- Email: [email protected]
Countercurrent Washing of Solids
15 Countercurrent Washing of Solids L. Svarovsky Department of Chemical Engineering, University of Bradford
15.1 INTRODUCTION Washing of a particular product (contaminated with a solvent, solute or ultrafine particles) by reslurrying is possible with separator arrangements in simple series connections without recycle, by adding washwater to the underflows in between the stages. Wash liquid requirements can be minimized, however, by countercurrent operation if the additional cost of the necessary equipment can be justified. In this arrangement, as shown m Figure 75.7, the feed slurry and the wash liquid move through the separator series in opposite directions, with the wash liquor becoming gradually more contaminated with the mother liquor while the concentration of the mother liquor in the solids stream reduces.
Figure 15.1. Schematic diagram of a countercurrent washing train
The separators in this context may mean any dynamic separators such as hydrocyclones, sedimenting centrifuges or gravity thickeners, but much of the following also applies to countercurrent washing with filters, with or without reslurry. In the case of filters, the washed cake then represents the 'underflow' from the filter whilst the filtrate is the 'overflow'. In the case of dynamic separators, the solids leave the washing train as a slurry in the system 533
534
COUNTERCURRENT WASHING OF SOLIDS
underflow whilst most of the contaminated wash liquid leaves through the system overflow. Systems used in industry may or may not employ intermediate sumps between individual stages, depending on the type of separator used in the train. Gravity thickeners, for example, provide the bulk and the residence time necessary for any mixing or mass transfer to take place. Hydrocyclones usually need sumps between stages, although closed systems without sumps are often found in starch washing, for example. 15.2 MASS BALANCE CALCULATIONS Mass balance calculations of countercurrent washing systems can be quite involved. Assuming perfect mixing in the feed tanks and for a simple case of the fresh wash liquid containing no solubles, Fitch1 showed a simple way of working out the algebraic solubles balance. The dotted lines in Figure 15.1 show rectangles representing the different stages, each containing a separator and its feed tank and pump. The critical information needed for easy calculation of a general case such as that in Figure 15.1 is the ratio, in each stage, of the quantity of solubles carried in the feedback flow to that carried in the advancing flow. The ratio for perfect mixing in the tank and separator is equal to 1 /St in each stage /, if S, is the free liquid underflow/overflow split. The algebraic solubles balance can thus be made, starting at the final stage. An unknown value, x, is assigned to the mass flow rate of the solubles in the advancing flow of washed solids from the final stage (the system underflow). This unknown x will carry through the system and appear as a factor in the solubles balance for all stages in the system. The difference between the advancing flow and the return flow between any two stages in the system must therefore be equal to x. Taking the wash liquid introduced in the final stage to be clean, free of any mother liquor, the return flow from the last stage in Figure 15.1 would contain x/S3 of the solubles while the advancing flow, entering stage 3, would contain x more, i.e. x/S2 + x. Application of the method by Fitch1 to the three-stage system in Figure 15.1 yields the following equation for the overall loss of the solubles to the system underflow2: x/Ms = 1/[1 + [1/SJ + [\/(SrS2)]
+ [1/(51-S2-S3)]p)
(15.1)
or, in terms of the underflow-to-throughput ratios, Rf (again as free liquid ratios): x/MH = [RnRi2R{3] /[l - (1 - Rn)'(Rn
+ #f2)]
(15.2)
where Ms is the mass flow rate of solubles in the solids feed. The amount of wash liquid added to the circuit only affects the dilution of the solubles in the system underflow and overflow and has no effect on the overall washing efficiency. Another important overall performance parameter is the loss of washwater in the system underflow. This can be calculated from the mass balance for the washwater: Fitch's method (starting this time from the other end of Figure
