- Email: [email protected]
Factorial Design and Analysis to Obtain Optimum Operation Conditions
THEORY
Copyright :(' IFAC Automation in Mining, Mineral and Metal Processing, Helsinki, Finland, 1983
FACTORIAL DESIGN AND ANALYSIS TO OBTAIN OPTIMUM OPERATION CONDITIONS O. Vartiainen and V. Tinnis Ekono Oy, Helsinki, Hnland
Abstract. It is very astonishing that despite the availability of efficient equipment and well developed methods with more advanced systems a majority of experimental ,,,ork and plant operation management is carried out by using conventional techniques in the mining, mineral processing and metal lur gical industry. It is true that high quality products have been produced for decades without any sophisticated procedures. However, one is not convinced that the processes are run at their optimum performance level. On the con trary, there is an inclination to believe this not be the case. When determining the influence of various process variables and parameters on the results of the production operation a two-dimensional evaluation technique is usually applied. The decisions made on the basis of these results either for control or ope rational instructions purposes are far from optimum. When one variable is changed, it will affect many others. Although the methodology is well documented and efficient modern equipment such as fast analyzers and powerful computers are on the shelf,a yawning gap between theory and practice exists. A special aim of this work is to improve the reliability of the conclusions drawn from test results and indicate the relative significance of dif ferent variables quantitatively. It is also possible to determine the level of stable operation of a process. Emphasis should be placed on these matters now when automation is gaining more and more ground . The paper refers to a previously published article which appeared ai -out twenty years ago and described how Factorial Experiments can practically be utilized when determining the right operating conditions in metallurgical processes. This presentation illustrates the method with a practical example from a pyrometallurgical process and shows how to relate significantly various information data to the qualitative, quantitative and economic results of the production establishment. The purpose of this presentation is to make a contribution towards bridging the gap between theory and practice. Keywords. Multivariable systems; statistics; factorial design; system ana lysis; metallurgy.
INTRODUCTION
and at the utmost with a parameter as a third variable .
When examining international publications on process studies in the mining industry such as ore- and mineral processing and pyro- and hydrometallurgical processes, one finds that the studies have been designed according to the principle 'one variable at a time'. The determination of the effect of the various factors on the processing results is essentially based on this ap proach. Thus the findings are usually presented as curves in two-dimensional graphs
However, when one process variable is changed many other variables ,,,ill c hang e at the same time so that the eff e ct of the ma nipulated variable alone is overshadowed . This increases the risk for drawing ,,,rong conclusions. The authors have reviewed the publications from th e two latest International Mineral Processing Congresses, i.e. j'Jarsaw - 19 79
AM-K*
311
312
0. Vartiainen and V. Tinnis
and Toronto - 1982 Congresses (1), (2). None of the presented papers at these meetings deal with e.g. at least the effect of the combined main factors in analyzing the various processes. The application of factorial design to a pyrometallurgical process is described in this article. Although the application has been demonstrated by one of the authors (3) already 20 years ago, factorial design has not been used extensively even in Finland. THE FACTORIAL DESIGN METHOD The factorial design and analysis method is well documented in the literature (4), (5). Therefore, the method is only described in this article in brief since the main aim is to describe its application to a pyrometallurgical process (3). Factorial design and analysis for a system of 4 factors (denoted e.g. K, T, H and V) on two levels (1 and 2) can be carried out as 24 -factorial experiment, table no. 11 page 4. The statistical analysis of the measured effect - e.g. the sulphur content in calcine product when roasting iron sulphide matte - will yield both the main effects of the various fa~tors as well as their interactions. An analysis of variance provides also the significance data for the evaluation of the specific effects. In many cases the interactions of the various factors are important. In order to determine the effects more clearly, a 2 3 -factorial analysis can be done separately for the two levels and for some of the most important factors (e.g. T and H).
