Thermodynamics of Resource Recycling W. B. Hauserman University of North Dakota, Energy and Mineral Research Center, P.O. Box 8123, University Station, Grand Forks, ND 58202 In considering schemes for the recycling of metals, glass, paper, or water, most feasibility studies are limited to a single part of the closed cycle, seeking to optimize the processes of collection or upgrading of reclaimed materials. The most profitable sequence for a processor of reclaimed materials may not necessarily fit the optimum closed cycle for the national economv as a whole. To exalore this aossihilitv requires an economically quantifiable basis to evaluate overall economic efficiencv of a closed resource cvcle. Such a basis is suggested by the elementary thermodydamic definition of overall thermal efficiency. For closed resource cycles, the overall economic efficiency may he defined as the ratio of total value delivered by the system to the total cost of making i t run. Let us define a system as all the physical facilities and organizational struc&re reauired to take a auantitv of some material through its complete cycle of production, use, disposal, and reclamation, hack to its initial state. In thermodvnamics. the overall thermal efficiency is defined as the iatio of "seful work performed hv such as a boiler and steam engine. .asvstem. - to the total input energy. Let us review briefly a basic tool of elementary thermodvnamics, the temperature entropy, or T-S diagram. As an example, the well-known T-S diagram for water is given in Figure 1,showing the process cycle of steam used to drive a turbine, condensed, and returned to the boiler for reuse. The total energy put into the system is the cumulative T S product, in Cal/g, for increasing entropy. The energy given up by the svstem as heat losses and friction is also eiven hv the cumilative T S product, hut for decreasing entropy, a i d is aronortional to area L (for loss) in Fieure 1.The useful work hoie by the system s k h as driving a generator or other machinery, is equal to the difference, area W (for work) on the T-S diagram. The total energy input to the system is proportional to the combined area (W L), and the overall thermal efficiency is equal to W/(W L). The ultimate design objective of such a system is to maximize W/(W L) for more economic performance, by rejecting heat from the system a t the lowest possible temperatures. Note the units of entropy, Cal/g-°C. This is a measure of energy per potential for a unit mass of substance. Temperature, in the case of steam, is the measure of potential for doing work. The entropy change between any two points (assuming no phase change) is evaluated by the relation: ~~~
~
.
~~
~~~
~
~
-
~~.
+
+
+
at constant volume, or AS = C, In (T2/T1) a t constant pressure, where C, or C , are heat capacities, Callg-'C. Next, to denart from eneineerine" units. consider the eeneral definition of entropy given by the astronomer and physicist: a measure of the deeree of disorder in a svstem. Anv collection of objects-such as atoms, galaxies, or empty heer cans-has a ereater entroav when wread randomlv into a larger available space thanif more concentrated. 0;a substance usually has ereater entropy when diffused through another medium t h a n in its concentrated form. For example, a ton of empty aluminum beer cans has a far higher entropy when spread along 10 miles of beach and highway, or mixed into 100 tons of refuse in a municipal landfill, than when in a neat pile
-
-
ENTROPY: CalIGrn "C
Figure 1. Temperature-entropy diagram for water,
awaiting reclamation. Is it then possible to evaluate this entropy numerically, as has been done in the case of water on the T-S chart of Figure I? To demonstrate this possibility, the specific example of aluminum has been selected. For aluminum. marketed and wasted in the form of heer cans, a possible value entropy, or V-S, diagram is shown in Fieure 2. Its validity deaends upon definingthe coordinates inecodynamic unks analogoub to thermodynamicunits of temperature and entropy. Value is a measure of a substance's potential to accomplish some economically useful purpose, and is easily quantified as simply the going market value of a commodity at any point around its use cycle. In the case of waste materials, their value is negative, and can be approximated by the cost of disposal. T o gather up or sort out discarded cans from the above high entropy states would require work, measurable in manhours, horsepower, Btu, calories, or the dollar equivalent of each. Numerically, the entropy change between any two points can be approximated by the relation: AS = C In (V,/V,)
(2)
