Contributions in Mineral Floatation Modeling and Simulation
B. L. Samoila, M. D. Marcu
University of Petrosani 20 University Str.
Petrosani, Hunedoara, Romania
Abstract: The paper deals with the mineral floatation study by
modeling and simulation. Some of the main functions characterising the floatation process were simulated using Matlab Simulink programs. By analysing the results of these simulations and comparing them, we reached a conclusion concerning the optimising factors of the floatation duration. We also elaborated a Visual Basic Application which allows the calculation of quantities and contents in every point of a simple floatation circuit, for any number of operations. It’s an easy to use, conversational application that allows studying more configurations in order to find the optimum one, sparing the researchers’ and designers’ time and effort.
1. INTRODUCTION
The term “Computer Aided Process Engineering” (CAPE)
summarizes computer applications for process design, process synthesis and process control. Flow sheet simulation [1] systems are a major application in this area. They calculate the whole plant performance, enable an easy comparison of process alternatives, and allow for a purposeful process synthesis by formulation of design specifications. In mineral processing engineering such programs are widely used and at least application of steady-state simulators for complex fluid processes has become state of the art [2].
A few commercial available simulators [3], [4], [5] have extensions to handle solids, but these solids capabilities are by no means as sophisticated as the capabilities for pure fluid processes. As a consequence the use of flow sheet simulation is not yet familiar in mineral processing and in chemical engineering process alternatives with solids are often ignored during process design, because of the lack of a useful tool to handle solids processing steps within the usual CAPE-environment.
Flow sheet simulation of solids processes faces special problems. On the one hand models for processing in particle technology are not derived from first principles, i.e. for each apparatus several models of different degree of sophistication and different application domains exists. On the other hand the usual information structure representing a process stream consists of pressure, temperature, components, and their partial mass flows. This structure is not sufficient for solids processes, where a particle size distribution must be considered and also additionally solid properties should be handled simultaneously, because further solid properties may be required by the process under consideration. Examples are many processes in mineral processing, processes of the gravel
and sand industry, and soil-washing, where at least liberation states, fractional densities, or fractional contamination, respectively, must be considered besides the particle size distribution.
The aim of this research project is the development of tools for the modeling and simulation of complex solids process. Currently a flow sheet simulation system for complex solids processes with following objectives is developed:
The information structure for process streams consists of
the usual fluid stream representation and “particle types”, which allows distinction of different solids phases, e.g. ore and gangue components. Each particle type is described by its components, its size distribution and other user-defined size independent attributes. For each attribute at this level further dependent attributes may be described. All attributes may be described as distributions or by mean values.
Models with different degree of sophistication and for different application domains are provided and model parameters are adjustable, to take into account empirical or semi-empirical model derivations [6]. A well-structured model library is therefore essential. Within the model library a general unit operation model with an appropriate interface has been defined. This leads to a flexible structure, supports further extensions and allows a simple intern program communication. A specific model is derived from the general model by adding functions and data through stepwise specialization. Alternative, the structuring of necessary functions and data may take place in two distinct class hierarchies. The first hierarchy is then used exclusively for specialization of apparatus features, while the second hierarchy organizes specialization of modeling approaches. A concrete process model is then obtained by combining these two branches in one object.
2. FLOATATION TWO PHASE MODEL
Analyzing, optimizing and designing flotation circuits
using models and simulators have improved significantly over the last 15 years.
• a process stream structure which describes solids not only by particle size distribution. • an extensible model library for solids processing steps
with models for different apparatuses, different application areas and with short-cut and rigorous approaches. • an object-oriented software design.
In order to calculate a floatation technological flow sheet, we should previously know the following elements [7]:
- the quantities of material in the feed, output products and all intermediate points;
- valuable mineral contents in all of the formerly mentioned products;
- water quantities, that is dilution, for each product. It becomes necessary to calculate the flow sheet in the
following situations: - to design an installation or a new section in an
installation; - to know the products characteristics all along a
technological flow sheet, for a certain functioning regime. From time to time, we must know the characteristics of an
installation, in order to be able to modify or to correct the existing technological scheme without supplementary investments as well as to improve the technical and economical indexes. That may be needed when the raw material quality has been changed or the customers requests are different.