FACTORIAL DESIGN APPLIED TO A PYROMETALLURGICAL PROCESS Short Process Description Factorial design as applied to a fluidized bed iron matte roasting process has shown very interesting test results. The basic elements of this process are described ~n general terms in the following (6). Roasting of iron sulphide matte, of the grain size distribution as shown in figure no. 1, takes place mainly according to the following chemical reactions: 4FeS + 702 ---> 2Fe 0 + 4S0 2 2 3 4FeO + 02
---> 2F e 0 2 3
Both reactions are exothermal and the amount of heat release is about 5900 kJ per kg of iron sulphide matte. The required completeness is such that the residual sulphur content in the calcine is less than 1 %. Sulphur dioxide is recovered for the production of sulphuric acid. The released heat produces superheated steam (500 °C, 6.5 MPa), which is fed to the power plant. Furthermore steam of 0.5 MPa pressure is produced in the iron calcine cooling process. A cross section of a fluidized bed roasting furnace is shown in figure no. 2. In table no. I. data showing typical process conditions are listed for one of thre e r e actors of the investigated iron sulphide roasting plant.
The experiment in this case is planned according to the standard 23 -factorial design procedure of 8 observations in the following manner:
Obser- K T H KT KH TH KTH I vation J1 J2 J3 J4 J5 J6 J7
J8
+ + + + +
+ + + +
+ + + +
+
+ +
+ + +
+ + +
+ +
+
+ +
+
+ + + + + + + +
Treatment combination (r)
k t kt h kh th kth
The sign + denotes the higher level and the sign - the lower level. An analysis of variance concludes the procedure, which enables a pertinent discussion of the various effects and interactions.
~ 101~+t/:ttti J=t==t==t=W /
:;;; Sf-
~ 6~--vl/--~V~~~--~--~-+-H
l5
~
41 /
~:
0.1
I.
I
2 4 6 a 10 ft'S MATTE PARTICLE SIZE DISTRIBUTlON,mm 02
Figure 1.
04
1.0
Screen analysis
Factorial Design and Analysis
313
Amount of steam developed 686 tld = 1.39 tons per ton FeS matte Temperature of feed water 213 °c Iron content of total calcine 67.4 % Sulphur content of total calcine 0.35 % Sulphur content of coarse calcine 0.20 % Sulphur content of fine calcine 0.75 % Total power need 28 kWh per ton FeS matte
·' .iili
Process Technical Requirements
-:;~ o;~
The amount of inert material in the reactor is approximately 30 tons, and the amount of fresh iron sulphide feed about 20 t / h. The gas velocity at 1000 °c is about 3.3 mls against the free-grate area of the reactor. The roasting temperature has to be controlled very closely. This is done so that the air feed is kept constant and the amount of iron sulphide is regulated according to the temperature. The following reaction conditions among others are important:
Figure 2.
Fluidized bed roasting furnace (cross section)
- The reaction time has to be kept constant. - In order to achieve desired chemical results the material has to stay at conditions favorable to the reaction for a specific minimum of time, which among other things is a function of the grain size.
Table I.
Typical roasting conditions of iron sulphide matte
Amount of air
3
38,000 m nlh
Pressure drop in grate and bed total 2,000 mm H 0=20 kPa 2 S02 content of gas after furnace 9.5 % SO content of gas afier electrost~tic precipitator 8.5 % Temperature in reaction zone 1,020 - 1,045 °c Temp e rature before the boiler 965 °c Temperature after the boiler Pressure of superheated steam 6.5 MPa Temperature of superheated steam 495 °c Feed of iron sulphide matte 494 tld Iron content of iron sulphide matte 62 i. Sulphur content of iron sulphide matte 30 % Moisture content of iron sulphide matte 1.4 %
Abnormal particles (grain Size diff e ring greatly from the average) have to be removed from the reaction zone. Thus iron sulphide 'clumps', large pieces of calcine, and pieces dropping from th e walls of the reactor, should not be allowed to accumulate inside the reactor. The removal of the material from the reactor is carri ed out by means of a gas-tight mechanism. Process Variables The variables which characterize the roasting process are mainly the following: Input variables: - Iron sulphide feed rate - Air flow - Fuel flow (at start) - Iron sulphide composition - Feed material grain size distribution Output variables: - Flue gas temperature - Flue gas composition - Dust content in flue gases - Outlet flow rate of roasted material - Roasted material composition and grain
314
O. Vartiainen and V. Tinnis
size distribution - Temperature of roasting material cooling
Table Ill. Reciprocal sulphur content, x 10 b\~fore
H
State variables: - Amount of roasting material in bed - Bed (gas-solid material mixtllre) temperatur.e and distribution - Gas temperature above bed - Geometry of the reactor Mixing condit ions of material - R.esidence time
H2
HI K
T
V
V VI
V
VI
V
Tl
1.91
2.43
4 . 08
2 . 83
T2
2.35
13 . 51
9 . 52
2 1.74
Tl
2.73
3 . 83
6.95
(ZZ .Z9)
T
(9.13)
4.79
( 15.92)
50.00
Kl
KZ
FACTORIAL EXPERI!'1ENTATION AND ANALYSIS
Z
z
z
The result of the statistical analysis are shown in table no. IV
In order to quantitative ly relate these variables factorial design and experimentation are found to be a very powerful tool.
