A Flotation Cell Model for Dynamic Simulation

A Flotation Cell Model for Dynamic Simulation

16th IFAC Symposium on Automation in Mining, Mineral and Metal Processing August 25-28, 2013. San Diego, California, USA A Flotation Cell Model for D...

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16th IFAC Symposium on Automation in Mining, Mineral and Metal Processing August 25-28, 2013. San Diego, California, USA

A Flotation Cell Model for Dynamic Simulation ? Jos´ e Manuel Ortiz ∗ Rodrigo Toro Olmedo ∗ ∗ Honeywell Chile S.A., Santiago, Chile (e-mail: [email protected], [email protected])

Abstract: In this paper a dynamic model of ore flotation is presented. The model has been conceived in such a way that its tuning is easily carried out by the use of commonly available information: flotation kinematics experiments results (used in plant design process), plant dimensions and design throughput, valves and nozzles specifications, and some minor assumptions. The basic modeled module is a flotation cell with two phases: slurry and froth. The phenomena involving the transportation of rich particles from the slurry to the froth by air bubbles is addressed. In spite of its simplicity, the model has proven to be highly effective for operator training, control system verification and commissioning, and plant design verification. The model is presented in detail along with an operator training case study. Keywords: Dynamic modelling, metals, simulation, industrial control. 1. INTRODUCTION Kinematics-based models have historically been used to characterize flotation circuits (see Garc´ıa-Z´ un ˜iga (1935)). The two-phases flotation model has been widely discussed in the industrial and academic communities (see Bascur (2005), Herbst et al. (2005) and, Herbst and Harris (2005) for further details) and is the base of the model stated in this work. Simulators based on dynamic models have been widely used for operator training simulators (OTS), an example for the flotation process has been presented in Roine et al. (2011), Toro et al. (2012), among many others. Further, such models are also applied for control system tunning (Sirkka-Liisa (1992)), plant design validation (Toro et al. (2013)), and pre-comissioning. In simulation projects where the entire plant was simulated for pre-comissioning, design verification, control system validation and operator training (see Toro et al. (2013) for further details), a model that could be tuned with the commonly available information was needed. The literature offered many different model approaches, but the fact is that most of these models where hard to tune due to the lack of needed plant data. In this paper, a simple dynamic model of an ore flotation cell is presented. The focus was put from the start in the possibility of tunning using flotation kinematics, which are commonly available for green field plants, as well as for brown fields. The main contribution of this paper is the statement of a two-phases dynamic model, that has proven to be easily adjusted with real plant data, generated by typical laboratory tests, and include the most used variables for process control and monitoring, allowing it to become an excellent tool for process engineering validations and ? Work of J. M. Ortiz and R. Toro has been supported by Kairos Mining and Honeywell Chile S.A.

978-3-902823-42-7/2013 © IFAC


operator training. Furthermore, the static data, plant dimensions and minor assumptions are enough for tuning a dynamic model. This paper has been structured in the following way: In Section 2, the proposed model is descripted; in Section 3 the model parameterization method is stated; in Section 4 a real plant case study is presented. Finally, in Section 5 conclusions and possible future work is discussed. 2. MODEL DESCRIPTION The cell contents are modeled in two phases: slurry and froth. The core of the model is a mass balance equation on each phase, where streams of material going into the cell, out of it and between phases, are accounted for. The mass balance equations for the slurry phase are as follows: H˙ SA = mF A − mSF A F ˙ HSk = mk − mTk − mSF k , for k =, ..., nc

(1) (2)

and the froth phase: H˙ F A = mlA − mC A + mSF A H˙ F k = mSF k − mC , for k = 1, ..., nc k

(3) (4)

where, HSA : air holdup in slurry phase, HSk : component k holdup in slurry phase, HF A : air holdup in froth phase, HF k : component k holdup in froth phase, mF A : air feed mass flow, mF k : component k feed mass flow, 10.3182/20130825-4-US-2038.00064

IFAC MMM 2013 August 25-28, 2013. San Diego, USA

cally as if they were organized in wave fronts, as shown in Fig. 2

Fig. 2. Bubbles front With such assumptions, the inter-phase mass flow can be modeled as follows Fig. 1. Schematic of flows and holdup in flotation cell model. mSF k =

mC A : air mass flow in concentrate overflow,

mk n T



mC k : component k mass flow on concentrate overflow,

mk : mass of mineral type k attached to the bubble,

mTk : component k mass flow on tail, mla : air loss mass flow (bubbles that don’t reach the concentrate stream), mSF A : air mass flow from slurry to froth phase, and mSF k : component k mass flow from slurry to froth phase. Inter-phase reverse flows are not considered and hence, mSF A and mSF k , are assumed non-negative net mass flows.

