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FILTER.SIM: A NEW TOOL TO OPTIMIZE INDUSTRIAL FILTERING

PLANTS

L.E. Gutirrez, J.M. Menacho and E.A. Pealoza

De Re Metallica IngenieraSantiago, Chile, [email protected]

ABSTRACT

A new filtration model based on porous media transport theory is presented. It

predicts capacity and final moisture content in the filtered cake as function of design and

operational variables at the plant.

FilterSim is the computer code where this new model is programmed. Applicationof FilterSim to ten-month operation of an industrial copper concentrate filtration plant is

shown on a daily basis and using a single set of internal parameters for the whole period.Average error is less than 5%, both in capacity and moisture estimation.

FilterSim abilities to optimize industrial filtration plants as well as to estimate

future budget are illustrated with several real examples.


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BACKGROUND

Filtration is the operation of separating solid particles from a fluid phase by meansof a filter medium, which retains solids and permit the pass of fluid. This process has been

used for many years in the mining and chemical industry, usually applied as finaldewatering step. Many efforts have been made to improve design of new equipments, as

well as to formulate new process models and also to find out better methods to estimate

intrinsic parameters.

This paper is centered in modeling of vertical plate press filters, eventhough

extension to other design may be straightforward. The filtering cycle in a vertical plate

press unit includes four basic steps: (i) feeding, (ii) pressing, (iii) drying and (iv) clothwashing. It has been noted from experimental observation that capacity is primarily

determined by the feeding rate and the final moisture is controlled by the drying dynamics.These are the only two steps considered in the present description.

Most of the existing models consider filtration either at constant pressure operation

or constant feedrate operation [1-4]. This is not realistic because both the pressure and fluid

flowrate are variables along the time when using centrifugal pump to feed the pulp into the

chambers.

Earlier approaches to describe the drying step include semi-empirical correlations to

determine drying times and final cake moisture content [5-7], but nowadays the two-phase

theory of flow in porous media is preferently used to model the drying step [4].

Given the importance of porosity in filtration, efforts have been made by several

authors to relate this property to particle size distribution of the solids [8-11]. Resultsindicate that porosity depends mainly on the mean and the standard deviation of particle

size distribution.

Reviewing the technical literature it becomes evident the lack of realistic models

with application to engineering design as well as to optimization of existing plants,

particularly for copper concentrate filtration. Consequently, a novel filtration model for

plates press filters is presented in this paper. This is based on current knowledge butimproving potential to predict throughput and final moisture content in the filtered cake as

function of design and operational variables existing at industrial plants. It includes: steptimes, characteristics of the material to be filtered, characteristics of the filter media

including clogging along the time, characteristics of the fluid and characteristics of

pumping system. The whole system is packed in a new computer code called FilterSimproperty of De Re Metallica, Chile.

FEEDING MODEL FOR VERTICAL PLATES PRESS FILTER

Feeding step in a vertical plate press filter is schematized in Figure 1. Filter medium

has an associated permeability and it supports the cake formed over it along the time.


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Pulp

Feed

lcl m

P2P1

P2P1P0

Fluid

Cake

FilterMedium

Pulp

Feed

lcl m

P2P1

P2P1P0

Fluid

Cake

FilterMedium

Figure 1 Modeling scheme for the feeding step

Modeling assumptions for the feeding step are as follows:

Laminar flow in saturated porous media, that is, Darcys law is valid. Even cake thickness in the normal direction relative to plates. Cake is formed since the feeding operation start up. Non compressible cake. Filter medium resistance is a function of time and content of insoluble material inthe concentrate. Pumping pressure is variable during the filling step. A characteristic curve pressure

versus pulp flowrate for the centrifugal pump is considered.

Internal behavior of the cake is average considered.Applying Darcys law to cake and filter media, the following relationship is

obtained:

+=

fm

fm

c

c

fluidtotal

k

l

k

lqP (1)

Where,

Ptotal : Total drop pressure.q : Specific liquid flowrate.

Fluid : Viscosity of the liquid.lc, lfm : Respective thickness of cake and filter media.kc, kfm : Respective permeability of cake and filter media.


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The specific flowrate q is related to filtrated fluid volume according to the following

expression:

( )

f

ff

td

tVdSq = (2)

Where,S : Filtration area.

Vf(tf) : Fluid filtrated during the feeding time.

tf : Feeding time.

A relationship between volume of filtrated fluid V(tf) and cake thickness lc is

obtained by considering a balance between the volume concentration of solids in the pulp,

cake thickness and filtrated fluid volume,

S)(1

)t(Vl

00

ff0

C = (3)

Where,

0 : Volume concentration of solids in feed pulp.0 : Cake porosity.

