The recirculation process - Concentration control and stock losses - Part 2 -

- Part 2 - Discontinuous recirculation; metal discharge in the recirculation process / continued from Galvanotechnik 10/2024

The recirculation process consists of a coating process followed by a recirculation rinse. The use of soluble anodes results in deficit or excess operation, depending on whether the metal concentration is below or above the desired target value. Mathematical models of continuous and discontinuous feedback processes are presented. The models are used to demonstrate process engineering methods for controlling the concentration. Possibilities for minimizing material loss are also discussed. It is made clear that in surplus operation, reducing the current yield difference is the only way to reduce metal losses.

4 Discontinuous recirculation

4.1 Recirculation of the entire recirculation tank

In the previous sections, continuous recirculation from the recirculation sink to the deposition process was considered. In practice, however, discontinuous recirculation is often used. This means that the recirculation sink is operated as a real stationary sink for a certain period of time. No recirculation takes place during this time. During the deposition process, evaporation leads to a reduction in the electrolyte volume. If there is a sufficient volume deficit, solution is pumped from the recirculation sink into the separation process. The recirculation sink is then refilled with fresh water.

If the volume of the separation process is significantly greater than that of the recirculation sink, the entire recirculation sink can be recirculated and refilled with fresh water in one step. In this case, the concentration in the recirculation sink _c1 fluctuates between zero and the maximum value at the moment of recirculation, see Figure10. In contrast, relatively small fluctuations in the concentration _c0 occur in the comparatively large volume of the separation process.

The concentration curve in the recirculation sink, which is operated as a stationary sink, is to be calculated. For this purpose, it is assumed that the concentration in the significantly larger volume of the separation process fluctuates only slightly around an average value _c-0. This results in the solution of the differential equation (25) for the concentration in the recirculation sink after starting with fresh water:

<35>

with:

_c1(t) - concentration in the recirculation sink

(at the time t)

_c-0 - average carryover concentration

from the separation process

_V1 - volume of the stand sink

V._d - carryover rate

Recirculation is possible when the volume of the recirculation sink _V1 has evaporated in the separation process. The time until the entire recirculation sink is recirculated is determined by the evaporation rate in the separation process V._evap:

<36>

The concentrations resulting from the discontinuously operated recirculation process can in turn be calculated on the basis of a mass balance. The corresponding derivation can be found in Appendix 2. Accordingly, the concentration in the separation process results as a fluctuation around an average value:

<37>

The mean value is calculated as:

<38>

where _Qrd is the ratio of evaporation and carryover:

<39>

The width of the concentration fluctuation is calculated with

<40>

where the concentration of the recirculation sink at the time of recirculation _c1(Δt) can be calculated with

<41>

4.2 Recirculation of part of the recirculation loop

In the previous section, the discontinuous recirculation of the entire volume of the recirculation bowl was considered. However, it is also possible to recirculate a partial volume that is smaller than the volume of the recirculation bowl and fill it up accordingly with fresh water in the recirculation bowl. This results in a fluctuation of the concentration in the recirculation sink _c1 between a minimum and a maximum value, see Figure11.

Figure 11: Concentration curves with discontinuous recirculation of a partial volume

Here, too, it is assumed that the concentration in the significantly larger volume of the separation process only fluctuates slightly around an average value _c-0. The concentration in the recirculation sink is then obtained as a solution of the differential equation (25), whereby the initial concentration _c1(0) of each cycle results from the dilution after recirculation of the partial volume:

<42>

A partial volume is recirculated that is smaller than the volume of the recirculation sink(_Vrt<V1). The volume fraction of the recirculation volume is defined as:

<43>

Recirculation is possible when the recirculation volume _Vrt has evaporated in the separation process. The time until recirculation results from the evaporation rate in the separation process V._evap:

<44>

Here too, the concentrations can be calculated on the basis of a mass balance. The corresponding derivation can be found in Appendix 3.

