37 Source Reduction RED


Define and discuss the differences among the following terms:

1. Pollution prevention

2. Pollution control

3. Waste minimization


1. Pollution Prevention: Pollution prevention refers to the reduction or prevention of pollutant generation at the source. This concept was first defined as "waste minimization," but waste minimization can refer to methods that reduce the volume of waste after it is generated. In contrast, pollution prevention implies prevention of waste before it is generated.

2. Pollution Control: Pollution control refers to "downstream" reduction of pollution, i.e., treatment of process streams after waste has been generated. Frequently, pollution control simply may involve the transfer pollutant from one medium to another (e.g., air pollutants to waste water).

3. Waste Minimization: Waste minimization was defined by the Environmental Protection Agency (EPA) in its 1986 report to Congress (EPA/530-SW-86-033) as: "The reduction, to the extent feasible, of hazardous waste that is generated or subsequently treated, stored, or disposed of. It includes any source reduction or recycling activity undertaken by a generator that results in either:

a. The reduction of total volume or quantity of hazardous waste.

b. The reduction of toxicity of hazardous waste.

c. Or both (a) and (b), so long as such reduction is consistent with the goal of minimizing present and future threats to human health and the environment."


The major components of a company's source reduction program include the following:

1. Management commitment

2. Communication of the program to the rest of the company

3. Waste audits

4. Cost/benefit analysis

5. Implementation of the program

6. Follow-up

Describe each of these general principles necessary for a successful pollution prevention program involving source reduction.


1. Management Commitment: Gaining the approval and support of top management is vital to the success of the source reduction plan. It will be necessary to educate management about the pollution prevention program and its benefits through seminars and meetings.

2. Communication of Program to the Rest of the Company: Those in the best position to make suggestions as to where process improvements can be made are middle managers and employees with direct process line experience. In addition, a monetary incentive and corporate recognition of employees for practical source reduction ideas will also be effective.

3. Waste Audits: The company must identify the processes, the products, and the waste streams in which (hazardous) chemicals are used. Mass balances of specific (hazardous) chemicals will help to identify source reduction opportunities. Engineering interns could be very valuable in conducting such audits. An outside person can achieve significant progress in this area as well, due to the fact that he or she may be able to cut through some of the management and personnel barriers of the industry.

4. Cost/Benefit Analysis: Since any change or modification in the process requires additional capital, operation, and maintenance cost, a cost analysis must be included to help management make informed decisions. These factors may include cost avoidance, enhanced productivity, and decreased liability risks from the pollution prevention effort. Federal and state agencies have provided matching grants to small industries to implement source reduction programs.

5. Implementation of Source Reduction Programs: An impediment for the implementation of the source reduction program is a resistance to change by management and employees. People known to resist new ideas and changes


in the company must be included in the planning stages of the program. The CEO must be convinced of the merits of the program and must fully support the implementation of it.

6. Follow-up: Reduced energy costs, reduced raw materials, and reduced waste disposal fees must be tracked and communicated to the company personnel. This information will be very useful in the filing of the company's waste manifest and biennial reports on its source reduction efforts. In addition, this information will convince employees and management that pollution prevention programs, in general, make sense environmentally as well as economically.

The legislation enacted under the Clean Air Act Amendments of 1977 provided the foundation for EPA's controlled-trading program, the essential elements of which include:

1. Bubble policy [or bubble exemption under Prevention of Significant Deterioration (PSD)]. The bubble policy was under the state implementation plans (SIP) first. PSD does not allow bubbles; it only allows netting.

2. Offsets policy (under nonattainment).

3. Banking and brokerage (under nonattainment).

While these different policies vary broadly in form, their objective is essentially the same: to substitute flexible economic-incentive systems for the rigid, technology-based regulations that specify exactly how companies must comply. Although still not fully developed, these market mechanisms could make regulating easier for EPA and less burdensome and costly for industry.