T : bubbles wave front arrival period, n: number of bubbles in a front. The mass of mineral of type k attached to a bubble is considered to be a fraction of the total mass of that mineral surrounding the bubble during its residence time inside the slurry phase. Hence, mk = τ ak hk


As depicted, mass flow variables with the superscript F (Feed) are inputs (hence, independent variables) and mass flow variables with superscript C (Concentrate), T (Tail), and l (loss) are outputs (hence, dependent variables). Further, the subscript SF (Slurry to Froth) is used to specify the inter-phase mass flows.


Given that the independent variables are assumed known from a previous production stage or determined by the operator and that the model holdups are determined by equations (1) through (2), what is left to define is the relation between holdups and inputs through model parameters that determines the inter-phase and output mass flow values. Description of such relations follows, with which the model is fully defined.

τ is the travel (or residence) time of bubble in slurry, which is given by

2.1 Inter-phase Streams

hk is the mass of mineral type k surrounding the surface of the bubble (candidate to become attached to the bubble), ak is called attachment efficiency, the fraction of mass that attaches to the bubble,


VS Avb


where, VS is the slurry volume, which is calculated from the mass holdups and components’ densities, A: cell base area,

The inter-phase flows describe the actual flotation process, in which air bubbles carry the rich components to the froth to form the valued product of this process unit. Let us begin by describing the mass flow of rich components. Under the simplifying assumption that air bubbles in the slurry are uniformly distributed along the whole slurry volume, bubbles arrive at the froth phase periodi162

vb : bubble terminal velocity, calculated by r vb = where, g: acceleration of gravity,

gdb 3cd


IFAC MMM 2013 August 25-28, 2013. San Diego, USA

db : bubble diameter (assumed known) cd : drag coefficient. In this case, bubble is assumed perfectly spherical, for which cd = 0.47. Considering the total mass of mineral type k in the slurry calculated by (2), slurry volume, bubble diameter and particle mean size, apparent superficial density of particles type k can be calculated, with which we obtain HSk hk = dk πd2b VS



mSF A =



2.2 Outputs Assuming perfect mix in the slurry, mineral type k tail mass flow is given by HSk q T (16) VS where q T is the tail total volumetric flow and it is given by Torricelli’s equation: mTk =

dk : mean diameter of particle type k s

db : mean bubble mean diameter


Given the assumed uniformity on the distribution of bubbles in the slurry and equal diameter for all bubbles, bubbles front arrival period is simply

q = Cv

P atm + ρS ghS − Po a ρS


where, ρS is the slurry density,

T =

db vb



ρA : air density. Equations (6) through (11) can be replaced in (5) to obtain inter-phase mass flow 6dk mSF k = ak HSA HSk , (12) ρA V S d b where it can be noted that the amount of mineral going from the slurry phase to the froth phase depends directly on the amount of air in the slurry, which of course is related to the amount of air fed into the cell through (1), and also on the amount of mineral of type k present in the slurry. Attachment efficiency ak is the key parameter for tuning. Its value is tuned in order to reproduce the mass balance resulting from flotation kinematics. This parameter allows the use of generally available information, such as flotation kinematics for tuning, as will be shown in the next section. With the same assumptions taken for mineral components, inter-phase air mass flow is calculated by mb n (13) mSF A = T where mb is the bubble mass, calculated from spherical geometry and air density as follows 1 ρA πd3b 6

slurry height in cell,

Po : head pressure at next cell’s inlet or Patm if there is no next cell, Cv : characteristic flow coefficient of outlet valve, a: outlet valve opening fraction. This is an independent (input) variable. Air in the slurry phase is assumed to go entirely to the froth phase, which means the tail stream does not contain air.


mb =

VS A :

Patm : atmospheric pressure,

Finally, the number of bubbles in a front can be calculated from the air holdup in the slurry (1), cell geometry, air density and again the assumption of uniformity, resulting in 6AHSA n= πρA d2B VS

hS =


Hence, by the use of (10), (11) and (14) in (13), we obtain 163

Again, assuming perfect mix now in the froth, concentrate mass flow for component k and air is modeled as follows HF k q C (18) VF where q C is the concentrate total volumetric flow, which exists only if there is froth overflow. Hence, mC k,A =


q =

rC (VS + VF − V ) , VS + VF > V 0 , VS + VF ≤ V


where, V is the cell total volume, rC is a constant parameter called overflow rate, which is tuned for bubbles overflow velocities (as measured by froth vision systems, for example). 3. MODEL TUNING As mentioned in the previous section, the main parameter to tune is the attachment efficiencies ak . These values determine the dynamics as well as the steady state of the model. Given the cell dimensions, head grade of each component, nominal mass flows and percent of solid in the feed stream, and the flotation kinematics of the plant, a steady state mass balance can be built. As a result, input and output

IFAC MMM 2013 August 25-28, 2013. San Diego, USA

mass flow values are obtained from said mass balance. Which means the following values are known in steady state: T C mF k , mk , mk

An HMI, based on the DCS schematics, was developed and implemented on USO in order to provide the students with a working environment as similar as possible to the real plant (see Fig. 4). Regulatory controls are simulated as well, which allows for training on the best use of them by facing situations such as wind-up.