Where VI and Vy are the initial and final values and Cis the cost ot effecting thechange, i l l S. S,g. It is inlportant to keep in mind the diilinction between S,,dollars ot value or price, and ,$, the dollar equivalent of man-hours and/or calories of work done. Note that eq 2 is analogous to the thermodynamic expression defining entropy. To apply eq 2 requires some reference datum of value, a t or below the lowest value that can occur around a closed cycle. In the case of solid waste components, this could be Volume 65
Number 12 December 1968
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of technology to solid waste presenting a disposal problem. At this point, the heer drinker can do any of several things with his empty can: (71 He may desecrate a beach or roadside with it. This represents the maximum possible drstribution, or mrnimum concentration in cans or tuns per square mile, and thus the maxim~rmentrop!. (8) He may commit the empty heer can to his garbage can. Its negative value thus decreases slightly. The entropy may increase by virtue of admixture with other household solid waste or decrease by virtue of increased concentration, in cans per cubic foot. The latter is assumed here. (9) As an alternative. he can nut the can in a box and save it for reclamation. At this point, the cans still have a slight nrgauve value, since their p0sit:Vr \,nllle only applies at a r?demption crnter. \Vhile piled in the consumer's garagr, thry till conititute a disposal problem. (10,ll) The consumer receives the value of his empty cans, about $2M)/tan (in 1973), by hauling them to the redemption center, from which they are further transported and processed to aluminum ingots. The cycle is thus closed. The areas L and Ware defined, establishing the overall economic efficiency of a cycle. ~
Empty Can in C0nrum.r'~ Hand
Lit1.r
ENTROPY
On Rodrid. or B m r h
$JAVE
Figure 2. Value-entropy diagram for closed aluminum cycle.
based on the cost of eatherine un refuse spread over the area inhabited by the populationgenerating it. This amounts to the cumulative man-seconds actually spent in filling and emptying waste baskets, ash trays,-a& kitchen ga;bage cans, raking yards, and clearing tables after meals. While this sounds like units of work, ,$, it also serves to define the value, in $, placed upon the absence of waste in a household. A good approximation of this value would he the costltonl acre of collecting refuse over parks, fairgrounds, and sports arenas. This evaluation has not been carried out, however, and for purposes of illustration, the value coordinate of Figure 2 is expressed with respect t o zero in real prices. Since numerical evaluation of entropy and most value points on Figure 2 has not yet been undertaken, the abscissa is not given values. The sequence of steps around the closed cycle of Figure 2, starting with ingots of aluminum, is as follows: (1) Aluminum is shipped to a can factory and formed into cans. Work is done to effect an increase in value. While the ingots are moved, the finished product is stillgeographicallyconcentrated, say in tons per acre of warehouse space. Its volume occupied, however, is shared by cartons and pallets, resulting in a slightly higher entropy through dilution. (2) The cans are transferred to a brewery and filled with beer. Though occupying the same volume, the aluminum is now "mixed" with the heer and cardboard six-packs, as well as cartons and pallets, giving it astill greater entropy. Thevalue of the can alone,once filled with beer and sealed, is a matter of the brewery's internal accounting. It issimply thevalue charged bythe brewer for holding the beer together, which will be something in excess of the cost of handling, filling, and sealing the cans. (3-5) Canned beer is distributed to wholesaler, retailer, and consumer. The decreasing density, say in tons of aluminum or cans per square mile, represents a major entropy increase. It is through this part of the cycle that most of the economically useful work of the cycle is done; ie., profit made. The value of the can, to the consumer, is taken as the difference between the cost of the can of heer and the cost of the same ouantitv of tao brrr. On this basis. R CUTSOT). S U ~ V C can) wrighrs .~ nnd prmr of hrrr in cnnr versus k e p in 197:l showrd the rnnr I < >haw s value of S3,'00 per tun at the rctsil cuut~tcr! (61 The cmaunwr opens the ran and drinks his brrr. With this nct the can undergwa wntroprr devaluation from a usef~dpruduct ~
1046