Note: Additional details on pollution prevention, and source reduction in particular, are available in the text/reference book, Pollution Prevention, Dupont and co-workers (CRC Press, Boca Raton, FL, 2000).


Consider a degreasing operation in a metal finishing process. Give an example of process modification that might be made to this part of the process that would represent source reduction.


Degreasing or solvent metal cleaning employs nonaqueous solvents to remove soils from the surface of metal articles that are to be electroplated, painted, repaired, inspected, assembled, or further machined. Metal work pieces are cleaned with organic solvents because water or detergent solutions exhibit a slow drying rate, electrical conductivity, high surface tension, a tendency to cause rusting, and a relatively low solubility for organic soils such as greases. A broad spectrum of organic solvents is available, such as petroleum distillates, chlorinated hydrocarbons, ketones, and alcohols. Although solvents may vary, there are basically three types of degreasers: cold cleaners, open-top vapor degreasers, and conveyorized degreasers. A description of these three degreasing processes follows.

Cold cleaners are the simplest, least expensive, and most common type of degreaser. They are used for the removal of oil-base impurities from metal parts in a batch-load procedure that can include spraying, brushing, flushing, and immersion. The cleaning solvent is generally at room temperature. Although it may be heated slightly, the solvent never reaches its boiling point. When parts are soaked to facilitate cleaning, it is not uncommon for the solvent to be agitated by pumps, compressed air, mechanical motion, or sound. There are several methods for materials handling in cold cleaning operations. Manual loading is used for simple, small-scale cleaning operations. Batch-loaded conveyorized systems are more efficient for complex, large-scale operations. Loading systems can be set to automatically lower, pause, and raise a workload. By dipping in a series of tanks, each with increasingly pure solvent or possibly a different solvent, a "cascade" cleaning system is established.

The open-top vapor degreaser cleans by condensing vaporized solvent on the surface of the metal parts. The soiled parts are batch loaded into the solvent vapor zone of the unit. Solvent vapors condense on the cooler surface of the metal parts until the temperature of the metal approaches the boiling point of the solvent. The condensing solvent dissolves oil and grease, washing the parts as it drips down into the tank. Sometimes the cleaning process is modified with spraying or dipping. To condense rising vapors and prevent solvent loss, the air layer or freeboard above the vapor zone is cooled by a series of condensing coils that ring the internal wall of the unit. Most vapor degreasers also have an external water jacket that cools the freeboard to prevent convection up hot degreaser walls. The freeboard protects the solvent vapor zone from disturbance caused by air movement around the equipment.

Conveyorized degreasers operate on the same principles as open-top degreasers; the only difference is the materials handling. In conveyorized cleaners, parts may be dipped but manual handling is mostly eliminated. In addition, conveyorized degreasers are almost always hooded or covered. There are many designs for conveyorized degreasers. These include monorail, cross-rod, vibra, ferris wheel, belt, and strip degreasers. Each conveying operation can be used with either cold or vaporized solvent. The first four designs listed above usually employ vaporized solvent. Conveyorized degreasers are used in a wide range of applications and are typically found in plants where there is enough production to provide a continuous stream of products to be degreased.

An example of a process modification is the substitution of a different, nontoxic or nonpolluting solvent. For example, a citric-acid-based solvent could replace a toxic solvent such as 1,1,1-trichloroethane (TCE).


Perchloroethylene (PCE) is utilized in a degreasing operation and is lost from the process via evaporation from the degreasing tank. This degreasing process has an emission factor (estimated emission rate/unit measure of production) of 0.78 lb PCE released per lb PCE entering the degreasing operation. The PCE entering the degreaser is made up of recycled PCE from a solvent recovery operation plus a fresh PCE makeup. The solvent recovery system is 75% efficient, with the 25% reject going offsite for disposal. (Adopted from EPA 560/4-88-002, December 1987, "Eliminating Releases and Waste Treatment Efficiencies for the Toxic Chemical Release Inventory Form," Office of Pesticides and Toxic Substances, Washington DC).