Volumetric flow values in steady state can be calculated as well given that volumetric densities of each component are known: qT , qC For each cell in a flotation line, the following values are considered known: VS , mF A Furthermore, given these known values, solving from (16) and (18) for componet k and air holdup in slurry is possible. Hence, holdups are known: HSA , HSk , HF A , HF k Taking (2) and (3) to steady state and using (12) results in 6dk HSA HSk (20) ρA VS db where ak can be solved for and its value for each k can be calculated assuming db and dk are known. mC k = mSF k = ak

4. CASE STUDY The described model has been implemented on Honeywell R R Unisim Design (USD) and Unisim Operations (USO) and used on OTS projects. USD is the platform for plant design and simulation, while USO serves as Instructor and Trainee Interface, as well as provider of means to connect to a DCS. On Codelco Chuquicamata, a model of one primary flotation line was constructed and tuned using kinematic models, historic data and site engineers knowledge. As shown on Fig. 3, the plant consists on a flotation line of six cells, arranged on groups of two cells per level.

Fig. 4. HMI for flotation OTS in UniSim Operations 4.1 OTS Scenarios Scenarios that operators must face cover from plant stabilization, abnormal operating situations to external situations. They are defined as follows: (1) Process Stabilization: trainee is faced to high concentrate and tail grades, and cells without concentrate overflow. They must return the plant to a normal operation situation. (2) Low throughput from milling plant: due to an upstream issue, feed flow suffers a sudden decrease. Trainee must compensate situation, keeping recovery values normal. (3) Concentrate tank overflow: due to foaming, the concentrate tank may overflow. Trainee must keep tank level in normal range. (4) Feed grade increase: sudden grade increase. Trainee must compensate to maintain recovery and low tails grade. (5) Concentrate overflow speed control: disturbance on air feed and grade are applied to the plant. Trainee must apply proper overflow speed profile in order to maintain plant in correct operational range. Each case is applied and evaluation is carried out by the use of excursion-based method, as described in Toro et al. (2012). 4.2 Other OTS projects The model has also been used for a number of stages in project Ministro Hales (Codelco’s new division). This is a large project in which simulation is being used in the entire concentrator plant (including all flotation stages) for:

Fig. 3. Dynamic model of flotation line in UniSim Design The customer’s goal is to educate operators and engineers on: best operational practices, ability to identify variables on the process that are key to efficiency, and understand how operational actions affect the cost of the process. 164

• • • •

Plant design verification Comissioning procedures verification Control strategy assessment and tuning Operator Training

IFAC MMM 2013 August 25-28, 2013. San Diego, USA

5. CONCLUSIONS AND FUTURE WORK A flotation cell model has been developed. A practical approach has been used for tuning, which uses data commonly available on real plants. A case study has been presented, in which the model has been used to reproduce the behavior of an entire primary flotation cell. The model has proven effective in the representation of the plant’s steady state as well as the dynamics, enabling its use for operator training. The model has also been used for plant design verification and control system pre-commissioning, with positive results. Currently, our simulation team is implementing a separate model for column flotation, seeking better results with different pH conditions and washing water. ACKNOWLEDGEMENTS The authors would like to acknowledge Kairos Mining CEO, Claudio Zamora, for his continued support on the development of simulation models for the mining industry. Also, the work of Honeywell Chile simulation team: Sandy Ramirez, Jenny Bustos, Juan Carlos Jarur and Freddy Gomez. REFERENCES Bascur, O. (2005). Example of a dynamic flotation framework. In Centenary of Flotation Symposium. Garc´ıa-Z´ un ˜iga, H. (1935). La eficiencia de la flotaci´on es una funci´ on exponencial del tiempo. Bolet´ın Minero, Sociedad Nacional de Miner´ıa, 47, 83–86. Herbst, J.A. and Harris, J. (2005). Modeling and simulation of industrial flotation processes. In Centenary of Flotation Symposium. Herbst, J.A., Potapov, A.V., Pate, W.T., and Lichter, J.K. (2005). Advanced modelling for flotation process simulation. In Centenary of Flotation Symposium. Roine, T., Kaartinen, J., and Lamberg, P. (2011). Training simulator for flotation process operators. In Preprints of the 18th IFAC World Congress. Sirkka-Liisa, J.J. (1992). Simulation study of self-tuning adaptive control for rougher flotation. Powder Technology, 69, 33–46. Toro, R., Ortiz, J., and Yutronic, I. (2012). An operator training simulator system for mmm comminution and classification circuits. In IFAC Workshop on Automation in the Mining, Mineral and Metal Industries. Toro, R., Ortiz, J., and Zamora, C. (2013). An integrated simulation-based solution for operator effectiveness. In Proceedings of The 15th IFAC Symposium on Control, Optimization and Automation in Mining, Minerals & Metal Processing.