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The aluminum producer has gotten a bargain if the cost of sten I I, reclamation and reprocessing, is less than the cost of exGact'ion of virgin aluminum from bauxite ore. The entropy of aluminum in bauxite ore is quite high by virtue of being mixed and chemically combined with other elements. It is easily evaluated, however, from the costs of processing. In step 10, a time-and-motion study of the consumer would reveal extreme inefficiency in terms of cumulative manhours per ton delivered to the redemption center, as well as in tons per vehicle mile. Now consider the more usual destiny of an empty beer can following step 8. It is picked up by a municipal refuse collection truck and hauled to a landfill for disposal, either directly or via a transfer station. These activities are designated as steps 12 and 13. The negative value of discarded cans was based upon the refuse disposal cost per ton for a typical California community in the early '70's, which was on the order of $20 to $25 per ton. Although the cans are still mixed throughout the solid waste, the entropy is decreased by virtue of geoeranhical concentration. from the area of collection to t h a i ofon; day's addition to a landfill site. The value of waste materials in a landfill is still shown as slightly negative in Figure 2, due to limitations imposed on later use of the real estate. T o close the cycle after step 13 requires processes to reclaim aluminum from whole municipal solid waste. T o date, such processes have proven generally uneconomical. In addition to simple hand-sorting operations, these include the Hvdranulner n r o ~ e s s .which ~ has demonstrated technical -,~~a feasibility of reducing solid waste to a fluid pulp to reclaim its 40 to 60%nauer content. and wotentiallvother reclamates from the residues. Based on laboratory results, a dry p n x w s built around the Z~eraeAlr Classii~erdevelourd bv Stanfurd Research 1nstituteC3&pears technically feasible for separation of several major components of municipal solid waste. The chances of economic success for any multiproduct reclamation system are a t present severely limited by three major factors: ~~L~
~
~A~
~
~
~
..
(1) Virginmaterials are still plentiful and cheap enough so that the
secondary materials markets are easily saturated. (21 So single reclam~tecould economi~allysustain n wphiitirated
process requiring wveral millivn dollars of inrunl invertmrnl. Thus, any such operatiun, rcprvuenterl hy step 14 m Figure 2.
' Franr, M. Compost Sci. 1970, a4).
Boettcher. R. A. Air Classification for Reclamation of Solid Wastes. Stanford Research Institute: Irvine. CA. 1970. Environmental Protection Agency. Air Classification of Solid Wastes-Performance of ~xoerimentaiUnits and Potential Application for Solid Waste ~eclamation;1972.
must be a joint venture of the paper, aluminum, glass, scrap iron, and perhaps compost industries. (3) The risk to the invested developmental capital by each contributing industry is compounded by its dependence on the success of each of the others. As an example of how entropy changes can be numerically evaluated, consider AS for steps 12 and 13 combined, using value reference datum of -$I00 per ton. If we assume the cost of refuse in a landfill to b e approximately zero, the entropy decrease of disposal is
a
AS = C In (V,lV,) = 25 ln (100175) = 7.13 $,I$, ton
(3)
Here the cost of collection, C, was used to establish the value before collection. Similarly, to evaluate AS for step 10, consider the initial value of scrap cans in the beer-drinker's garage to be approximately 0. If he hauls a 500-pound load of empties 20 miles to a redemption center, a t a standard 106 per mile (in 1973), using an hour of his time a t a minimal $2.00, the entropy decrease for reclamation is
+
AS = [(LOO 4.00) In (300/100)]/(500/2M)0)= 26.4 $,&/$,ton (4)
Note that AS for this step can varv. ereatlv e the - - d e-~ e n d i n on consumer's load of cans and distance to drive. The selection of aluminum for the V-S cycle of Figure 2 was an arbitrary one. Essentially similar diagrams could describe the use cycle of tinned steel cans or glass containers. In the case of glass reclaimed from whole municipal solid waste, there would be one more fairly expensive step required to isolate glass of a single color suitable for reuse in c o n t a i n e ~ sIn . ~the case of paper, the problem is complicated by the mixing of many grades, and partial degradation of fiber quality through each use cycle. Aluminum in the form of foil would have a V-S diagramonly slightly different from Figure 2. The same approach may be applied to water resources to evaluate alternative seauences of sewage - treatment and aquifer recharging for reclamation. While discussion of nrocess techniaues to close the loop is beyond the scope of this work, the-overall value of skch processing steps-even though economically unfeasible themselves-is demonstrated by the thermodynamics of the closed cvcle. If aeneral reclamation of materials is to he practiced, to ioiserve either resources or environmental auality, the greatest efficiency for the system as a whole can be achieved by investing reclamation efforts in waste materi-