Our model considers the froth and the pulp as two distinct phases dynamically equilibrated (fig. 1).
The significance of the notations in the figure 1 is: M – floated material mass; V – pulp volume, except air; r, s – the ratio between the pulp volume (including air) and
the airless one, respectively between the froth volume (including air) and the airless one;
Q – volumetric flow rate, except air; C* - concentration (ratio between mass and volume unit,
including the air in the pulp); a - speed constant, regarding the concentrate transfer from
the pulp to the froth; b - speed constant, regarding the concentrate transfer from
the froth to the pulp; p, s, c, t – indexes, referring to the pulp, froth, concentrate
and waste. The differential equation reflecting the pulp composition
change, for ideal mixing cells, is:
r V tdC d = C V s b + C Vr a - C Qr - *C Q =
tdM d
pp
s sp pp tp
(1) The differential equation reflecting the froth composition
change, for the same cells, is:
s V tdC d = C Vr a + C V s b - C Q s - =
tdM d
ss
ppssscs (2)
We determined the transfer functions, which are:
1 + s Tk =
) s ( Q) s ( M = ) s ( H
p
1p1 (3)
1 + s Tk =
) s ( C) s ( M = ) s ( H
p
2p2 (4)
1 + s Tk =
) s ( Q) s ( M = ) s ( H
s
3s3 (5)
1 + s Tk =
) s ( Q) s ( M = ) s ( H
s
4s4 (6)
where we expressed the time constants Tp, Ts and the proportionality constants k1, k2, k3, k4, depending on Vp, Vs, Qt, Qc, Q, which have the significance according to fig. 1.
3. FLOATATION CELL SIMULATION USING MATLAB - SIMULINK SOFTWARE
We studied the mineral floatation of the raw material
exploited in the Baia-Mare area, Romania, processed in the mineral processing plant from this town. We considered a primary floatation cell, for which we evaluated the
characteristic constant values in the transfer functions (table 1).
The response of the considered system was searched, for unit input signal of the feeding flow rate Q and of the concentration C*, as well as for “white noise” signal, in the case of C*.
Fig. 1 Flotation cell block diagram
Ms, Vs, C*s, sM,V,C
Mc, Vc, C*c
bQ
a
Qc
QtMp, Vp, C*p, r Mt, Vt, C*t
FeedCell
(froth)
Cell(pulp)
Concentrate
Waste
Table 1. Values for time and proportionality constants in the transfer functions
Constant Relation
Value
Tp Vp /Qt
0,004808
Ts Vs /Qc
0,025749
k1 Tp C*
0,003468
k2 Tp Q
1,153920
k3 Ts C*
0,018572
k4 Ts Q
6,179760
SAMOILA AND MARCU 290
The results of the simulation are presented in figure 2, figure 3 and figure 4.
Analysing the system response, we may conclude: - the stabilising time for the pulp composition is 1.5-2 min.,
a sudden variation of the feeding flow rate or the feeding concentration being reflected in the system for about 2 min.; the concentration influence is more significant;
- the froth composition stabilisation time is about 6 min; - the “white noise” stochastic variation of the flow rate
influences more the froth composition.
The optimum duration of floatation in a cell can be determined
using the transfer functions which allow studying the mechanism of the mineral particles transfer from the pulp to the froth and reverse, respectively the process stabilisation time.
Considering the estimating relations for the time and proportionality constants, it can be told that these ones depend
on pulp flow rate, processed mineral composition, useful elements content in the raw material, weight recovery, aeration and dilution.
For a certain material and a given floatation technological line, our conclusion is that the optimisation parameters are the aeration and the feeding dilution.
4. SIMPLE FLOATATION CIRCUITS MODEL Using the balance equations [8], [9] written for different
types of monometallic mineral simple floatation circuits, we calculated the quantities and valuable metal contents in each point of the circuit.
