P. D. d'Entremont and R. H. Ross
Westinghouse Savannah River Company
Aiken, SC 29808

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In order to safety restart the 2H evaporator, plans are to add depleted uranium (DU) as uranyl carbonate to Tank 43 to lower the ²³⁵U enrichment in the supernate.¹ This memo examines the enrichment and location of uranium precipitates formed in Tank 43. An assessment of the risks associated with precipitating uranium shows that there is no criticality concern during this operation.

To ensure that all the precipitates formed are low in enrichment, plans are to begin the uranyl carbonate addition process at high addition rates. The addition system has a designed maximum rate of 38 gpm, and plans are to increase this flowrate to 60 gpm. The initial quantity of uranyl carbonate, probably the first 8,000 gallons, will be added at a high rate to ensure that any precipitated uranium (insoluble uranium) will be less than 0.96% enrichment. With a high addition rate, the ²³⁵U will be inefficiently precipitated, so the precipitate formed will be at low enrichment. After the first 8,000 gallons are added, the enrichment of all the supernate will be low, so the addition can proceed at any rate. The remainder of the uranyl carbonate will be added more slowly to ensure efficient precipitation of the remaining ²³⁵U from solution.

The assessment also considered possible malfunctions or errors that could occur during uranyl carbonate addition. It was concluded that the process is inherently safe with respect to criticality. The process is safe if the injection system malfunctions, if the Flygt mixer malfunctions, if the uranyl carbonate concentration is wrong, if the uranyl carbonate is added at the wrong time, or any combination of these malfunctions. Each of these malfunctions could prevent the supernate enrichment from being properly reduced, which would require that the process be repeated to achieve the reduction in enrichment needed to restart the 2H evaporator. But there is no set of reasonable malfunctions that would present a criticality risk in Tank 43.

The main factors that cause the process to be inherently safe are that the amount of ²³⁵U is small and it is in the form of small particles that will be dispersed. To exceed areal density limits for criticality, the estimated 1.2 kg of ²³⁵U in the supernate would have to be precipitated into an area of less than 4 square feet, which is not possible. Also, the material being added to the tank is DU, which is inherently safe with respect to criticality.

Tank 43 supernate was sampled in early 2000. At that time, the average uranium concentration was about 15 mg/l,² and the enrichment was about 3 ¹/₄% (See Appendix A). Tank 43 has about 1,060,000 gallons of supernate, so these concentrations are equivalent to a ²³⁵U inventory of about 2.0 kg.

The most recent samples from Tank 43 were taken in October 2000. Samples were taken at 201, 101, 86, 72, and 66 inches from the bottom (The current waste level is about 357 inches³ with a sludge level of about 53 inches⁴). The average uranium concentration in the samples at 201, 101, and 86 inches was about 8 mg/l with an average enrichment of 3.83% (See Appendix A).⁵ Based on these results, the soluble uranium currently in the supernate is about 1.2 kg, which is the best estimate of ²³⁵U in the supernate at this time.

The bottom two samples in October 2000 (at 72 and 66 inches) had very high concentrations of uranium, around 190 mg/l at 3.12% ²³⁵U enrichment, and iron, about 19,000 mg/l. These values are well above the solubility limits for uranium and iron at the highly alkaline conditions in Tank 43. The high results are probably due to colloidal sludge solids. This hypothesis was validated by turbidity measurements in Tank 43. On 3/2/01, a vertical scan was conducted in Tank 43 G riser using a turbidity instrument. The instrument has a light with a nearby photocell, so it actually measures the opacity of the supernate. Starting near the top of the liquid, the opacity was measured at varying increments until an opaque layer was found.

The results show that the opaque layer starts at about 69 inches.⁶ This is about the highest level at which high iron and uranium were detected in October (The intended level of the sample was 72 inches). The fact that the top of the opaque layer is within a few inches of where high iron and uranium were found in October is consistent with the hypothesis that the iron and uranium are in colloidal solids. These sludge solids are critically safe and not a concern for criticality because the iron-to-²³⁵U ratio is about 3000 The inherently safe ratio for criticality is 76 or greater.⁷ Therefore, these solids are subcritical with a wide margin of safety. Additional Tank 43 samples have been taken at 66 inches and are currently being analyzed.