1. Draw a flow diagram for the process.

2. Develop a mass balance around the degreaser.

3. Develop a mass balance around the solvent recovery system.

4. Develop a mass balance around the entire system.

5. Determine the mass of PCE emitted per pound of fresh PCE utilized.

Quantify the impact of the emission factor in the degreasing operation on the flowrates within the solvent recovery unit.


1. A flow diagram for the system is provided in Figure 103.

PCE Emissions t _

PCE Emissions












Figure 103. Flow diagram for Problem RED.4.

Recovered PCE

Figure 103. Flow diagram for Problem RED.4.

2. Assume a basis of 1 lb of fresh PCE feed. A PCE mass balance around the degreasing tank can now be written for the unit pictured in Figure 104.

0.78(1 +X) Ib PCE Emissions

1 Ib

Fresh PCE

Degreasing Tank

Spent Emissions


Recovered PCE

Figure 104. PCE mass balance around degreasing tank.

Output = PCE emissions + Spent PCE = 0.78(1 +X) + Spent PCE

Equating the input with the output gives

3. A PCE mass balance around the solvent recovery unit is shown in Figure 105.

Output = Recycle PCE + Reject PCE


Recycle PCE = 75% of spent PCE

0.22(1 +X) lb


0.055+0.055X Ib



Reject "



„ Xlb

Figure 105. PCE mass balance around solvent recovery unit.

Figure 105. PCE mass balance around solvent recovery unit.



Input = Output 0.22(1 + X) = 0.75[0.22(1 +X)] + Reject PCE Reject PCE = (1 - 0.75)[0.22(1 +X)] = 0.055 + 0.055^ lb

4. PCE mass balance around the entire system is shown in Figure 106.

Input = 1 lb PCE Output = PCE emissions + Spent PCE


Input = Output 1 lb PCE = (0.78 + 0.78X) + (0.055 + 0.055X) = 0.835 + 0.835X X = 0.165/0.835

5. From the flow diagram in Figure 106,

= 0.94 lb PCE emitted per lb fresh PCE

Fresh PCE 1 lb

PCE Emissions 0.78(1 +X) lb

Degreasing Tank

Solvent Recovery

Reject PCE 0.055+0.055X lb

Recovered PCE X lb

Figure 106.

PCE mass balance around entire system.

If the emission factor were lower, the flowrates to the solvent recovery unit and the recycle stream would be higher. Additionally, there would be less PCE lost from the system. To determine the effect of the emissions factor on the system flow streams, the equations above were solved using three different emission factors: 0.78, 0.60, and 0.40. These results are summarized below.

Emission Factor




Fresh PCE




Recovered PCE




Spent PCE




PCE emissions




Reject PCE




The sum of the recovered and fresh PCE provides a measure of the degreasing capability of the system per kilogram feed. Notice that, as the emission factors decrease, this sum goes up significantly.


Surface coating entails the deposition of a solid film on a surface through the application of a coating material such as paint, lacquer, or varnish. Surface-coating operations are significant volatile organic compound (VOC) emission sources. Most coatings contain VOCs, which evaporate during the coating application and curing processes, rather than becoming part of the dry film.

The use of the following expressions will help solve many of the coating calculations.

1. Emission factor (EF) in reasonable available control technology (RACT) units of lb VOC/gal H20.

1 — ws where EF = emission factor, lb VOC/gal H20

v = volume fraction of organic volatiles in solvent w = volume fraction of H20 in solvent s = volume fraction of solvent in the paint py = density of organic volatiles, lb/gal

2. Emission factor on a solids basis (lb VOC/gal solids).


where EF' is the emission factor, lb VOC/gal solids. 3. Percent emission reduction:

where EForig = emission factor on a solids basis for original coating

EFrep = emission factor on a solids basis for replacement coating

Using the equations above, determine the emission factors EF and EF' for an organic solvent-borne coating that contains 40% organic solvent having a density of 7.361b/gal. Also determine the emission factors EF and EF' for a waterborne coating containing 65% solvent with 80% of the solvent being water. The density of the organic portion of the solvent is 7.36Ib/gal. Finally, calculate the percent reduction in volatile organic emissions achieved by switching from the solvent-borne to the waterborne coating.