Again, the concentration in the separation process fluctuates around a mean value according to equation (37). The mean value is calculated as:

<45>

The width of the concentration fluctuation is

<46>

whereby the concentration of the recirculation rinse at the time of recirculation can be calculated with

<47>

4.3 Throttling the recirculation

So far, the case of unthrottled recirculation has been considered for discontinuous recirculation. This means that as much volume is recirculated from the recirculation sink into the coating process as the evaporation allows. As with the continuously operated recirculation process, discontinuous recirculation can also be throttled. In this case, only part of the evaporation losses in the coating process are replaced by recirculation. The remainder is replenished with fresh water.

Throttled recirculation of the entire recirculation sink

For the discontinuous recirculation of the entire rinsing volume, the formula given in section 4.1 can be used in a slightly modified form to calculate the throttled case. The average concentration in the separation process can be calculated by modifying equation (38):

<48>

Here V._-rt corresponds to an average recirculation rate that is lower than the evaporation V._evap. In practice, this can be achieved by supplementing part of the evaporation losses with fresh water between the recirculations. This results in an increased time interval between recirculations compared to equation (36):

<49>

Throttled recirculation of a partial volume

The discontinuous recirculation of a partial volume of the recirculation sink can also be combined with throttling. The average concentration in the separation process is calculated analogously to equation (45):

<50>

Here too, V._-rt is an average recirculation rate that is lower than the evaporation V._evap. In practice, this can be achieved, for example, by replacing only a certain part of the evaporation loss in the process with recirculation at the time of recirculation, and the other part with fresh water. This results in the conditions of reduced evaporation in the recirculation process.

4.4 Example nickel process

In the following, we will calculate how the nickel process described in section 2.4 behaves in discontinuous operation. The total volume of the coating tanks is 20000l and the volume of the recirculation rinse is 1000l.

Recirculation of the entire recirculation tank

First, the recirculation of the entire rinsing volume described in section 4.1 is considered. With an evaporation of 50l/h, according to equation (36), after 20 hours in the nickel process a volume corresponding to the recirculation rinse has evaporated. If recirculation is carried out accordingly every 20 hours, the concentration in the nickel process fluctuates in a small range around a mean value, which is 109g/L according to equation (38). The fluctuation range of the concentration is set to 3.75g/L according to equation (40), i.e. the nickel concentration fluctuates from 107.1g/L (after recirculation) to 110.9g/L (before recirculation).

Recirculation of part of the recirculation sink

If recirculation is to take place once per shift, i.e. after every 8 hours, instead of every 20 hours, only a partial volume can be recirculated as described in section 4.2. With an evaporation rate of 50 l/h, a recirculation of 400 l is possible. According to equation (43), the volume share of the recirculation volume is therefore 40%. After setting a constant concentration fluctuation, the concentration in the recirculation sink at the time of recirculation is 23.8g/L according to equation (47). The average concentration in the separation process can be calculated using equation (45) and results in 78.6 g/L. According to equation (46), the fluctuation range of the process concentration is then 1.1 g/L, i.e. the concentration in the process fluctuates between 78.1 g/L and 79.2 g/L.

Throttled recirculation of the entire recirculation sink

The discontinuously operated nickel recirculation process can also be throttled in order to reduce the concentration in the electroplating nickel process. As described in section 4.3, when the entire rinsing volume is recirculated, part of the volume deficit of 50 l/h caused by evaporation is replaced by fresh water. If, for example, 20 l/h of fresh water is dosed directly into the separation process, the average recirculation is reduced to 30 l/h. According to equation (49), this results in a time interval of 33.3 h between the recirculations. Equation (48) can be used to calculate the average concentration in the nickel process, which in this case is 70.9 g/L.

Throttled recirculation of a partial volume

Throttling is also possible when recirculating a partial volume. If, as described above, only a partial volume of 400 l is recirculated discontinuously and an additional 20 l/h of fresh water is dosed directly into the separation process, the time interval between recirculation is 13.3 hours. According to equation (50), this results in an average nickel concentration of 54.7g/L.