MASS BALANCE CALCULATIONS
535
15.1) yields the loss of washwater in the underflow (w), for the simple case where no washwater comes with the solids, as w/W=
1/[1 + {/(S&S, + S2S3 + S3)]
(15.3)
where Wis the wash liquid feed flow rate. It can be seen that this ratio only depends on the splits in each stage and increasing the washwater supply merely dilutes the underflow solids stream. Reducing the washwater supply will therefore thicken the solids underflow stream, but in so doing the separation efficiency of the solids may be diminished causing some solids to leave through the overflow of the particular stage. In the limit, there is a minimum washwater flow required to carry the solids, and the washwater supply cannot be reduced below this point. For hydrocyclones, for example, the maximum solids concentration in the underflow is of the order of 45% or 50% by volume and enough water must be provided at all stages for the solids to be able to pass through to the system underflow. The mass balances of simple washing trains with clean washwater and with the solids being dry on entering the system can be calculated manually using the above-described method proposed by Fitch1. If some washwater enters with the solids or if the washwater feed contains some solubles, the mass balance becomes more complicated and is best carried out with a computer. An iterative calculation may then be used to introduce an artificial, hidden stage at the front and also one at the back o.f the train, which would produce the wet solids and dirty washwater feeds to the train as required. This is the principle behind the programme distributed by Fine Particle Software3. The programme has been used to study the countercurrent washing systems and to make the conclusions presented here; it has also been used to compare the predicted performance with experimental tests on washing hydrogel, as reported in the literature4. 15.2.1 Examples of mass balance calculations Figure 15.2 sets out three cases of a three-stage countercurrent washing train in which the solids enter dry (no wash liquid with the solids feed) and the wash liquid comes in clean (no solubles in the wash liquid). All three cases are designed to give the same washing efficiency (from 1 g s"1 with the feed to 0.008 g s"l in the system underflow) they all have the same minimum amount of liquid in any underflow along the train to carry the solids along (0.261 1 s"1), as indicated in Figure 15.2. The three cases are shown at this stage only as a demonstration of how a programme like this can be used to test a system and optimize it quickly. It is also set out to show the effect of the values and the order of the flow ratios on the wash liquid requirement and the position of the thickest underflow in the system. The example will be discussed later, but it can be noted from Figure 15.2 that, for the case of the Rf ratios increasing along the train, the wash requirement is highest and the system underflow is very dilute (the thickest underflow is in the first stage). As it happens, this case is also very bad for the
536
COUNTERCURRENT WASHING OF SOLIDS
Case 1: worst No. of stages Solids feed: Flow rate of wash, Is" 1 Mass rate of solubles, g s'1 Stage
Wash: Flow rate of wash, 1 s~ ' 3.64 (high) Mass rate of solubles, g s~ ' 0
0 1
Input
*f
No. 1
0.100
2
0.200
3
0.300
Wash Solubles Wash Solubles Wash Solubles
Output
Feed
Feedback
Overflow
Underflow
0.000 1.000 0.261 0.110 0.653 0.026
2.613 0.103 3.005 0.018 3.640 0.000
2.352 0.992 2.613 0.103 3.005 0.018
0.261 0.110 0.653 0.026 1.288 0.008
Case 2: best for wash requirement No. of stages Solids feed: Flow rate of wash, I s 1 Mass rate of solubles, g s -1 Stage
Wash: Flow rate of wash, Is - 1 1.52 (low) Mass rate of solubles, g s"' 0
0 1
Input
*t
No. 1
0.180
2
0.180
3
0.180
Wash Solubles Wash Solubles Wash Solubles
Output
Feed
Feedback
Overflow
Underflow
0.000 1.000 0.261 0.218 0.318 0.046
1.450 •0.209 1.507 0.038 1.520 0.000
1.189 0.992 1.450 0.209 1.507 0.038
0.261 0.218 0.318 0.046 0.331 0.008
Case 3: best for solids separation No. of stages Solids feed: Flow rate of wash, Is - 1 Mass rate of solubles, g s"1 Stage
Wash: Flow rate of wash, Is" 1 2.11 (medium) 0 Mass rate of solubles, g s"!