Table IV. Resul ts of Factorial Experimentation
For the determination of the relationship of the most important process variables at steady state conditions a fac torial design procedure has been carried out. The following variables have been included in the experimentation:
Sum of squares
Effect
Degree s Mean of freedom square
Signif icance (X)
Main effect:
-----------
Air £10'01 ratio
- Air flow ratio (actual air/theoretically calkulated air)
change
(K)
Temperature change
(T)
399.10
1.5
Bed he igh t change
( H)
536. 10
( 1
Air velocity change
(V)
296.10
204 .99
Combined effec t:
--------------
- Bed tempera tu re - Bed height (pressure drop of air/reaction time)
Level I
Temperat ur e ,
Bed height, Air veloc ity ,
°c
(T)
mm H O
(H)
2
m/ s (V)
950-
I 989 (TI
I 095-1 470 (HI 2 . 56-2.99
(V I
}
20.36
The changes in bed height and temperature are very significant. On the other hand it can be seen from table no. III that the sulphur co ntent data cor responding to temper~ture T2 are, without exception, better than those for temperature T • Also the figures l are better for a greater amount of material in bed (H) than for a l ess material amount.
2.
The changes in air velocity and air flow ratio as well as the combined effects KH and HV are significant on a 5 % level. According to table no. III one can conclude that a higher air velocity (V ) is better than a lower 2 velocity (V ) and that a higher air L flow ratio lK ) results in better product quality than a lower ratio (K ). The latter is, however, uncerl tain because the result is based on the calculated data rather than measured.
1. 400-1.650 (K ) 2 990-1 025 (T ) Z I 471 -1 850 (H ) 2 3.00-3.53 (V )
The su l phur content in the calcine product has been chosen as the criterion for the anal ysis, being the most important output variable. In order to facilitate the calculations the reciprocal value of the sulphur content has been taken as a basis for the analysis. This data is shown in table no. Ill. The figures in parenthesis have been calculated according to the Yate's method because the corresponding test data were not available.
28.49
1. Level 2
1 . 152-1.399 (K
KTHV
The following conclusions can be drawn from table no. TV:
Table 11. Experimentation levels
(K)
THV
17.00 7. 30 178.08 45.66
8 10 4.5
(Co1'llbined effect· int e raction)
These variahles have been manipulated at two experimentation levels according to table no. 11.
Variable
201.00 34 .60 110.93 87.47 168.68
KTH KTV KMV
- Air velocity in the bed (calculated for the free cross section of furnace above the grate)
Air flow ra tio
4.17
KT KM KV TH TV HV
z
Factorial Design and Analysis 3.
The combined effects of TH and TV are significant on a 10 % level.
In order to obtain the effect of the various 3 process conditions a 2 -Factorial Experimentation analysis has been done such, that the calculation has been carried out separately for two temperature levels: Tl and T . This enables on to eliminate the effect 2 of the temperature.
