodynamic minimum when using this particular solvent for this system. In the case study being considered, another option to consider is counter-current extraction with reflux, which will yield an extract stream richer in gold, allowing the solvent rate to be reduced below the limit obtained above. This is achieved by adding a series of enriching stages between the feed and the extract withdrawal, with reflux of an aqueous stream (14). If this is done, it is then possible to separate the scrub liquor stream from the feed stream and to introduce it into the extractor at a more appropriate point. In this particular case study, this produces a similar solution to the one obtained using pinch technology in the next section, but this would not be the situation in general, especially for more complex mass exchange networks.
Pinch Technology Approach In a Pinch Technology analysis of this problem, the first step is to specify the characteristics of the streams being treated as well as the MSA(s) available. The process is then analyzed using a new tool, developed by the current authors, the y-x composite curve plot, shown in Figures 5 and 6. This plot consists of a composite operating line (Figure 5) and the extraction equilibrium curve. Figure 5 shows how the composite operating line is constructed, and Table 1 gives the stream data for the case study, on which it is based. The rich stream compositions, yf and yp, and the lean stream inlet compositions, xf, are fixed. Note that, as shown in Table 1, mass balances reveal that the lean stream exit composition for stream G2, xp2, is 4148
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FIGURE 5. y-x diagram showing construction of composite operating line.
FIGURE 6. y-x diagram showing changes to composite operating line.
TABLE 1. Stream Data for Case Study Problem stream
flow (L/min)
G1 G2
2.0 L1
yf
yp
xf
xp
5.0 15.0
0.1 0.1
0.45 0.45
0.45 + 2.0/L1 15.45
independent of flow rates because G2 ) L1, whereas for stream G1 the exit composition, xp1, is a function of L1. Each individual operating line goes from the coordinates (xf, yp) to (xp, yf) and has a slope equal to the ratio between the solvent flow rate, L1, and the aqueous stream flow rate, G1 or G2. The individual operating lines are then combined by vector addition within the horizontal concentration intervals shown in Figure 5 in order to give the composite operating line, which has a slope equal to the ratio of solvent flow rate to total aqueous flow rate within each interval. Interval I in Figure 5 is between y values of 0.1 and 5.0: 0.1 ) yp1 ) yp2 and 5.0 ) yf1 (see Table 1). This interval contains both G1 and G2, so the composite operating line is the sum of the two individual operating lines in the interval. Interval II is between y values of 5.0 and 15.0: 5.0 ) yf1 and 15.0 ) yf2. This interval contains only G2, so the composite operating line follows the operating line for G2, shifted to start where the operating line in interval I ends. Figure 6 shows the composite operating line together with the equilibrium line for this system. The distance between the composite operating line and the equilibrium curve represents the mass transfer driving force. Now, a decrease in the solvent flow rate, L1, will correspond to a decrease in the slope of each of the sections of the composite operating line. The minimum solvent flow rate is given when the locus of either the end of the composite operating line or of one of its points of inflection intersects the equilibrium curve (whichever does so first). The point of intersection is termed the pinch point, and, as before, it is a thermodynamic limit to reducing the solvent flow rate. The composite operating line for minimum solvent flow is also shown in Figure 6. The locus of the point of inflection
is the horizontal line yf1 ) 5.0, i.e., it is fixed by the inlet composition of stream G1. The point of inflection intersects the equilibrium curve at an x value of 45.35. The minimum flow rate corresponding to this is 0.245 l/minsa reduction of 43% as compared to the maximum reduction with the current process of 29%. The desired reduction of 40% is therefore attainable, at a solvent flow rate of 0.258 l/min. The methods developed by us may also be used to predict the number of extraction stages and hence the capital cost of those stages (4-6). What this paper will demonstrate is how to predict the minimum capital investment for retrofit of such a system before doing any process design, using these techniques, based on the approach used for retrofit of heat exchanger networks (15). This differs from grassroots designs in that account must be taken of existing equipment. As with grassroots designs, the targets give the minimum capital investment required to achieve a particular MSA rate (which in retrofit corresponds to a particular reduction in operating cost and/or effluent).