We expressed these parameters only depending on recoveries in weight for each operation (vik, vcj), total weight recovery (v), feed quantity (A) and contents in: feed (a), concentrate (c), floated products of each enriching operation (dk) and cleaning operation (gj).
From our point of view, a floatation circuit can be represented as in figure 5, where the notation significance is:
k - enriching operation number; j - cleaning operation number; (xk) - vector of enriching operation parameters; (yj) - vector of cleaning
operation parameters. Analyzing the
calculation results, we observed the existence of some general relations. That was possible by noting the input and the output parameters in each block representing a floatation operation as in figure 6.
The indexes significance is: - “i” means “input”; - “e” means output. It must be said that the operations were numbered from the
Fig. 3 System response to the stochastic variation of the feeding flow rate (a) concerning the pulp (b) and the
froth (c) composition
a)
b)
c)
a)
b)
Fig. 4 System response concerning the froth composition variation when the unit input is the feeding flow rate (a)
and the feeding concentration (b)
Fig. 2 System response concerning the pulp composition variation when the unit input is the
feeding flow rate (a) and the feeding concentration (b)
a)
b)
FLOATATION CIRCUIT
A v
(vik) (vcj) a c
(dk) (gj)
BC
(Dk) (Fk) (Ej)
(b) (fk)
(Gj)
(ej)
Fig. 5 Simple floatation flow sheet
CONTRIBUTIONS IN MINERAL FLOATATION MODELING AND SIMULATION 291
circuit end to the beginning, in order to express the relations in a more simple form [10].
The relation between the output material quantity and the input one, for an enriching block, is:
vD100=Dik
ekik (7)
The recirculated quantity in the enriching circuit is:
D-D=F ekikk (8)
The output quantity for the primary floatation is:
F-D=D 2-k1-ki,ep (9)
The output material quantities from enriching blocks 2 and 3 (if they exist) are:
F-D=D ; D=D 12i3e1i2e (10)
The relation between the input quantity for a cleaning
block and the output one for the same block, k, is:
v-100E100=E
ck
ekik (11)
The floated material quantity in the cleaning circuit, which
is recirculated, is:
100Ev=G ikck
k (12)
If there are two cleaning operations, the output 2 is equal to
the input 1 and the waste quantity from the primary floatation is:
G-E=E ; E=E 2-k1-ki,ep1i2e (13)
The waste content and the input content in an enriching operation are:
FdD-dD=f
k
ekekikikk (14)
DfF+dD=d
ik
1-k1-k1+ke,1+ke,ik (15)
The input content for a cleaning operation is:
EgG+eE=e
ik
kkekekik (16)
The waste content from the primary floatation, when there
are one or two cleaning operations, is:
EgG-2e2E=e
e=e
ep
11iiep
ikep
(17)
We identified also the restrictive conditions which have to
be respected:
v100ac < (18)
ikvik100d
ekd < (19)
( )2100
c2v100c1v1gi2e
−> (20)
c...ekd...epda;1jgjg;ejejg <<<<<−>> (21)
5. VISUAL BASIC APPLICATION FOR SIMPLE
FLOATATION CIRCUITS DESIGN
Using Visual Basic programming tools, we developed an application that allows the calculation of any floatation circuit.
In the main window, the operator has to introduce the values of the input variables, including the number of both kinds of operations (figure 7).
The data are verified and, if they are not properly introduced, a message appears to worn the operator (figure 8).
After introducing the number of enriching operations, a window is opening to introduce the values of weight recoveries and contents in the floated outcomes (figure 9).
A library of flow sheet diagrams is included and, according
Fig. 6 Simple floatation flow sheet
SAMOILA AND MARCU 292
to the specified number of operations, the appropriate one can be visualized in order to see the specific notations (figure 10).
After the operator introduces the number of cleaning
operations, another window opens that allows him to introduce the weight recoveries and floated outcome contents in this kind of operations (figure 11).
The calculation results are displayed in a table (fig. 12). Further development of this application let the data and the
results be saved. Thus, the designer or the researcher can compare different sets of values in order to establish the optimum configuration of the technological line.