Plans are to add DU as uranyl carbonate to Tank 43 to reduce the enrichment of the supernate.¹ The enrichment of the DU is about 0.2% ²³⁵U. The planned uranyl carbonate solution is 10 gm/liter of uranium and has about 4% sodium carbonate.

The reason for adding uranyl carbonate solution is that it allows the addition of highly concentrated uranium. The planned concentration is 10,000 mg/liter, or about three orders of magnitude higher than concentrations in the supernate. Thus, a relatively small amount of solution can be added that will have a large effect on the uranium enrichment of the supernate. The uranium remains soluble in the uranyl carbonate solution because of the high carbonate concentration and relatively low ionic strength. The solubility of uranium in Tank 43 supernate is much lower. Tank 43 supernate has lower carbonate concentration and higher ionic strength than the uranyl carbonate solution. The solubility of uranium is on the order of 15 mg/liter, with a range of perhaps 5 to 25 mg/liter.^8,9,10 After the two solutions mix, the uranyl carbonate solution will have a very small effect on the concentration of the much larger volume of supernate, so the solubility of the mixture will be essentially the same as supernate.

The uranyl carbonate will be added to a line that exits the addition pipe just behind the Flygt mixer. The uranyl carbonate solution will be made up in F-area by NMS&S Outside Facilities and and transported by tanker truck to H area. Each tanker truck will be connected to the unloading facilities on Tank 43, and the contents of the tanker, a few thousand gallons, will be pumped from the tanker into Tank 43. It is anticipated that the interval between tanker trucks could be a day or more. This process will continue until all of the uranyl carbonate, about 20,000 gallons, has been added. The Flygt mixer will be operated continuously until all the uranyl carbonate has been added.

The mixer is a 9,000-gpm Flygt mixer, which is essentially an underwater fan. Uranyl carbonate will be swept into the mixer along with supernate from the tank. As the mixture of uranyl carbonate and supernate contacts the blades of the mixer, the DU mixes into the supernate, reducing the supernate enrichment. At the time this memo was written, the addition system had a designed maximum rate of 38 gpm of uranyl carbonate solution.

After enough DU has been added to exceed the solubility limit for uranium in the supernate, uranium begins to precipitate as sodium diuranate. The precipitate particles will mostly be kept suspended by the Flygt mixer. By the end of the uranyl carbonate addition process, the supernate will have a considerable quantity of suspended solids that are circulating around the tank. When the Flygt mixers are turned off, these solids will slowly settle to the bottom of the tank.

The addition process has been modeled.¹¹ The model shows that the most efficient removal of ²³⁵U from the supernate occurs when the uranyl carbonate is added slowly to a well-stirred tank. Once the uranium concentration reaches saturation, a kilogram of uranium is precipitated for each kilogram of DU added.

In the bounding case of 100% efficiency, each kilogram of DU uranium precipitated has about the same enrichment as the supernate enrichment at the time that the uranium is precipitated. Thus, at the ideal case of 100% efficiency, the first kilogram precipitated will have an enrichment near the supernate enrichment when saturation is reached. The second kilogram will have a lower enrichment because some ²³⁵U was precipitated in the first kilogram. The third kilogram will have a lower enrichment, and so on.

The process has also been experimentally tested at SRTC using waste simulants in 100-ml beakers, and limited tests have been conducted with real Tank 43 supernate. In 100-ml beakers, the precipitate and supernate come to isotopic equilibrium in a few hours regardless of the addition rate, suggesting that the addition rate is not as important as suggested by the mathematical model. However, the process has never been tested on a large scale.