Finally a general relation between the filtrated fluid flowrate and the drop pressure

across the porous media is obtained.

f

ff

ff

0C00

0

fm

fm

fluidf td

)(tVd)(tV

)(k)(1S

k

lS))(t(QP

+= (4)

Where,

P(Q(tf)) : Filter pressure.Q(tf) : Pulp feeding flowrate.

A relation between the pressure and the pulp feeding flowrate is also considered

when centrifugal pump is employed to feed the filter:

)t(Q)t(Q))t((QP fff2 ++= (5)

Where,

, , : Constants depending on each specific pumping system.

Industrial data illustrating validity of equation 5 are shown in Figure 2.


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Figure 2 Fitting of centrifugal pump modeling

Combining equations 4 and 5 and integrating drives to an expression for the filtrated

fluid volume.

A2

C)A4(BB)t(V

2

ff

++= (7)

Where,

)(k)1(2S

A

0c00

2

0

= (8a)

fm

fm

kS

lB = (8b)

)t,,,(fCf

= (8c)

From the filtrated fluid volume it follows an expression for the filter capacity:

)tttt(t

3600)t(V

)(1

)(1(dmt/h)Capacity

owdpf

ffS

00

00

++++

= (9)

Where,


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tp : Pressure time, s.

td : Drying time, s.

tw : Washing time, s.to : Additional time, s.

s : Specific gravity of solids.

DRYING MODEL FOR VERTICAL PLATES PRESS FILTER

Air is a second fluid participating at the drying filtration step. Accordingly, two-

phase flow through the cake and filter is considered by extending Darcys law. Other

assumptions are: incompressible cake, constant blowing pressure, unit initial saturation and

descending along the time, relative permeability is a function of the insoluble content in theconcentrate, granulometry and liquid saturation. In symbols:

q)S,(k)(k

l

k

l

P

T0L0

c

fm

fm

fluid

s

+= (10)

Where,

Ps : Drying pressure.kL(0, ST) : Relative liquid permeability in the unsaturated porous media.q : Specific flowrate of liquid in the unsaturated porous media.

ST : Liquid saturation.

Saturation and filtrated fluid volume are related as follows.

( ))t(S1lS)t(VdT0df

= (11)

Applying the first derivative with respect to time to last equation and then

combining with equation 10, a new expression representing the two-phase flow in the

drying step is obtained:

d

dT

T0L0

c

fm

fm

0

fluid

S

dt

)t(dS

)S,()kk(

l

k

ll

P

+= (12)

Using the definition of reduced saturation, re-arranging and integrating equation 12

the following expression is obtained:

( )( ) ( )

+=

1

S0L0

c

r

fm

fm

0c

dS

r

d),(k

1

)(k

lS1S1S1

k

l

l

tP(13)

An exponential relation between relative liquid permeability and saturation is

assumed in this work,


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)Sk(expk)S,(kr10r0L

= (14)

Where,

k0, k1 : Constants depending on compression system and concentrate

characteristics.

An expression for the cake moisture content H is obtained by combining the last

two equations and integrating:

( )%S)1(

SH

LT0S0

LT0

= (15)

ADDITIONAL SUB MODELS

Three additional sub models are included in FilterSim code: (i) permeability sub model

based on the classical Kozeny-Carman equation, (ii) porosity sub model described asfunction of the first and second order momentum of the particle size distribution and (iii)

hydraulic resistance of the filter medium, empirically modeled based on colmatation

industrial data and laboratory measurements.

FILTERSIM CODE

FilterSim code contains models and sub model above-described and it isprogrammed on MS Visual Basic platform on a daily basis. Operational strategies include

feeding the chambers (i) by fixed times or (ii) by fixed weight. In last case feeding time is a

response. General input data include: (i) design variables (chamber dimensions, number ofchambers, filtrating media permeability, pumping capacity and blowing system capacity);

(ii) characteristics of solid material (insoluble contents in feed, density, particle size and

shape of solids); (iii) characteristics of the liquid phase (viscosity, density and surface

tension of liquid, pulp dilution and pulp temperature); (iv) characteristic of the air phase(density, viscosity and temperature); (v) operational variables per cycle (feeding time or

filter load, pressing time, drying time, washing time, discharging time, total filtration time,

slurry pump pressure and blowing pressure). Saturated and non saturated permeability,porosity and hydraulic resistance of the filter media are then computed. This leads tocompute throughput and moisture content in filtered product. A detailed description of the

code is beyond the scope of this paper.