0 1
Input
Rr
No. 1
0.300
2
0.160
3
0.100
Wash Solubles Wash Solubles Wash Solubles
Output
Feed
Feedback
Overflow
Underflow
0.000 1.000 0.792 0.425 0.503 0.079
2.641 0.417 2.352 0.072 2.110 0.000
1.849 0.992 2.641 0.417 2.352 0.072
0.792 0.425 0.503 0.079 0.261 0.008
Figure 15.2. Mass balances for three cases of three-stage countercurrent washing. Note: cases 1 and 3 have the same washing efficiency (0.008 gs~ '); all cases have the same minimum wash with solids (0.261 Is1)
WASHING TRAIN DESIGN RECOMMENDATIONS
537
separation of the solids, as will be discussed later. Case 1, therefore, must be rejected. Case 2, of equal flow ratios, is clearly good for wash requirement but the thickest underflow is still at the front of the train rather than at the end of it as is most often required in practice. It could be shown, however, that the point of thickest underflow may be moved to the back end of the train by adding some of the wash liquid with the solids rather than having it all come in at the end of the train. Case 3 is best from the point of view of solids separation because the separator in the first stage, as the unit responsible for passing solids in the system overflow, operates with dilute underflow, i.e. high separation efficiency. The point of thickest underflow is firmly at the back end of the train and the wash liquid requirement is still fairly low. The conclusions drawn from the mass balances presented in Figure 15.2 are discussed further in the following section. 15.3 WASHING TRAIN DESIGN RECOMMENDATIONS The countercurrent washing trains installed in industry often represent the most complex parts of the overall processes and are usually installed and operated at conditions far from optimum. Experimenting with and optimizing such systems is difficult, particularly in cases where no interstage sumps are used and samples of the intermediate streams cannot easily be taken. It is, therefore, advantageous to use a computer model to find out how such systems work and how they respond to operational or design changes. The following recommendations may be drawn from the mass balance calculations performed on different possible scenarios encountered in industry. Consulting experience with several working systems in industry confirms the conclusions given below. 15.3.1 Washing efficiency The washing efficiency of a countercurrent washing train is primarily determined by the values and order of the flow ratios, Rp used in the train, and by the number of stages employed. It is not affected by the washwater supply rate, irrespective of whether the water comes in with the solids or through the washwater feed at the end of the train; the washwater supply only determines the dilution of the solids in the underflows in the different stages. and overall. 15.3.2 Washwater requirement The washwater requirement of an existing washing train designed for a given washing efficiency and for a given maximum underflow solids concentration anywhere in the train is also determined by the values and order of the flow ratios, Rp and by the number of stages employed. Fewer stages require lower Rf ratios and higher washwater supplies if they are to achieve the same
538
COUNTERCURRENT WASHING OF SOLIDS
washing efficiency and to operate at the same maximum underflow solids concentration. 15.3.3 Setting of the flow ratios It is clear from equation 15.2 that the washing efficiency is maximized by minimizing the flow ratios in all stages. The solubles/wash system cannot be considered in isolation, however, and the transport of the solids along the washing train and the solids separation efficiency both in the individual stages and overall must also be taken into account. The problem is, therefore, one of optimizing a three-phase separation system. In order to be able to optimize the system, we need to know how the flow ratio affects the separation of the solids. In the case of hydrocyclones, the effect of the ratio is two-fold: increasing Rf leads to improvements in the separation efficiency through the contribution of 'dead flux'; and a further improvement is caused by a reduction in the crowding of the underflow orifice. Both of these effects can be described analytically for certain hydrocyclone geometries2 and the above-mentioned optimization is, therefore, possible, using the entropy index5 as a general criterion for the optimization. It is often the case that the flow ratios are about the same in all stages for some engineering reasons (like in the case study reported by Svarovsky and Potter4), but if this is not the case and they can be varied along the train, the following general conclusions may be stated. The best design of a countercurrent washing train using hydrocyclones is such that the flow ratios decrease along the train, so that: 1. the overall solids recovery is high; 2. the solids concentration is always highest at the end of the train; 3. the wash liquid requirement is low. The actual design depends on how sensitive the grade efficiency curves of the individual stages are to the changes in the flow ratios. The overall grade efficiency of the train G, which determines the amount of the solids lost in the system overflow, may be calculated from the individual efficiencies of the stages G, as for a series connection on underflow with overflow recycle2. The following equation allows such calculation for a three-stage system as an example: G = G,G 2 G 3 /(1 - Gx-
G2 + GXG2 + G2G3)
(15.4)
Total recoveries in the individual units combine into the overall recovery of the whole train in exactly the same way as do the grade efficiencies in the above equation. 15.3.4 Mass transfer from the solids The mass balance calculations outlined in section 15.2 assume that the mass transfer of the solubles from the solids into the suspending liquid is complete; this is reasonably true if the solids are non-porous and if enough time and
APPLICATIONS
539
shear is provided in the hydrocyclone or in the sump before it for the mass transfer to take place before the solids leave the unit with the underflow. Mass balance calculations are further complicated if the above assumptions are not true such as in the case of porous materials and where the mixing sumps are not large enough to accommodate the mass transfer. The net result, as shown in the case study given by Svarovsky and Potter 4 , is that the liquid in the pores within the individual particles has more solubles than the surrounding liquid and this complicates not only the mass balances but also the analyses of the samples taken from a working washing train.