100% efficiency is an ideal case that will not be realized in practice. Because the uranyl carbonate is added to the tank in one spot, it will not be effectively mixed into the entire tank contents immediately, and much precipitation will occur before the DU has propagated into the tank. Also, other inefficiencies such as premature precipitation of the DU will lower the overall efficiency of the process. These inefficiencies will lower the enrichment of the precipitate.

For the purposes of this report, efficiency is defined as the effectiveness of the process compared to the ideal process of slowly adding DU to a perfectly-mixed tank. For example, 75% efficiency means that each kilogram of DU added is as effective in precipitating ²³⁵U as 0.75 kilograms of DU added to a perfectly mixed tank. At 75% efficiency, the precipitate enrichment is also reduced to 75% of the ideal case because more DU must be added to precipitate the same amount of ²³⁵U.

To reduce the enrichment of the uranium that might be precipitated without poisons, plans are to initially add the uranyl carbonate at a high flowrate, so that the initial precipitation will occur at low efficiency. Lower efficiencies decrease the initial enrichment of the precipitate.

The amount of precipitate that could be formed above 0.96% ²³⁵U enrichment was estimated using the mathematical model that was developed for the uranyl carbonate addition process.¹¹

The process was modeled at the following set of conditions:

A number of cases were considered:

• 5 gpm—This is the planned flowrate for precipitation with good efficiency. It is desirable that at least part of the precipitation be conducted at this rate to ensure that the supernate is sufficiently depleted to restart the evaporator.
• 15 gpm
• 30 gpm
• 38 gpm—At the time this report was written, this was capacity of the uranyl carbonate addition system.¹²
• 60 gpm—This is the capacity of the uranyl carbonate pump. The system could be modified to reach this capacity with relatively little impact on schedule.

The efficiency of the uranyl carbonate precipitation, assuming good mixing at the Flygt mixer, is given by¹¹

where F is the flowrate of uranium through the mixing zone

I is the injection rate of DU into the mixing zone

This formula assumes that there is very good mixing in the mixing zone, so actual performance will be lower. However, the planned method of adding the uranyl carbonate near the Flygt mixer will ensure that the mixing is fairly good, so this formula should yield a good estimate that will be slightly conservative.

For each flowrate, the addition process was modeled using the equations in Appendix B. The results of the calculation are shown in the table below and are displayed graphically in Figure 1.

The amounts of ²³⁵U shown in the rightmost column are the amounts that are precipitated before the average enrichment of the precipitate is equal to 0.96%. For example, at 5 gal/min the average enrichment of all the uranium precipitated will be 0.96% when 1.11 kg of ²³⁵U have been precipitated. Note that 115.5 kg of DU was added to reach this point, so (115.5 kg)·(0.002) = 0.23 kg of the ²³⁵U came from the DU that was added.

A more conservative case is presented in Appendix C. In this case, the supernate is assumed to have a uranium concentration and isotopics similar to early 2000, i.e. 15 mg/liter uranium and 3.25% enrichment. In this case, 40.7 gpm is the break point at which the first precipitate produced is exactly 0.96% ²³⁵U enrichment.

After the initial fast addition of uranyl carbonate to Tank 43, it is desirable to add uranyl carbonate more slowly. Although the projections up to now have assumed fast mixing of all the supernate in the tank, in reality the Flygt mixer will require some time to mix the supernate, perhaps as much as a day to reach all portions of the tank. When the uranyl carbonate is added fast there may be portions of the tank that are not well depleted.

For example, when uranyl carbonate is added at 60 gpm, a 4,000-gallon tank truck would be emptied in 67 minutes, about an hour. Good mixing of the tank with the Flygt mixer is expected to occur on the time scale of hours.¹³ This is not a concern with regards to precipitate enrichment, because less-than-perfect mixing decreases the precipitate enrichment. But the slow mixing time makes it difficult to lower the supernate enrichment as much as possible, which is the primary purpose of the uranyl carbonate addition.