Using such an application, time can be spared in floatation
technology design and the accuracy of the results is improved.
Fig. 7 Main window
Fig. 8 Warning message
Fig. 9 Window for enriching operations
Fig. 10 Floatation flow sheet diagram
Fig. 11 Window for cleaning operations
CONTRIBUTIONS IN MINERAL FLOATATION MODELING AND SIMULATION 293
6. CONCLUSIONS Floatation can be considered a physical and chemical
separation process of solid products, by establishing a contact in three phases: the floating mineral, the liquid phase and air. The great number of parameters involved in floatation, due to the high complexity of the process, requires a new kind of approach of studying this process. The development of computers hardware and, most of all, software, allows a new method of experimental research by simulation.
In order to simulate a primary floatation cell, we adopted a two-phase model, considering the pulp and the froth as two distinct phases. Using MATLAB SIMULINK software, we were able to obtain the process response when the feed flow rate and composition has a sudden step variation or a stochastic one. For a certain material and a given floatation technological line, the conclusion was that the optimisation parameters are the aeration and the feeding dilution.
In order to use computers in floatation circuit calculation, we elaborated the mathematical model for simple circuits which allowed pointing out the relations between the material quantities and between the metal contents. We developed an application using Visual Basic programming tools to calculate
any kind of circuit. As any real floatation circuit, no matter how complicated, may be decomposed in simple circuits, like the types we studied, the calculation could be simpler and faster, using this application.
Attempting to make out the algorithm, we found some new general relations between parameters, as well as restrictive conditions in the circuit calculation. Using this application, we created new possibilities to analyze and optimize the floatation circuit configuration and the operations number.
The software has been developed to provide the mineral processing specialists and researchers a tool to better understand and optimize their flotation circuits. This methodology has been found to be highly useful for plant metallurgists, researchers and consultants alike. Plans are already made to extend the program for a complete flotation circuit analysis package.
REFERENCES
[1] B.L. Samoila, “Introducerea tehnicii de calcul in conducerea procesului de flotatie a substantelor minerale utile”, Doctoral thesis, University of Petrosani, 1999. [2] M.C. Harris, K.C. Runge, W.J.,Whiten, R.D. Morrison, “ JKSimFloat as a practical tool for flotation process design and optimization”. Proceedings of the SME Mineral Processing Plant Design, Practice and Control Conference, SME, Vancouver, 2002, pp. 461-478. [3] http://www.metsominerals.in. [4] http://www.mineraltech.com/MODSIM. [5] S.E.E. Schwarz, D. Alexander, “Optimisation of flotation circuits through simulation using JKSimFloat”. Proceedings of the 33rd International Symposium on the Application of Computers and Operations Research in the Minerals Industry. APCOM 2007, Santiago, Chile, pp. 461-466, 2007. [6] J. Villeneuve, J.C. Guillaneau, M. Durance, “Flotation modelling: a wide range of solutions for solving industrial problems”, Minerals engineering ‘94. International conference Nr.4, Lake Tahoe NV, USA, vol. 8, pp. 409-420, 1995 [7] B.L. Samoila, “Sistemul tehnologic multivariabil de flotaţie. Traductoare, modelare, simulare”, Universitas Publishung House, Petrosani, 2001. [8] K.C. Runge, J. Franzidis, E. Manlapig, “Structuring a flotation model for robust prediction of flotation circuit performance” Proceedings of the XXII International Mineral Processing Congress. IMPC 2003, Cape Town, South Africa, pp. 973-984, 2003 [9] A.C. Apling, J. Zhang, “A flotation model for the prediction of grade and recovery.” Proceedings of the IV International Mineral Processing Symposium, Antalya, Turkey, pp. 306-314, 1992 [10] B.L. Samoila, L.S. Arad, M.D. Marcu, „A Mathematical Model of Simple Floatation Circuits”. Proc. of the 17 th International Mining Congress and Exhibition of Turkey, IMCET, Ankara, Turkey, 2001, pg. 711- 714.