15.4 APPLICATIONS Countercurrent separator systems can be found in many diverse industries. One example of the use of such systems is in the production of potato or corn/wheat starch. Washing here usually means removal of one solid from another, i.e. gluten from starch. The gluten must be sheared off the starch particles and hydrocyclones are ideally suited to this duty. The density of the solids is low, however, and this combined with low particle size necessitates the use of small diameter (10 mm) cyclones in parallel arrangements and the number of stages used must be high (eight or nine, up to 24 in extreme cases). Removal of solubles from the feed solids is achieved using identical washing arrangements, sometimes known as countercurrent décantation. This may be used either when the solids represent the product, like gypsum in the phosphoric acid process, or when the solvent is the product, like the leaching residues (leached uranium, copper, etc. 68 ). Hydrocyclones here compete strongly with the conventional means of décantation in gravity thickeners but offer lower installation costs and greater ease of control. A case study of a pilot test series for washing solubles off a solid product is given by Svarovsky and Potter 4 by way of illustration of the problems involved in testing such a system and of the complexity of countercurrent washing arrangements in general.
15.5 CONCLUSIONS Countercurrent reslurry or cake washing has been used in many areas of chemical, mineral and food processing and some filters, gravity thickeners and hydrocyclones are particularly suitable for this process. Very little is known, however, about the optimum operating conditions and design of such washing trains, and many installations can be much improved if some basic rules and recommendations are followed. In this chapter we have evaluated the process of countercurrent washing from the point of view of washing efficiency, washwater requirement and separation of the solids, and have given the basic rules for the best operation and design of such systems. A microcomputer model has been used to carry out the mass balances and illustrate the theoretical performance of different systems under different operating conditions.
540
COUNTERCURRENT WASHING OF SOLIDS
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
Fitch, B., 'Countercurrent filtration washing', Chem. Eng., 22, 119-124 (1962) Svarovsky, L., 'Hydrocyclones', Holt, Rinehart and Winston, London (1984) 'Counter-current Washing of Solids', Fine Particle Software, Low Shann Farm, Keighley, West Yorkshire Svarovsky, L. and Potter, J. K., 'Counter-current washing with hydrocyclones', BHRA Conference on Hydrocyclones (Oxford, 30 September to 2 October 1987) 'Solid-Liquid Separation', Continuing Education Course sponsored by the Institute of Chemical Engineers, Bradford (15-18 September 1987) Trawinski, H., 'Counter-current washing of thickened suspensions by repeated dilution and separation by sedimentation', Verfahrenstechnik, 8, 28-31 (1974) Trawinski, H., 'Counter-current washing of leaching products in thickeners and hydrocyclones, including the mathematical calculation', Aufbereitungs-Technik, 18,395-404 (1977) Chandler, J. L., 'Deep thickeners in counter-current washing', Inst. Chem. Eng. Symposium on Solid/Liquids Separation Practice and the Influence of New Techniques (Leeds, 3-5 April 1984), Paper 22, pp. 177-182, Institute of Chemical Engineers, Yorkshire Branch (1984)
15.1 INTRODUCTION Washing of a particular product (contaminated with a solvent, solute or ultrafine particles) by reslurrying is possible with separator arrangements in simple series connections without recycle, by adding washwater to the underflows in between the stages. Wash liquid requirements can be minimized, however, by countercurrent operation if the additional cost of the necessary equipment can be justified. In this arrangement, as shown m Figure 75.7, the feed slurry and the wash liquid move through the separator series in opposite directions, with the wash liquor becoming gradually more contaminated with the mother liquor while the concentration of the mother liquor in the solids stream reduces.