As long as the Flygt mixer is operating, most of the uranium solids will remain in suspension, forming a "cloud" of solids that circulates around the tank. Recent experiments have shown that in a well-mixed 100-ml beaker the solids and the supernate reach isotopic equilibrium in a matter of hours, i.e. the solids and the supernate are at about the same enrichment.

Figure 2 shows the enrichment of the supernate and the solids assuming isotopic equilibrium. Note that after about 3200 gallons of uranyl carbonate solution added, the enrichment of the supernate (and the average enrichment of the precipitate) is about 0.96%. For conservatism, it is acceptable to begin slow additions after about 8,000 gallons of uranyl carbonate added. At this time, the enrichment of the supernate should be near 0.5%.

Plans are to add uranyl carbonate at high rate, probably 60 gpm. However, it is possible that the addition rate could be lower, through an accidental condition or because of operator error. At a slow addition rate it is possible that a small quantity of ²³⁵U would be precipitated at an enrichment higher than 0.96%. However, the amount of ²³⁵U that would be precipitated is small enough so that this is not a safety concern. The next few sections address this concern in addition to other malfunctions that might occur during the addition process. the possibility of failure of the Flygt mixer.

Laboratory experiments show that sodium diuranate solids are small and easily suspended. In studies conducted in the early 1990s on sodium diuranate precipitates forming in supernate, the maximum settling rate was calculated to be 3-4 feet per day, with a range of 0.25 to 4 feet per day.¹⁴ Such particles are easily kept suspended by mild agitation and will require days to weeks to settle in a million-gallon tank. In the last few months, experiments were performed in which depleted uranyl carbonate was added to simulated supernate solutions. Although settling rates were not measured as part of this experiment, experimenters noted that the solids were easily suspended with slow agitation and required about a day to settle in a 100-ml beaker.¹⁵

Such particles will be easily kept in suspension by the Flygt mixer and will take a number of days to settle in a million-gallon waste tank. When they eventually settle, they will form a light dusting of solids on the sludge surface. Also, because of the mixing action of the Flygt mixers, the solids will be dispersed over most of the tank.

The areal density of the precipitate will be extremely low compared to the criticality safety limit of 0.4 grams per square centimeter.¹⁶ Areal density is the mass of ²³⁵U solids per area of the tank bottom. The limit of 0.4 grams per square centimeter is the lowest areal density at which criticality can occur under optimal conditions of no neutron poisons, optimum moderation, and optimum density.

According to Tank Farm records, Tank 43 sludge currently contains about 13.7 kg of ²³⁵U and 1.7 kg ²³⁹Pu.¹⁷ Assume that the supernate contains another 3 kg ²³⁵U (the 1.2 kg of soluble ²³⁵U plus a conservatively high estimate for the ²³⁵U in the colloidal sludge layer). Assuming that a kg of ²³⁹Pu is equivalent to 1.92 kg ²³⁵U, the estimated equivalent ²³⁵U in Tank 43 is

Thus, the areal density in Tank 43 is 0.0038 grams per square centimeter (20 kg divided by the tank area of 5631 square feet), which is about 1% of the criticality safety limit.

Given the small particle size and slow settling rate, it is not possible that the 1.2 kg of ²³⁵U precipitate formed when uranyl carbonate is added would be concentrated sufficiently to exceed 0.4 grams per square centimeter. For example, if it is assumed that the 1.2 kg is concentrated but the other sludge solids remain dispersed throughout the tank (they are already dispersed and there is no mechanism to concentrate them), the 1.2 kg would have to precipitate in less than 4 square feet to exceed 0.4 grams per square centimeter. The calculation is as follows:

where "sludge" refers to the compacted sludge, "Colloidal Sludge" refers to the colloidal solids in the supernate, and "Precipitate" refers to the ²³⁵U that will be precipitated when the uranyl carbonate is added.