Retrofit Targeting For the process in this study, the capital cost of a single mixer-settler stage is given by the following correlation, which was obtained by correlating local industrial data:
cost (installed) ) $1200V 0.6
(3)
where V is the volume of the mixer-settler (in l). This means that in order to predict the minimum capital investment for a given reduction in solvent flow rate, we need to estimate the minimum volume to be added. This can be done by using the y-x composite curve plot. For a particular solvent flow rate, the number of stages can be stepped-off for each concentration interval. The following equation is then used to target the minimum total extractor volume required for that flow rate (3):
Vmin )
τ intervals Eo
∑
rich streams
Nstages,k(
k
∑
lean streams
Gi,k +
i
∑
Lj,k)
(4)
j
where τ is the residence time per stage (min), Eo is the overall average stage efficiency, Nstages,k is the number of equilibrium stages for interval k, Gi,k is the flow rate of rich stream i in interval k (l/min), and Lj,k is the flow rate of lean stream j in interval k (l/min). In this case study, the rich streams are the aqueous feed and scrub liquor streams, and the only lean stream is the organic solvent. A grid diagram similar to Figure 3 is used to show the streams present in each interval. Equation 4 is applied over a range of solvent flow rates, and the results are plotted as a volume-flow rate diagram (Figure 7). This shows the target for the minimum exchanger volume as a function of the solvent flow rate. Note that the discontinuities on this curve are due to rounding up the number of stages to integer values. The existing process is also plotted as a point on this diagramsas it uses more volume than the target for the existing solvent flow rate it lies above the target curve. In approaching a retrofit design, it is helpful to first quantify the efficiency with which the existing process uses volume. The volume efficiency, R, is defined as the ratio of the target (i.e., minimum) volume to that actually used at a specific solvent flow rate:
R(L1) )
Vtarget Vactual
|
(5) L1
This should not be confused with the stage efficiency, Eo,
FIGURE 7. Volume-flow rate diagram showing possible retrofit paths. defined above, which is used to account for nonequilibrium stages. The higher the value of R, the better the overall use of volume. In this case study, the existing process has a volume efficiency of 77%. This reflects the loss of driving force caused by the mixing of aqueous streams at unequal gold concentrations. A retrofit of this process would aim to reduce the solvent flow rate by adding volume (extra stages), moving leftwards and upward from the existing design on the volume-flow rate diagram. The exact shape of the retrofit curve is unknown, but it can be estimated as follows: The target curve on the volume-flow rate diagram may be regarded as an ideal situation that cannot be bettered. This makes the region below the target curve an infeasible region, so this curve is the lower bound to the retrofit path. An upper bound to the retrofit path may be found by assuming that the overall efficiency, R, will remain constant as extra volume is added, as was done for heat exchanger networks (15). Applying this gives the constant-R curve shown in Figure 7. If the efficiency of the existing design is low (as in this case study), it is desirable that extra volume should be added at a higher efficiency, so the constant-R curve provides an upper bound to the retrofit path. A likely retrofit path is obtained by using the idea that R should improve as more volume is added. Ahmad and Polley (16) did this for heat exchanger networks by using an incremental efficiency, ∆R. The equivalent definition of ∆R for mass exchange networks is
∆R )
(
∆Vtarget ∆Vactual
)|
(6)
∆L
where ∆Vactual is the new volume installed during retrofit to reduce the solvent flow rate by ∆L, and ∆Vtarget is the minimum targeted new volume required to reduce the solvent flow rate by ∆L. Ahmad and Polley showed that for networks in which the existing R is low (less than 0.9), taking ∆R to be 1.0 gives a good estimate of the retrofit path. This will be used in this case study as the efficiency is 0.77. The resulting curve is also shown in Figure 7 (marked ∆R ) 1). This curve lies between the upper and lower bounds and moves from the upper bound toward the lower bound as more volume is added. Moving left from the existing process on the ∆R ) 1 curve therefore gives an estimate of how much volume must be present in order to achieve a certain reduction in flow rate. Subtracting the existing volume (85.8 l) then indicates how much volume needs to be added. The capital investment required may be determined from the extra volume needed by using eq 3 in combination with the number of extra stages required. Note that the minimum number of stages required is determined in eq 4 as part of VOL. 34, NO. 19, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 8. Impact diagram showing the relationship between effluent reduction and capital investment. the minimum volume calculation, so the number of extra stages is simply obtained by subtracting the existing stages from this. If the two aqueous streams had to remain segregated throughout, the minimum number of stages target for a given solvent flow rate would be (4) rich streams
∑
Nstages )
Nstages,i
(7)
i
with ke
Nstages,i )
∑N
stages,k
(8)
k)ks
where ks is the starting interval of rich stream i, ke is the interval where the stream ends, and Nstages,k is determined from the y-x composite curve plot. However, in this case study, the only reason the aqueous streams should remain separate is to avoid mixing at unequal gold concentrations and hence to avoid a driving force loss. There is no constraint preventing mixing. Indeed, mixing is a feature of the existing design (Figure 2). Recognizing that the streams may be mixed once they are at equal concentrations reduces the number of stages target to intervals