The emission factor, EF, for the organic solvent-borne coating in lb/gal H20 is first calculated:

The emission factor, EF', for the organic solvent-borne coating in lb/gal solids is

Similarly, the emission factor, EF, for the waterborne coating in lb/gal H20 is

EF = (0.2)(0.65)(7.36)/[l - (0.80)(0.65)] = 1.99 lb/gal H20

and the emission factor, EF', for the waterborne coating in lb /gal solids is

EF' = (0.20)(0.65)(7.36)/(l - 0.65) = 2.73 lb/gal solids

The percent reduction achieved in VOC emissions by switching from the solventborne to the waterborne coating is then

% reduction = 100(EF;rig - EF^/EF^ = 100(4.91 -2.73)/4.91 = 44.4%

The reader should note that the same volume of coating solids must be deposited on an object to coat it to a desired film thickness regardless of the type of coating or volatile organic compound content of the coating used. Solids make the film. Volatiles (VOC, water, and nonphotochemically reactive solvents) evaporate. For example, 4 gal of a 25 vol % solids coating must be used to get 1 gal of coating solids. However, only 2 gal of a 50 vol % solids coating must be used to get 1 gal of coating solids. This means that twice as much "work" can be done with a gallon of 50 vol % solids coating than with a gallon of 25 vol % solids coating, i.e., twice as many gallons of 25% solids coating are needed than gallons of 50% solids coating to do the same job.


Metal furniture coating involves the application of prime and top coatings to any piece of metal furniture or any metal part that will be assembled with other metal, wood, fabric, plastic, or glass parts to form a furniture piece. Most metal furniture is finished with a single coat. However, some furniture pieces require a prime coat application. The prime coat is applied by electrostatic spraying, conventional spraying, dipping, or flowcoating techniques. The topcoat of a single coat is also applied by spraying, dipping, or flow-coating techniques.

EPA's Control Technology Guide (CTG) document recommends a single emission limit for metal furniture coating applications. This limit is based on the use of low organic solvent-borne coatings. These coatings include waterborne, high solids, electrodeposition, and powder coatings. The limit can also be met by the installation of add-on control equipment. To comply with the limit, 80% of the VOC solvent vapor emitted from the application of conventional coatings must be destroyed (using an afterburner) or recovered (using a carbon adsorption unit).

An existing metal furniture coating operation uses a coating with a VOC content of 4.5 lb/gal of coating minus water (lb/gal H20). The process utilizes a new minibell automatic electrostatic spray system recently purchased as part of a pollution prevention program that has a transfer efficiency of 80%. The allowable VOC content of the coating is 3.01b VOC/gal H20. The reasonable available control technology (RACT) transfer efficiency is 30%. Does the operation meet the equivalency requirements and is it operating in compliance with air quality


regulations? If in compliance, how much credit could be given for a bubble or offset? The density of the VOC (solvent) is 7.36 lb/gal.


Calculate the lb VOC/gal solids for the coating presently in use employing the equation provided in Problem RED.5.

The lb VOC/gal solids for the RACT coating is similarly calculated:

The lb VOC/gal solids applied for the coating presently in use is

= 14.5 lb VOC/gal solids applied

The lb VOC/gal solids applied for the RACT coating is

= 16.9 lb VOC/gal solids applied

Thus, the coating line is in compliance. The credit available is

Credit = RACT coating — Coating in use = 16.9 - 14.5

= 2.4 lb VOC/gal solids applied

When spray guns are used to apply coatings, much of the coating material either bounces off the surface being coated or misses it altogether. Transfer efficiency (TE) is the ratio of the amount of coating solids deposited on the coated part to the amount of coating solids used. Regardless of the TE, all of the VOCs in the dispensed coating are emitted whether or not the coating actually reaches and adheres to the surface. Consequently, improved TE can reduce VOC emissions because less coating material is used.