We have shown that the Areal Density of the sludge + colloidal sludge + precipitate is 0.0038 gram per square centimeter. If we now assume that the 1.2 kg of ²³⁵U precipitates in a small enough area of the tank so that the total Areal Density of the sludge plus the precipitate is 0.4 grams per square centimeter, then Areal Density of the precipitate must be

There is no reasonable set of conditions that could cause all the ²³⁵U to precipitate in this small an area. Also, the areal density limit does not take into account neutron poisons that will also be present, as described in the next section. These poisons will increase the margin of safety.

Another factor ensuring safety is that the ²³⁵U will be diluted by other solids in the supernate. The small amount of precipitated uranium solids will settle into the sludge at the bottom of the tank. The surface of sludge is not a hard surface. There is a transition zone from supernate, to supernate with fine particles, to light sludge, and then to thick, compacted sludge. As discussed earlier, there is a layer of suspended solids that extends perhaps 20 inches above the compacted sludge layer. This layer was detected by samples taken at the 72-inch and 66-inch elevation in the tank. These samples were dip samples of liquid supernate, not of sludge, so the solids in this layer will be easily mobilized by the Flygt mixer.

When the uranium solids mix with the solids in this layer, the resulting mixture will be critically safe. Sludge soundings of Tank 43 indicate the layer of compacted sludge solids is about 53 inches high.⁴ If one assumes that the layer of supernate with colloidal sludge solids extends from 53 inches to 72 inches (the highest elevation at which samples showed high iron) the quantity of iron in this layer is about 4800 kilograms. These 4800 kilograms of iron-containing solids are in a very light, mobile layer that will easily be suspended by the Flygt mixer. These solids will be available to act as nucleation sites for the formation of sodium diuranate solids when the uranyl carbonate solution is added to Tank 43.

After the uranium and iron in the supernate has settled, the iron to ²³⁵U ratio in the settled solids will be approximately 1800:1. The safe ratio for preventing nuclear criticality is 76:1 or greater. Thus, these solids will be critically safe with a considerable safety margin. The calculation is shown in the table below.

Iron to ²³⁵U ratio in Tank 43 Supernate
Based on Sample of October 2000

A number of different malfunctions could occur that would affect the effectiveness of the process and perhaps delay restart of the 2H Evaporator. However, no reasonable malfunction would introduce a criticality risk in Tank 43. The following possible failures were examined:

• Failure of the Flygt mixer
• Improper injection point
• Improper uranium concentration or enrichment in uranyl carbonate

Another possibility is that the Flygt mixer would fail or be inadvertently shut off. In this case, If the Flygt mixer were to fail there would be very little mixing between the uranyl carbonate stream and the supernate, so the precipitated solids would be primarily depleted uranium. It would be possible for the solids from this operation to fall to the sludge layer in the region directly below the uranyl carbonate injection point. But the solids would be of low enrichment and pose no concern.

There is also no concern about degraded operation of the mixer. The uranyl carbonate solution being added has a uranium concentration about three orders of magnitude higher than the tank contents (10,000 mg/l for the uranyl carbonate solution versus 5-15 mg/l for the supernate). Thus, if the precipitates formed are not effectively swept from the mixing zone, the large concentration of DU in the uranyl carbonate solution will overwhelm the small concentration of uranium in the supernate, and the precipitates formed will be essentially all DU.

Also, degraded operation of the mixer would limit the mass of ²³⁵U that could be precipitated. For ²³⁵U to be precipitated, it first has to be drawn into the zone around the Flygt mixer so that it can contact uranyl carbonate. So the Flygt mixer has to stir a large fraction of the tank for a large fraction of the ²³⁵U to precipitate. If the mixer does not stir a large fraction of the tank, then only a small fraction of the ²³⁵U can precipitate, and there is no concern. If the mixer does stir a large fraction of the tank, then it must be generating flow on the order of a few feet per second, which is much more than needed to suspend the slow-settling solids produced by the precipitation.

The uranyl carbonate could be injected at the wrong point, through a design or construction error, or if the injection pipe were to break. If the new injection point is near the Flygt mixer, then some of the uranyl carbonate will be swept into the mixer and will precipitate as described in the earlier sections of the report. If the new injection point is far from the Flygt mixer, then there will be poor mixing between the uranyl carbonate and the supernate, and the precipitates produced will be primarily depleted uranium. There is no injection point that could produce precipitates in higher enrichments or quantities than already analyzed.