Nstages )
∑
Nstages,k
(9)
k
Retrofit curves showing the number of stages versus flow rate can then be generated similarly to Figure 7. This means that, for a given reduction in solvent flow rate, estimates for both the minimum additional volume and the minimum number of extra stages can be obtained. Equation 3 is then used to cost the additional stages, assuming the added volume to be distributed evenly among the additional stages. This targeting process is repeated along the span of the retrofit curve, starting from the existing process, and the results are plotted as the impact diagram shown in Figure 8 (after El Halwagi (17)). This shows what reduction in effluent can be expected for a given capital investment or vice-versa. The difference between the impact diagram used by El Halwagi and this one is that the former requires completion and costing of designs, whereas this diagram is developed without having to generate or evaluate any network designs. It is a prediction of design costs based solely upon the problem data and thermodynamic considerations. Being able to generate this diagram before any design saves much unnecessary work and also gives confidence that a final design is performing as well as it could be. 4150
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A number of features of this impact diagram should be noted: (i) The diagram shows that a 40% reduction in effluent flow will require an investment of approximately $28 000. (ii) The impact diagram shows where capital will be invested most efficiently. The curve is steepest until approximately 33% reduction, which indicates that capital would be used most effectively up till this point. At reductions above this, the curve levels off, signaling that diminishing returns will be obtained. (iii) The diagram shows clearly that the maximum possible effluent reduction is 43%. This is limited by thermodynamics and cannot be exceeded no matter how much capital is invested. Where effluent reduction is effected by a network of mass exchangers, such a diagram would be very useful in setting reasonable and realistic improvement targets during negotiations with the relevant regulatory authorities. It may also be used to compare alternative technologies, such as using a different MSA.
Retrofit Design The impact diagram just presented will only be of value if the target costs and reductions can be met, or at least closely approached, in actual designs. This will be addressed in this section. Design is carried out following the approach of Tjoe and Linnhoff for heat exchanger network retrofit (15), as developed by Fraser and Hallale for mass exchange network retrofit (10). The following steps are followed: (i) The first step is to draw the existing network on the grid diagram introduced earlier to identify cross-pinch exchangers. (ii) The second step is to eliminate any mass transfer occurring across the pinch in the existing design, because it causes a solvent flow rate in excess of the minimum (2). In the existing design (Figure 2), cross-pinch mass transfer occurs in the only mass exchanger; it is therefore removed. (iii) The next step is to redesign the network using established design guidelines (2, 4, 6, 10). (a) First, avoid cross-pinch mass transfer (as in step 2, to meet the solvent flow rate target). (b) Second, try to make good overall use of driving force (to approach the capital cost target). Good driving force use is achieved by ensuring that the operating lines of all exchangers provide a reasonably good fit to the composite operating line (4). (c) Third, aim to use a low number of exchangers. Satisfying a stream with every match will ensure the minimum number of exchangers is used, but it has been shown that this may lead to poor designs if driving force is not used properly (6). (iv) Besides following these guidelines, the designer should aim to make the design as compatible as possible with the original one, attempting where possible to reuse exchangers removed in step (ii). A design carried out in accordance with this procedure will probably require some new exchangers as well as additional stages on existing ones. Figure 9 shows a network designed using the procedure outlined above. The MSA flow is at the target rate. The scrub liquor gold concentration is reduced to 5 g/l in exchanger 1, which is a new exchanger. This liquor is then mixed with the main feed, and the combined stream is reduced to 0.1 g/l in exchanger 2, which is the existing exchanger reused, with two more stages. The solvent flows in series through the two mass exchangers. This design has achieved the desired effluent reduction from the process (by reducing the solvent circulation rate) at a capital investment of $29 500 (within 6% of the target).
The approach to the target is good enough for preliminary design purposes and to make the targets meaningful.
easily assessed using targets, with no actual design being necessary. Although this paper dealt with solvent extraction using mixer-settlers, this is by no means the only type of problem that can be considered. Virtually any direct-contact mass transfer operation can be dealt with, for example, absorption, stripping, adsorption, or ion exchange. Capital cost targets have also been developed for other equipment types including tray columns and packed columns (6, 7). The retrofit techniques presented in this paper can thus be applied to a wide range of problems. The impact diagram, which shows the investment required to achieve a particular reduction in effluent as well as the maximum effluent reduction possible, is a powerful tool that should find wide application in assessing the potential for effluent reduction in the process industries both using existing technologies and using different ones.