An automobile coating facility utilizes a prime coat and topcoat operation. The prime coat has a VOC content of 2.75 lb VOC/(gal H20) at 100% transfer efficiency using a dip coating operation. The top coat has a VOC content of 4.25 lb VOC/(gal H20), is equipped with minibell electrostatic sprays, and operates with a transfer efficiency of 80%. The topcoat has an allowable VOC content of 2.841b VOC/(gal H20). The state implementation plans (SIP) assumed that the transfer efficiency is 30%. The prime coat has an allowable VOC content of 1.92 lb VOC/(gal H20). The prime coat transfer efficiency is 100%. The plant processes 50 cars per hour with a paint usage of 1.5 gal/car for prime coat and 1.0 gal/car for topcoat. Since the prime coat is not in compliance, the company has requested a bubble determination. As a regulatory official, you are asked to determine if the company has a viable bubble. Assume the density of the VOC is 7.36 lb/gal; in addition, the paint contains no water. Also indicate source reduction measures that can be taken to reduce emissions.


The actual emissions for the prime coat, ep, in lb VOC/h is

Similarly, the actual emissions for the topcoat, et, in lb VOC/h is

The total actual emissions becomes etot — ep + et


The emission factor on a solids basis, EF', for the prime coat (p) is

EFp = 1.92/[1 -(1.92/7.36)] = 2.60 lb VOC/gal solids

Similarly, the emission factor on a solids basis for the topcoat (t) is

EF; = 2.84/[l - (2.84/7.36)] = 4.62 lb VOC/gal solids

The fraction of solids in each coating, /, may now be calculated:

The allowable emissions, E, in lb VOC/h for the prime coat is

Ep = (EFp)( /pX1.5 gal/car)(50 car/h)/1.0 = (2.60)(0.626)(75) = 122.0 lb/h

Similarly, the allowable emissions for the topcoat is

Et = (EFt')( /,)(1.0 gal/car)(50 car/h)(0.8)/0.3 = (4.62)(0.423)(133.3) = 260.5 lb/h

Finally, the total allowable emissions in lb VOC/h becomes

Since 418.72 is greater than 382.5, the company does not have a viable bubble.

The bubble concept was formally proposed as EPA policy on January 18, 1979, with the final policy statement being issued on December 11, 1979. The bubble policy allows a company to find the most efficient way to control the emissions of a plant as a whole rather than by meeting individual point-source requirements. If it is found less expensive to tighten controls of a pollutant at one point and relax controls at another, this would be possible as long as the total pollution from the plant would not exceed the sum of the current limits on individual point sources of pollution in the plant. Properly applied, this approach would promote greater economic efficiency and increased technological innovation.

There are some restrictions, however, in applying the bubble concept:

1. The bubble may only be used for pollutants in an area where the state implementation plan has an approved schedule to meet air quality standards for that pollutant.

2. The alternatives used must ensure that air quality standards will be met.

3. Emissions must be quantifiable, and trades among them must be even. Each emission point must have a specific emission limit, and that limit must be tied to enforceable testing techniques.

4. Only pollutants of the same type may be traded, that is, particulates for particulates, hydrocarbons for hydrocarbons, etc.

5. Control of hazardous pollutants cannot be relaxed through trades with less toxic pollutants.

6. Development of the bubble plan cannot delay enforcement of federal and state requirements.

Some additional considerations must be noted:

1. The bubble may cover more than one plant within the same area.

2. In some circumstances, states may consider trading open dust emissions for particulates (although EPA warns that this type of trading will be difficult).

3. EPA may approve compliance-date extensions in special cases. For example, a source may obtain a delay in a compliance schedule to install a scrubber if such a delay would have been permissible without the bubble.