Improper uranium concentration would not introduce a criticality risk. Modeling of the process shows that the important parameter is kilograms of DU added, not the concentration. If the uranium concentration were, for example, 5 gm/l (one-half the desired concentration), then adding 10,000 gallons would have the same effect as adding 5,000 gallons at 10 gm/l. At the lower concentration, more uranyl carbonate would have to be added to achieve the desired reduction in enrichment, but addition of either solution is safe in Tank 43. If the uranium concentration is too high, premature precipitation of the DU may occur, but this is also safe.

A lower uranium concentration could affect the initial precipitate enrichment. Based on the mathematical model, a low uranium concentration would reduce the effective DU addition rate and raise the precipitation efficiency (i.e. 60 gpm at 5 gm/l would be equivalent to only 30 gpm at 10 gm/l. Thus, control of the uranium concentration is needed to ensure that the initial precipitate enrichment is low. However, this is not a safety concern.

The process is relatively insensitive to enrichment as long as the DU enrichment is low, i.e. it doesn’t make any difference if the DU is 0.1%, 0.2%, or 0.3%. The uranyl carbonate will be made up from uranyl nitrate solutions that are low in enrichment, and there is no mechanism that could change the enrichment. The only concern would be if the wrong solution were sent to the Tank Farm, for example if enriched uranium were transferred rather than the depleted uranium. The uranyl carbonate solution is being made up in F-area A-line, which has no enriched uranium, so this is a small risk. Tank Farm Waste Acceptance Criteria specify that any material entering the Tank Farms be critically safe in infinite geometry, and a Waste Compliance Plan is required from the canyon to ensure that the Waste Acceptance Criteria is met. Plans are to use the same controls for acceptance of uranyl carbonate.

1. P. D. d'Entremont, "Operating Plan for 2H Evaporator", HLW-STE-2000-00517, January 2001
2. W. R. Wilmarth and R. A. Peterson, "Analyses of Surface and Variable depth Samples from Tank 43H", WSRC-TR-2000-00208, May 31, 2000
3. CST Morning Report, 2/28/01
4. Procedure 138-9-H-10T, "Transfer Jet/Pump/Waste Downcomer Levels And Adjustments", Revision 7
5. W. R. Wilmarth, Laboratory Notebook WSRC-NB-97-00534
6. Procedure SP-2001-HTF-E-010, Revision 0, "Measuring Sludge Level Using Turbidity Meter And a Glove Bag On Tank 43", Data Sheet from Evolution of 3/2/01
7. T. G. Williamson, "Metal Poisons in Waste Tanks", EPD-CTG-960046, August 28, 1996
8. D. T. Hobbs and T. B. Edwards, "Solubility of Uranium in Alkaline Salt Solutions (U)", WSRC-TR-93-454, March 29, 1994
9. D. T. Hobbs and D. G. Karraker, "Recent Results on the Solubility of Uranium and Plutonium in Savannah River Site Waste Supernate", Nucl. Techn., 114 (1996), 318 - 324
10. R. A. Peterson and R. A. Pierce, "Sodium Diuranate and Sodium Aluminosilicate Precipitation Testing Results", WSRC-TR-2000-00156, Rev. 0, May 15, 2000
11. P. D. d'Entremont, "Modeling of Uranyl Carbonate Addition Process", HLW-STE-2001-00009, January 22, 2001
12. William Vetsch, "Tank 43 Flygt Mixer Flowrate", E-mail, 2/28/01, 3:52 PM
13. P. D. d'Entremont, "Mixing Depleted Uranium Solution in Tank 43-Consultation with Dr. David Dickey: MixTech Report TR-021", December 7, 2000
14. D. G. Karraker, "Uranium Settling Rates in SRS Waste Supernate", WSRC-TR-94-058, January 26, 1994
15. Lawrence Oji, "Isotopic Dilution Experiments with Tank 54H Simulants: Qualitative Observations on Precipitated Uranium Particles", SRT-LWP-2001-00031, E-mail of 3/1/01, 11:34 AM
16. ANSI/ANS-8.1-1983, "Nuclear Criticality Safety in Operations with Fissionable Materials Outside Reactors", Prepared by the American Nuclear Society, Approved by the American National Standards Institute, October 7, 1983, Reaffirmed in 1996
17. J. R. Hester, "High Level Waste Characterization System", WSRC-TR-96-0264, December 1996