Figure 15.1. Schematic diagram of a countercurrent washing train
The separators in this context may mean any dynamic separators such as hydrocyclones, sedimenting centrifuges or gravity thickeners, but much of the following also applies to countercurrent washing with filters, with or without reslurry. In the case of filters, the washed cake then represents the 'underflow' from the filter whilst the filtrate is the 'overflow'. In the case of dynamic separators, the solids leave the washing train as a slurry in the system 533
534
COUNTERCURRENT WASHING OF SOLIDS
underflow whilst most of the contaminated wash liquid leaves through the system overflow. Systems used in industry may or may not employ intermediate sumps between individual stages, depending on the type of separator used in the train. Gravity thickeners, for example, provide the bulk and the residence time necessary for any mixing or mass transfer to take place. Hydrocyclones usually need sumps between stages, although closed systems without sumps are often found in starch washing, for example. 15.2 MASS BALANCE CALCULATIONS Mass balance calculations of countercurrent washing systems can be quite involved. Assuming perfect mixing in the feed tanks and for a simple case of the fresh wash liquid containing no solubles, Fitch1 showed a simple way of working out the algebraic solubles balance. The dotted lines in Figure 15.1 show rectangles representing the different stages, each containing a separator and its feed tank and pump. The critical information needed for easy calculation of a general case such as that in Figure 15.1 is the ratio, in each stage, of the quantity of solubles carried in the feedback flow to that carried in the advancing flow. The ratio for perfect mixing in the tank and separator is equal to 1 /St in each stage /, if S, is the free liquid underflow/overflow split. The algebraic solubles balance can thus be made, starting at the final stage. An unknown value, x, is assigned to the mass flow rate of the solubles in the advancing flow of washed solids from the final stage (the system underflow). This unknown x will carry through the system and appear as a factor in the solubles balance for all stages in the system. The difference between the advancing flow and the return flow between any two stages in the system must therefore be equal to x. Taking the wash liquid introduced in the final stage to be clean, free of any mother liquor, the return flow from the last stage in Figure 15.1 would contain x/S3 of the solubles while the advancing flow, entering stage 3, would contain x more, i.e. x/S2 + x. Application of the method by Fitch1 to the three-stage system in Figure 15.1 yields the following equation for the overall loss of the solubles to the system underflow2: x/Ms = 1/[1 + [1/SJ + [\/(SrS2)]
+ [1/(51-S2-S3)]p)
(15.1)
or, in terms of the underflow-to-throughput ratios, Rf (again as free liquid ratios): x/MH = [RnRi2R{3] /[l - (1 - Rn)'(Rn
+ #f2)]
(15.2)
where Ms is the mass flow rate of solubles in the solids feed. The amount of wash liquid added to the circuit only affects the dilution of the solubles in the system underflow and overflow and has no effect on the overall washing efficiency. Another important overall performance parameter is the loss of washwater in the system underflow. This can be calculated from the mass balance for the washwater: Fitch's method (starting this time from the other end of Figure
MASS BALANCE CALCULATIONS
535
15.1) yields the loss of washwater in the underflow (w), for the simple case where no washwater comes with the solids, as w/W=
1/[1 + {/(S&S, + S2S3 + S3)]
(15.3)