Source reduction measures that can be taken to reduce emissions include using coatings with lower VOC content.


A major chemical company has recently developed a new paint for can coating that contains a replacement organic solvent (MW = 136) with a density of 9.24 lb/gal. The solids are 63% of the coating material by volume. Show that this paint cannot meet RACT emission limits of 2.79 lb VOC/gal of coating material less water (gal H20).


Although the paint does not meet RACT requirements, the company argues that this new coating material is replacing a paint that is emitting a higher volume (ppm) of VOCs to the atmosphere. As a regulatory official, you are requested to act on their request for a variance and comment on their analysis from a pollution prevention perspective. The density and molecular weight of the previous solvent were 7.36 lb/gal and 68, respectively.


The emission of the new coating material (CH) in lb VOC per gallon of coating material is

Thus, the emission of the new coating material is less than the RACT emission limit of 2.791b VOC/gal CM.

The emission of the previous solvent (pre) in lb VOC/gal CM is

Thus, the previous solvent was in compliance.

The ratio of the volumes emitted may now be calculated:

_ Pnew/MWncw

~ Ppre/MWpre

The volume emitted by the new coating material is lower since the above ratio is less than 1. This simply means that less of the new coating solvent is being emitted on a volume basis.

The example presented above is a real-world application drawn from the files of a major chemical company located in the Northeast.


An automobile manufacturer that has a past history of applying sound pollution prevention procedures to its processes has proposed to construct a plant in a nonattainment area in Pennsylvania. The required offset is to be obtained by replacing emulsion asphalt by a waterborne mix. The area has traditionally used 200,000 lb/month of medium setting emulsion asphalt. Calculate the maximum annual offset (20%) if this conversion is adopted.

State of Pennsylvania regulations for cutback asphalt are given below. Note that a 20% offset indicates that the ratio of actual emission reductions to new emissions is equal to or greater than 1.2 to 1.

VOC regulations vary from state to state. The following is an excerpt from the regulatory provision provided by the state of Pennsylvania regarding VOC usage in cutback asphalt paving:

1. After April 30, 1980, and before May 1, 1982, no person may cause, allow, or permit the mixing, storage, use, or application of cutback asphalt for paving operations except when:

a. long-life stockpile storage is necessary;

b. the use or application between October 31 and April 30 is necessary; or c. the cutback asphalt is to be used solely as a penetrating prime coat, a dust palliative, a tack coat, a precoating of aggregate, or a protective coating for concrete.

2. After April 30, 1982, no persons may cause, allow, or permit the use or application of cutback asphalt for paving operations except when:

a. long-life stockpiles are necessary;

b. the use or application between October 31 and April 30 is necessary; or c. the cutback asphalt is used solely as a tack coat, a penetrating prime coat, a dust palliative, or precoating of aggregate.

3. After April 30, 1982 emulsion asphalts may not contain more than the maximum percentage of solvent as shown in the following table:

Emulsion Grade


% Solvent, Max.


Rapid Setting



Rapid Setting (Anionic)



Rapid Setting (Cationic)



Medium Setting



Medium Setting



Slow Setting (Soft Residue)



Slow Setting (Hard Residue)



Medium Setting (High Float)


E-l 1

High Float



Medium Setting (Cationic)


Source: The provisions of Section 129.64 amended April 21, 1981, effective June 20, 1981, 11 Pa. B. 2118.

Source: The provisions of Section 129.64 amended April 21, 1981, effective June 20, 1981, 11 Pa. B. 2118.



The average amount of medium setting emulsion asphalt used by the automobile manufacturer in pounds/year, m, is m = (200,000 lb/month)(12months/yr) = 2,400,000 lb/yr

The amount of solvent used per year, m s, is ms = 0.12 m

It will be the responsibility of industry to suggest alternative control approaches and demonstrate satisfactorily that the proposal is equivalent in pollution reduction, enforceability, and environmental impact to existing individual process standards.