Data from W. R. Wilmarth and R. A. Peterson, "Analyses of Surface and Variable depth Samples from Tank 43H", WSRC-TR-2000-00208, May 31, 2000. Wilmarth and Peterson reported that the supernate concentration was about 15 mg/l. The average enrichment is computed from the raw data on mass number analyses in the report, as shown below:

For the calculations in this report, the value of 3.11% was rounded to 3 ¼% (3.25)%.

Data from W. R. Wilmarth, Laboratory Notebook WSRC-NB-97-00534

Supernate zone (72 inches to 357 inches)
1,000,350 gallons

Sludge Fine zone (53 inches to 72 inches)
66,690 gallons

SUMMARY of data for October 2000

This appendix discusses the derivation of equations used in developing the tables and figures in this report. The equations used were all analytical solutions, with no finite element analysis. The graphs were developed using Microsoft Excel, but the points on the graphs were verified using hand calculations.

The following equations were used to compute uranium enrichment when uranyl carbonate is added to solutions below saturation. There is no precipitation below saturation, so the quantity of ²³⁵U and other uranium isotopes added are simply added to the quantities already in solution.

The quantity of ²³⁵U in solution at any time is given by Equation 6 from HLW-STE-2001-00009, "Modeling of Uranyl Carbonate Addition Process," January 8, 2001

Mass must be conserved, so the amount of total uranium in the precipitate must be equal to (z – z_sat) because the uranium inventory in the supernate is constant after saturation. The mass balance is as follows:

(Uranium added after saturation is reached) = (Uranium in precipitate)
z – z_sat = (Uranium in precipitate)

Now, compute the quantity of ²³⁵U in the precipitate by doing a mass balance of the ²³⁵U in solution. The starting point for the mass balance is the time at which uranium reaches saturation.

In the section "Ensuring That the Initial Enrichment is Low" the initial precipitate enrichment was calculated based on the sample results of October 2000, i.e. 8 mg/liter and 3.83% enrichment. This section shows the same calculation at the conditions of the sample in early 2000—15 mg/liter and 3.25% enrichment. This is a more conservative calculation than the one based on the samples of October 2000, and a higher flowrate is required to ensure that the initial precipitate is less than 0.96% ²³⁵U enrichment.

The process was modeled at the following set of conditions, which are conservative:

A number of cases were considered:

The efficiency of the uranyl carbonate precipitation, assuming good mixing at the Flygt mixer, is given by

where F is the flowrate of uranium through the mixing zone
I is the injection rate of uranium into the mixing zone

This formula assumes that there is very good mixing in the mixing zone, so actual performance will be lower. However, the planned method of adding the uranyl carbonate near the Flygt mixer will ensure that the mixing is fairly good, so this formula should yield a good estimate that will be slightly conservative.

For each flowrate, the addition process was modeled using the equations in Appendix B. The results of the calculation are shown in the table below and are displayed graphically in Figure 3.

The amounts of ²³⁵U shown in the rightmost column are the amounts that are precipitated before the average enrichment of the precipitate is equal to 0.96%. For example, at 5 gal/min the average enrichment of all the uranium precipitated will be 0.96% when 2.17 kg of ²³⁵U have been precipitated. Note that 226 kg of DU was added to reach this point, so (226 kg)·(0.002) = 0.45 kg of the ²³⁵U came from the DU that was added.