where Wis the wash liquid feed flow rate. It can be seen that this ratio only depends on the splits in each stage and increasing the washwater supply merely dilutes the underflow solids stream. Reducing the washwater supply will therefore thicken the solids underflow stream, but in so doing the separation efficiency of the solids may be diminished causing some solids to leave through the overflow of the particular stage. In the limit, there is a minimum washwater flow required to carry the solids, and the washwater supply cannot be reduced below this point. For hydrocyclones, for example, the maximum solids concentration in the underflow is of the order of 45% or 50% by volume and enough water must be provided at all stages for the solids to be able to pass through to the system underflow. The mass balances of simple washing trains with clean washwater and with the solids being dry on entering the system can be calculated manually using the above-described method proposed by Fitch1. If some washwater enters with the solids or if the washwater feed contains some solubles, the mass balance becomes more complicated and is best carried out with a computer. An iterative calculation may then be used to introduce an artificial, hidden stage at the front and also one at the back o.f the train, which would produce the wet solids and dirty washwater feeds to the train as required. This is the principle behind the programme distributed by Fine Particle Software3. The programme has been used to study the countercurrent washing systems and to make the conclusions presented here; it has also been used to compare the predicted performance with experimental tests on washing hydrogel, as reported in the literature4. 15.2.1 Examples of mass balance calculations Figure 15.2 sets out three cases of a three-stage countercurrent washing train in which the solids enter dry (no wash liquid with the solids feed) and the wash liquid comes in clean (no solubles in the wash liquid). All three cases are designed to give the same washing efficiency (from 1 g s"1 with the feed to 0.008 g s"l in the system underflow) they all have the same minimum amount of liquid in any underflow along the train to carry the solids along (0.261 1 s"1), as indicated in Figure 15.2. The three cases are shown at this stage only as a demonstration of how a programme like this can be used to test a system and optimize it quickly. It is also set out to show the effect of the values and the order of the flow ratios on the wash liquid requirement and the position of the thickest underflow in the system. The example will be discussed later, but it can be noted from Figure 15.2 that, for the case of the Rf ratios increasing along the train, the wash requirement is highest and the system underflow is very dilute (the thickest underflow is in the first stage). As it happens, this case is also very bad for the
536
COUNTERCURRENT WASHING OF SOLIDS
Case 1: worst No. of stages Solids feed: Flow rate of wash, Is" 1 Mass rate of solubles, g s'1 Stage
Wash: Flow rate of wash, 1 s~ ' 3.64 (high) Mass rate of solubles, g s~ ' 0
0 1
Input
*f
No. 1
0.100
2
0.200
3
0.300
Wash Solubles Wash Solubles Wash Solubles
Output
Feed
Feedback
Overflow
Underflow
0.000 1.000 0.261 0.110 0.653 0.026
2.613 0.103 3.005 0.018 3.640 0.000
2.352 0.992 2.613 0.103 3.005 0.018
0.261 0.110 0.653 0.026 1.288 0.008
Case 2: best for wash requirement No. of stages Solids feed: Flow rate of wash, I s 1 Mass rate of solubles, g s -1 Stage
Wash: Flow rate of wash, Is - 1 1.52 (low) Mass rate of solubles, g s"' 0
0 1
Input
*t
No. 1
0.180
2
0.180
3
0.180
Wash Solubles Wash Solubles Wash Solubles
Output
Feed
Feedback
Overflow
Underflow
0.000 1.000 0.261 0.218 0.318 0.046
1.450 •0.209 1.507 0.038 1.520 0.000
1.189 0.992 1.450 0.209 1.507 0.038
0.261 0.218 0.318 0.046 0.331 0.008
Case 3: best for solids separation No. of stages Solids feed: Flow rate of wash, Is - 1 Mass rate of solubles, g s"1 Stage
Wash: Flow rate of wash, Is" 1 2.11 (medium) 0 Mass rate of solubles, g s"!