Offsets were the EPA's first application of the concept that one source could meet its environmental protection applications by getting another source to assume additional control actions. In nonattainment areas, pollution from a proposed new source, even one that controls its emissions to the lowest possible level, would aggravate existing violations of ambient air quality standards and trigger the statutory prohibition. The offsets policy provided these new sources with an alternative. The source could proceed with the construction plans, provided that:

1. The source would control emissions to the lowest achievable level.

2. Other sources owned by the applicant were in compliance or on an approved compliance schedule.

3. Existing sources were persuaded to reduce emissions by an amount at least equal to the pollution that the new source would add.

The maximum annual offset assuming 75% of the solvent is vaporized is therefore:

The above calculation can be rejected assuming 100% of the solvent is vaporized:

Note that cutback asphalt contains VOCs, but the waterborne mix has no VOCs. The above result indicates that, if this conversion is adopted (using the 75% vaporization adopted in the solution), a new source could operate that emits a maximum of 180,000 lb/yr.


A nickel electroplating line uses a dip-rinse tank to remove excess plating metals from the parts. Currently, a single tank is used that requires R gal/h of fresh rinse water to clean F parts/h (see Figure 107). Assume the cleaning is governed by the following equilibrium relation:

fi ounces of metal residue/part r, ounces of metal residue/gal bath

1. Calculate the reduction in rinse water flowrate (a pollution prevention measure) if a two-stage countercurrent rinse tank is used (as compared to the single-stage unit), and 99% of the residue must be removed. Assume the drag-out volume is negligible.

2. Has the total metal content of the exit rinse water been altered? Discuss implications for further wastewater treatment/reuse.


Using the flow diagram provided in Figure 107, a material balance for the residue may be written:

This equation may be rearranged in terms of X. For the single-stage operation, set i= 1:

Figure 107. Flow diagram for one-stage operation.

Figure 107. Flow diagram for one-stage operation.

The fraction of residue removed, x, is

Now R/F may be expressed in terms of / and x:

The flow diagram for a two-stage (stage 1, stage 2) countercurrent operation is provided in Figure 108. Material balances on the residue for each stage are stage I: fmF + r2R = fxF + rxR stage 2: J\F + rmR = f2F + r2R

Each of these equations may be solved for R/F in terms of / and f[ using the defining equation for k stage 1: R/F = X{J\n -/,)/(/, -f2) stage 2: R/F = A(/, f2)/f2

If one substitutes x into the mass balance expressions,

The right-hand sides (RHS) of the stage 1 and stage 2 equations may be set equal to each other:

/,-/ta( 1-x) Ml-x) These equations may be rearranged to obtain a quadratic equation in fx: f?-[(\-x)fm]fx-W-x)fl] = Q

fin F

Figure 108. Flow diagram for 2-stage countercurrent operation.

Figure 108. Flow diagram for 2-stage countercurrent operation.

678 SOURCE REDUCTION (RED) Solving for fx yields fx = (M1 -x)± {[-/fa(l -x)]2 -4(l)x(l -x)flf-s)/2

This can be rewritten as:

/, =us»/2){l-x±[(3x+l)(l-x)J The following expression results if (1 —x) is factored out:

Only the "+ " term is physically reasonable; therefore,

The term f\ may be substituted into the stage 2 mass balance equation:

However,^ can be expressed in terms of x and fm:

This can be substituted into the above equation to yield

which reduces to

The rinse water requirements for both a single- and a two-stage countercurrent unit becomes.

I he rinse water flowrate reduction is therefore 99.0 IF - 9.46 AF

For fixed residue removal, the total mass of metals in the rinse water will be the same; with reduced water duty, the metals concentration increases. A smaller water volume now needs to be processed (or sewered). Alternatively, if the metals concentration is sufficiently high, it can be returned to the plating bath for reuse or can be recovered.

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