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FILTERSIM VALIDATION

FilterSim was applied on a daily basis for a period of 10 months of operation in afilter plant having 3 vertical plate press filter units. Typical values for capacity in these

filters are 60 dmt/h and 80 dmt/h, and 8.5% w/w and 10.5% w/w moisture in finalconcentrate. Figures 3, 4 and 5 show matching between real and simulated parameters for

both capacity and moisture at each of the three filter units. Accuracy of the model is

excellent showing less than 5% error along 10 months in both capacity and moisture, asshown in Table 1.

Figure 3 Matching between real and simulated results in Filter 1



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Table 1 Summary of statistical parameters

Capacity Moisture

Av. Error Std. Dev. Av. Error Std. Dev.Industrial

Unit% dmt/h % % wb

Filter 1 4.9 3.3 3.5 0.3

Filter 2 4.9 3.3 4.1 0.4

Filter 3 4.8 3.4 4.1 0.4

SENSITIVITY ANALYSIS

Software FilterSim not only can be used to estimate future budget and long time

planning, but also to optimize daily operation as shown below.

Daily data corresponding to one month of industrial operation were taken and

checking first that similar results are obtained for same input data. Then conditions were

changed by simulation such to maximize production but keeping moisture of the productnearly constant. Final results indicate +7.5% additional capacity for similar product

moisture if the plant is operated under conditions given by FilterSim instead of the real

ones (see Table 2). Figure 6 shows the capacity curves for the base case and the optimizedcase, while Figure 7 shows moisture content in filtered concentrate for both cases. Change

in feeding times and drying times are shown in Figures 8 and 9 also for both cases.


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Table 2 Summary of result for the sensitivity analysis

Parameter Units Base CaseOptimized

Case

Change

Percentage, %

Production dmt/month 39117 42071 7.6

Production wmt/month 42968 46195 7.5

Average Moisture % wb 8.96 8.93 -0.4

Figure 6 Capacity in base case and optimized case

Figure 7 Moisture in base case and optimized case


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Figure 8 Feeding time in base case and optimized case

Figure 9 Drying time in base case and optimized case

COMMENTS AND CONCLUSIONS

A powerful tool has been developed to estimate throughput and product moisture atindustrial filtration plants using plates press filters. Application to a given plant indicates

prediction error within 5%. A friendly computer code called FilterSim is available to use

for design, optimization, control and planning purposes. It operates on a daily basis and

includes applications to vertical and horizontal plates press filters depending on

requirement.


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REFERENCES

1. R.J. Wakeman and E.S. Tarleton, Filtration Equipment Selection, Modeling andProcess Simulation, Elsevier Advanced Technology, 1999, 55-96.

2. F.M. Tiller, T. Cleveland, R. Lu, Pumping Slurries Forming Highly CompactibleCakes, Ind. Eng. Chem. Res., Volume 38, 1999, 590-595.

3. E.S. Tarleton, A New Approach to Variable Pressure Cake Filtration, MineralsEngineering, Volume 11(1), 1998, 53-69.

4. F. Concha, Filtration and Separation Handbook. Cettem, University ofConcepcin, Chile, 2001.

5. R.J. Wakeman, Low Pressure Dewatering Kinetics of Incompressible Filter Cakes:I. Variable Total Pressure Loss or Low Capacity Systems, Int. J. Miner. Process.,5, 1979, 379-393; 395-405.

6. R.J. Wakeman, The Performance of Filtration Post-Treatment Processes: 1. ThePrediction and Calculation of Cake Dewatering Characteristics, Filtration andSeparation, 16, 1979, 655-660.

7. C. Hosten, O. San, Reassessment of Correlations for the DewateringCharacteristics of Filter Cakes, Minerals Engineering, 15, 2002, 347-353.

8. A.B. Yu, C.L. Feng, R.P. Zon, R.Y. Yang, On the Relationship between Porosityand Interparticle Forces, Powder Technology, 130, 2003, 70-76.

9. J. Duck, E. Zvetanov, T. Neesse, Porosity Prediction for Fine Grained FilterCake, Department of Environmental Process Engineering an Recycling, UniversityErlangen-Nuremberg, Schottkystr, 10, 91058, Erlangen, Germany, 2001.

10. J. Duck, E. Zvetanov and T. Neesse, Characteristic Number for Porosity and FlowResistance of Fine Grained Filter Cakes, Department of Environmental ProcessEngineering an Recycling, University Erlangen-Nuremberg, Schottkystr, 10, 91058,

Erlangen, Germany, 2001.

11. M. Mota, J.A. Teixeira, W.R. Bowen, A. Yelshin, Interference of Coarse and FineParticles of Different Shape in Mixed Porous Beds and Filter Cakes, Mineral

Engineering 16, 2003, 135-144.

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