0 1
Input
Rr
No. 1
0.300
2
0.160
3
0.100
Wash Solubles Wash Solubles Wash Solubles
Output
Feed
Feedback
Overflow
Underflow
0.000 1.000 0.792 0.425 0.503 0.079
2.641 0.417 2.352 0.072 2.110 0.000
1.849 0.992 2.641 0.417 2.352 0.072
0.792 0.425 0.503 0.079 0.261 0.008
Figure 15.2. Mass balances for three cases of three-stage countercurrent washing. Note: cases 1 and 3 have the same washing efficiency (0.008 gs~ '); all cases have the same minimum wash with solids (0.261 Is1)
WASHING TRAIN DESIGN RECOMMENDATIONS
537
separation of the solids, as will be discussed later. Case 1, therefore, must be rejected. Case 2, of equal flow ratios, is clearly good for wash requirement but the thickest underflow is still at the front of the train rather than at the end of it as is most often required in practice. It could be shown, however, that the point of thickest underflow may be moved to the back end of the train by adding some of the wash liquid with the solids rather than having it all come in at the end of the train. Case 3 is best from the point of view of solids separation because the separator in the first stage, as the unit responsible for passing solids in the system overflow, operates with dilute underflow, i.e. high separation efficiency. The point of thickest underflow is firmly at the back end of the train and the wash liquid requirement is still fairly low. The conclusions drawn from the mass balances presented in Figure 15.2 are discussed further in the following section. 15.3 WASHING TRAIN DESIGN RECOMMENDATIONS The countercurrent washing trains installed in industry often represent the most complex parts of the overall processes and are usually installed and operated at conditions far from optimum. Experimenting with and optimizing such systems is difficult, particularly in cases where no interstage sumps are used and samples of the intermediate streams cannot easily be taken. It is, therefore, advantageous to use a computer model to find out how such systems work and how they respond to operational or design changes. The following recommendations may be drawn from the mass balance calculations performed on different possible scenarios encountered in industry. Consulting experience with several working systems in industry confirms the conclusions given below. 15.3.1 Washing efficiency The washing efficiency of a countercurrent washing train is primarily determined by the values and order of the flow ratios, Rp used in the train, and by the number of stages employed. It is not affected by the washwater supply rate, irrespective of whether the water comes in with the solids or through the washwater feed at the end of the train; the washwater supply only determines the dilution of the solids in the underflows in the different stages. and overall. 15.3.2 Washwater requirement The washwater requirement of an existing washing train designed for a given washing efficiency and for a given maximum underflow solids concentration anywhere in the train is also determined by the values and order of the flow ratios, Rp and by the number of stages employed. Fewer stages require lower Rf ratios and higher washwater supplies if they are to achieve the same
538
COUNTERCURRENT WASHING OF SOLIDS
washing efficiency and to operate at the same maximum underflow solids concentration. 15.3.3 Setting of the flow ratios It is clear from equation 15.2 that the washing efficiency is maximized by minimizing the flow ratios in all stages. The solubles/wash system cannot be considered in isolation, however, and the transport of the solids along the washing train and the solids separation efficiency both in the individual stages and overall must also be taken into account. The problem is, therefore, one of optimizing a three-phase separation system. In order to be able to optimize the system, we need to know how the flow ratio affects the separation of the solids. In the case of hydrocyclones, the effect of the ratio is two-fold: increasing Rf leads to improvements in the separation efficiency through the contribution of 'dead flux'; and a further improvement is caused by a reduction in the crowding of the underflow orifice. Both of these effects can be described analytically for certain hydrocyclone geometries2 and the above-mentioned optimization is, therefore, possible, using the entropy index5 as a general criterion for the optimization. It is often the case that the flow ratios are about the same in all stages for some engineering reasons (like in the case study reported by Svarovsky and Potter4), but if this is not the case and they can be varied along the train, the following general conclusions may be stated. The best design of a countercurrent washing train using hydrocyclones is such that the flow ratios decrease along the train, so that: 1. the overall solids recovery is high; 2. the solids concentration is always highest at the end of the train; 3. the wash liquid requirement is low. The actual design depends on how sensitive the grade efficiency curves of the individual stages are to the changes in the flow ratios. The overall grade efficiency of the train G, which determines the amount of the solids lost in the system overflow, may be calculated from the individual efficiencies of the stages G, as for a series connection on underflow with overflow recycle2. The following equation allows such calculation for a three-stage system as an example: G = G,G 2 G 3 /(1 - Gx-
G2 + GXG2 + G2G3)
(15.4)
Total recoveries in the individual units combine into the overall recovery of the whole train in exactly the same way as do the grade efficiencies in the above equation. 15.3.4 Mass transfer from the solids The mass balance calculations outlined in section 15.2 assume that the mass transfer of the solubles from the solids into the suspending liquid is complete; this is reasonably true if the solids are non-porous and if enough time and
APPLICATIONS
539
shear is provided in the hydrocyclone or in the sump before it for the mass transfer to take place before the solids leave the unit with the underflow. Mass balance calculations are further complicated if the above assumptions are not true such as in the case of porous materials and where the mixing sumps are not large enough to accommodate the mass transfer. The net result, as shown in the case study given by Svarovsky and Potter 4 , is that the liquid in the pores within the individual particles has more solubles than the surrounding liquid and this complicates not only the mass balances but also the analyses of the samples taken from a working washing train.