als a t their lowest value. This is analogous to the thermodynamic principle that the greatest overall mechanical efficiency is achieved by rejecting heat from the system (i.e.. investing the effort of condensing steam to a lower entropy state) at the lowest posvible temperature. Since the basic laws of thermodynamics are presumed applicable to all pn)cesses involving transfers of energy, any process sequence in which identifiable unit amountsofa suhstance can be traced arounda cvcle to their initialstate for somedefinableuverall purpose may be subjected to the basic criterion of overall thermal efficiency. And, in practical economic terms, any transfer of energy may be expressed as a cost. While the approach presented here is preliminary, i t is predicted that numerical evaluation of the entropy a t all points around the V-S diagram for any substance willconfirm it to be in roughly inverse proportion to the geographical concentration (weightlarea) and to the degree of purity (weight or volume fraction) when mixed with other substances. The potential value of a valid V-S diagram for any substance will be an indication of the relative feasibility of alternative schemes for large scale reclamation of the substance. In the case of aluminum, the area bounded by the alternate reclamation routes in Figure 2 (steps 9 and 10, versus stens 8.12. and 14) is relatively small compared with the area bounded by the entire closed cycle. hi his hecause of the hiah value ($200 to $3,700 per ton1 of the product at most points around its use cycle. In the case of paper, where the value of secondary fiber stock varies between 0 and $20 per ton, while the newsprint made from i t is still under $150 per ton, the difference in the overall thermal efficiency of collection drives versus reclamation from municipal solid waste may be of major importance. At oresent. all schemes for laree-scale reclamation of wastes involve some form of government subsidy, in the form of municinal collection costs. and aenerallv federal research or demonkration grants. while the profit motive is adem a t e to optimize each of the private operations around a closed resource cycle, the funding required to close the cvcle should be allocated in such a way as to maximize the overall cycle efficiency in serving the economic system as a whole. Hauserman, W. 6. Air Separation of Glass from Municipal Solid Waste Stanford Research Institute: Irvine, CA, 1970.
Pittsburgh Conference Memorial National College Grants Award Program 1989 The Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Inc., and its cosponsoring technical societies, the Spectroscopy Society of Pittsburgh (SSP) and The Society for Analytical Chemists of Pittsburgh (SACP), announce the 16th vear of fundine of the Pittsbureh Conference Memorial National Colleee Grants Award Proeram. ~ the ourchaseof scientific eauioment. audio-visual or other teachine.. aids.. aidlor Awards are made t d s m a ~eo1leees"for . . library mnterinli for use rn the teaching uf science at the undergraduate lwei. Hased on submitted pn,posali, st least 10 colleges will be selected tu receive awards (53.000 maximum).To b~ eligible for an award, schools must meet the following criteria: (1) Enrollment must not exceed 2,500 students. (2) No more than 25% of operating budgets may come from national or state governments. Two-year community colleges sponsored by political subdivisions of a state are not bound by criteria 1and 2. (3) Requests for materials to be used only for research purposes shall not he funded. (4) Awards may be used as a part of a "Matching Grant" program for undergraduate studies as described above. Generating "MATCHING FUNDS" is recommended. (5) Previous awardee schools are not eligible for an award for a three-year period following receiving a PCMNCG award. Interested faculty members are urged to participate by completing an application form and submitting it along with a proposal (original and three copies of each), by March 1, 1989, to John A. Queiser, The Pittsburgh Conference, Inc., 12 Federal Drive, Pittsburgh, PA 15235. For applicationlproposal forms write to Pittsburgh Conferenceat address ahove. ~
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Number 12 December 1988
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