Appendix 2: Concentrations during recirculation of the entire recirculation sink

The mass can be balanced for the time of recirculation of the entire recirculation sink:

<51>

This means that the part of the dissolved substance is recirculated that has been carried over into the economy rinse up to the time _t1 = Δt and has not yet been carried over from there.

The carryover results from the process:

<52>

For a constant concentration fluctuation, the carryover from the recirculation sink must correspond to the metal released by the current yield difference:

<53>

The recirculation takes place at the time Δt with the concentration _c1. If equation (36) is inserted into equation (35) accordingly, the following follows

<54>

With the evaporation-carryover quotient:

<55>

the equation (54) reads:

<56>

Substituting equations (52), (53) and (56) into equation (51) results in

<57>

and equation (36) gives the average concentration in the separation process:

<58>

The concentration fluctuates around the mean value:

<59>

To calculate the fluctuation range, the mass of dissolved metal is balanced immediately before recirculation(t → -Δt) and after recirculation(t → +Δt):

<60>

With the respective concentrations and volumes, the result is

<61>

This equation can be solved according to the fluctuation range of the process concentration:

<62>

where the mean process concentration _c-0 is obtained from equation (58) and the concentration of the recirculation rinse at the time of recirculation _c1(Δt) from equations (35), (36) and (39):

<63>

Appendix 3 Concentrations when recirculating a partial volume of the recirculation sink

As with the recirculation of the entire volume, equations (51) to (53) apply analogously for partial recirculation. The recirculation of dissolved metal takes place at the time Δtwith the concentration _c1 according to equation (42):

<64>

With a stable concentration fluctuation, the initial concentration is equal to the diluted concentration after recirculation and topping up with fresh water:

<65>

Using equations (39), (42) and (44), the concentration of the recycled solution is as follows

<66>

If equation (66) is used in equation (65), the concentration of the recirculation rinse after recirculation and dilution can be derived:

<67>

Equation (65) can be used to calculate the concentration of the recirculation rinse before recirculation:

<69>

From equations (51) to (53) as well as (44) and (64), the following also follows

<70>

<71>

and equation (69) gives the average concentration in the separation process:

<72>

Here too, equations (59) and (60) can be used to derive the respective concentrations and volumes:

<73>

and again resolved according to the fluctuation range of the process concentration:

<74>

whereby the mean process concentration _c-0 is derived from equation (72) and the concentration of the recirculation sink at the time of recirculation _c1 (-Δt) from equation (71).

5 Metal discharge in the recirculation process

The recirculation process is considered in which the metal to be deposited is introduced by soluble anodes. Figure12 shows the input and output of the metal in question. If the process is operated without the addition of metal salt, the soluble anodes are the only metal source for the electrolyte solution. As already described in section 2, a significant proportion of the dissolved metal is deposited on the product to be coated. The metal input into the electrolyte is caused by the difference between the anodic and cathodic current yield Δη

Figure 12: Material discharge from the recycling process

Figure12 shows that there are three ways in which metal can be discharged from the recycling process:

1. discard from the coating process

When concentrated electrolyte solution is discarded from the coating process, a large amount of metal is introduced into the wastewater treatment. If the volume in the coating process is then refilled with metal-free or low-concentration electrolyte solution, the metal content in the recycling process decreases. Figure12 shows the discard as a continuous mass flow m._wa0. Discarding is of course also possible discontinuously. This is generally done as partial discard.

2. discarding from the recirculation sink

If solution is discarded from the recirculation sink, the metal contained in the diluted electrolyte solution enters the wastewater treatment system. Figure12 shows this discard as a continuous mass flow m._wa1. Discontinuous discharge is also possible here. This occurs in particular when the entire recirculation sink is discarded and replaced with fresh water.

3. carryover from the recirculation sink

Metal is constantly discharged via the drag-out from the recirculation sink m._do1. In the subsequent rinsing system, the metal-containing electrolyte solution is largely rinsed off the product and enters the wastewater treatment system via the rinsing water. Figure12 shows this as a continuous mass flow m._wa2.

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