15.4 APPLICATIONS Countercurrent separator systems can be found in many diverse industries. One example of the use of such systems is in the production of potato or corn/wheat starch. Washing here usually means removal of one solid from another, i.e. gluten from starch. The gluten must be sheared off the starch particles and hydrocyclones are ideally suited to this duty. The density of the solids is low, however, and this combined with low particle size necessitates the use of small diameter (10 mm) cyclones in parallel arrangements and the number of stages used must be high (eight or nine, up to 24 in extreme cases). Removal of solubles from the feed solids is achieved using identical washing arrangements, sometimes known as countercurrent décantation. This may be used either when the solids represent the product, like gypsum in the phosphoric acid process, or when the solvent is the product, like the leaching residues (leached uranium, copper, etc. 68 ). Hydrocyclones here compete strongly with the conventional means of décantation in gravity thickeners but offer lower installation costs and greater ease of control. A case study of a pilot test series for washing solubles off a solid product is given by Svarovsky and Potter 4 by way of illustration of the problems involved in testing such a system and of the complexity of countercurrent washing arrangements in general.
15.5 CONCLUSIONS Countercurrent reslurry or cake washing has been used in many areas of chemical, mineral and food processing and some filters, gravity thickeners and hydrocyclones are particularly suitable for this process. Very little is known, however, about the optimum operating conditions and design of such washing trains, and many installations can be much improved if some basic rules and recommendations are followed. In this chapter we have evaluated the process of countercurrent washing from the point of view of washing efficiency, washwater requirement and separation of the solids, and have given the basic rules for the best operation and design of such systems. A microcomputer model has been used to carry out the mass balances and illustrate the theoretical performance of different systems under different operating conditions.
540
COUNTERCURRENT WASHING OF SOLIDS
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
Fitch, B., 'Countercurrent filtration washing', Chem. Eng., 22, 119-124 (1962) Svarovsky, L., 'Hydrocyclones', Holt, Rinehart and Winston, London (1984) 'Counter-current Washing of Solids', Fine Particle Software, Low Shann Farm, Keighley, West Yorkshire Svarovsky, L. and Potter, J. K., 'Counter-current washing with hydrocyclones', BHRA Conference on Hydrocyclones (Oxford, 30 September to 2 October 1987) 'Solid-Liquid Separation', Continuing Education Course sponsored by the Institute of Chemical Engineers, Bradford (15-18 September 1987) Trawinski, H., 'Counter-current washing of thickened suspensions by repeated dilution and separation by sedimentation', Verfahrenstechnik, 8, 28-31 (1974) Trawinski, H., 'Counter-current washing of leaching products in thickeners and hydrocyclones, including the mathematical calculation', Aufbereitungs-Technik, 18,395-404 (1977) Chandler, J. L., 'Deep thickeners in counter-current washing', Inst. Chem. Eng. Symposium on Solid/Liquids Separation Practice and the Influence of New Techniques (Leeds, 3-5 April 1984), Paper 22, pp. 177-182, Institute of Chemical Engineers, Yorkshire Branch (1984)