Evaluation
Acknowledgments
There are a number of alternatives to the approach to be described in this paper. One is to use conventional design techniques such as extract reflux to achieve the desired objective. While this would yield the same result in the case study used, this will not be the case with more complex networks. In this case study, there were only two rich streams and one MSA, but more complex problems that have more streams of both types become large and combinatorial, not unlike typical heat exchanger network problems (2). Another possibility is to use the methodology of waste interception networks (WINs) to identify the best location in the process to remove a particular species (17). This is not applicable in this case as it is the flow of the waste stream that is the problem and not what it contains. Finally, the problem may be formulated as superstructure of possible mass exchangers and then solved using mixed integer non-linear programming (MINLP) to minimize a chosen objective function (18). This may also yield a similar solution, but for more complex networks it may not reach the global optimum. Pinch techniques have been shown to give much cheaper designs than MINLP methods (8). Also, the MINLP techniques developed so far for MENs are for grassroots design not retrofit. The most significant difference is that, as compared with the techniques proposed in this work, none of these techniques give targets for both reduction in operating costs and/or environmental impacts and also the capital costs required to achieve them without having to carry out detailed designs. In addition, they do not provide insights such as the retrofit path and the impact diagram developed by the Pinch Technology approach described in this paper. This paper has presented a new method for retrofitting mass exchange networks. The method was successfully applied to the reduction of the effluent from an existing process for the solvent extraction of gold. Targets can be set for the minimum capital investment required to achieve a given reduction in effluent, and these targets are meaningful because they can be approached closely in actual designs. The new method is simple and interactive and allows the designer to remain in control. The paper has also demonstrated that mixing of process streams prior to treatment is not ideal. Significant improvements may be achieved by segregating streams. The extent of these improvements is
The financial support of the South African Council for Mineral Technology (MINTEK), the South African Foundation for Research Development (FRD, now the National Research Foundation, NRF), and the University of Cape Town (UCT) is gratefully acknowledged.
FIGURE 9. Grid diagram of retrofitted process.
Literature Cited (1) Linnhoff, B. Trans. IChemE (Part A) 1993, 71, 503-522. (2) El-Halwagi, M. M.; Manousiouthakis, V. AIChE J. 1989, 35 (8), 1233-1244. (3) Hallale, N. Capital Cost Targets for the Optimum Synthesis of Mass Exchange Networks. Ph.D. Dissertation, University of Cape Town, 1998. (4) Hallale, N.; Fraser, D. M. Chem. Eng. Sci. 1998, 53 (2), 293-313. (5) Hallale, N.; Fraser, D. M. Comput. Chem. Eng. 2000, 23 (11-12), 1661-1679. (6) Hallale, N.; Fraser, D. M. Comput. Chem. Eng. 2000, 23 (11-12), 1681-1699. (7) Hallale, N.; Fraser, D. M. Trans. IChemE (Part A) 2000, 78, 202207. (8) Hallale, N.; Fraser, D. M. Trans. IChemE (Part A) 2000, 78, 208216. (9) Hallale, N.; Fraser, D. M. Adv. Environ. Res. 1998, 2 (2), 167178. (10) Fraser, D. M.; Hallale, N. AIChE J., in press. (11) Hayes, P. C. Process Principles in Minerals and Materials Production; Hayes Publishing: Brisbane, 1993. (12) Feather, A.; Sole, K. C.; Bryson, L. J. J. S. Afr. Inst. Min. Metall. 1997, 97 (4), 169-173. (13) Stewart, M.; Petrie, J. Planning for Waste Management and Disposal in Minerals Processing: A Life Cycle Perspective. In Environmental Policy in Mining: Corporate Strategy and Planning for Closure; Warhurst, A., Noronha, L., Eds.; Lewis Publishers: Boca Raton, 1999. (14) Treybal, R. E. Mass Transfer Operations, 3rd ed.; McGraw-Hill: Singapore, 1981. (15) Tjoe, T. N.; Linnhoff, B. Chem. Eng. 1986, April 28, 47-60. (16) Ahmad, S.; Polley, G. T. Heat Recovery Syst. CHP 1990, 10 (4), 369-385. (17) El-Halwagi, M. M. Pollution Prevention through Process Integration: Systematic Design Tools; Academic Press: San Diego, 1997. (18) Papalexandri, K. P.; Pistikopoulos, E. N.; Floudas, C. A. Trans. IChemE (Part A) 1994, 72, 279-294.
Received for review December 28, 1998. Revised manuscript received June 26, 2000. Accepted July 3, 2000. ES981347T
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