315
It can be seen from Table no. VI that a a higher bed (H ) and greater air velocity (V ) in combination provide better results. 2 As shown also in Table no. III a higher bed yields better results. In order ~o get clearer picture of the situation a 2 -Factorial Experimentation analysis has been carried out separately for the H - and 1 H -1evel. The results are presented in 2 Tab le no. VII.
Table no. V shows the obtained results. 2 3 -Factorial Experimentation.
Table V.
Statistical analysis, separately for T - and T -level. 2 1 T2
Tl
Influence Sum of squares
Degrees of freedom
Mean
Signifi-
square
cance (%)
Sum of squares
Degrees of freedom
Mean
square
Significance (%)
Main effect: ------------
Air flow ratio change
(K)
75.34
2
> 10
133.83
-
-
Bed height change(H)
79.69
2
> 10
567.85
1
6
Air velocity change
30.85
1
-
352.72
2
(V)
Combined effect: ----------------
KV HV KHV
50.55 36.85 19.44 32.04
Sum
47.05
!CH
10
-
i}3
35.61
-
-
-
n
167.45 5.06 194.83 174.47
4
126.96
-
93.59
-
It can be concluded that:
1.
The conditions are more stable at Tl -temperature level than at T . 2
2.
The changes in bed height and air flow ratio are significant on the Tl -temperature level. As shown in Table no. III H~ and K? give better product quality tlan the-corresponding RI and K . l
3.
4.
On the T2 -temperature level the bed height and air velocity are significant. H2 and V give better results than the 2 corresponding HI and VI' as shown in Table no. HI.
The results indicate the following: 1.
2.
3.
The combined HV-effect is relatively high. This effect is further analysed in Table no. VI on the T2 -temperature level.
On the HI-level the temperature change is statistically the most important. The T -condition provides better results 2 tfian T , as shown in Table no. Ill. 1 On the H -1evel the air flow ratio and 2 air velocity changes are very significant. A higher air flow ratio gives better results than a lower one. The same applies for a higher air velocity. On the H -1evel the significance of the 2 change in temperature, air flow ratio and air velocity is of the same order. However, it should be taken into account that the degree of freedom for the temperature change is zero.
Combined RV-effect at temperature T2
Table VI.
CONCLUSIONS The following general conclusions can be drawn from the analyses:
H
V
*
Hl
H2
V 1
11.48
25.44
36.92
V 2
18.30
71 .74
90.04
29.78
97.18
The best results are obtained under the level 2 conditions, i.e.: -
bed height temperature air velocity air flow ratio
1470 990 3.00 1.40
-
1850 mm H 0 2 1025 °c 3.53 m/s 1.65
316
0. Vartiainen and V. Tinnis
Table VII.
2
3
- Factorial Experimentation
Statistical analysis separately for H - and H -level. 1 2 HI
Influence
Sum of squares
H2
Degrees of
Mean
freedom
square
Significance (%)
Sum of
squares
Degrees of freedom
Mean
Signifi-
square
cance (%)
Main effect : ------------
Air flow ratio change
-
(K
0.01
2
405.98
1
Tempera tu re change (T
44.56
1
> 10
465.58
-
-
Air velocity change (V
8.90
1
-
455 . 87
1
6
-
19.00 184 . 80 129.69 3 . 47
-
KTV
2.16 27 . 83 3 . 38 32.32
Sum
40.68
6
Combined effect :
---------------KT KV
TV
Hs
On the other hand it has been found that a lower temperature 950-990 °c provides more stable conditions than a higher one.
*
*
At lower bed height (1095-1470 mm H 0) 2 the effect of the temperature is more significant in comparison with the other variables. This indicates that the process is sensitive to temperature variations. At a higher bed (1470-1350 mm H20) the effect of the temperature, air flow ratio and air velocity are about equally significant. This also means that the roasting process is more stable at a higher bed level.
Achieved results and their utilization in prac tice The above research work was originally carried out in connection with the pilot tests and repeated after three years when the practical siz e mill with two reactor lines was ready. Based on analysis of the pilot test results - the reactor main air blower maximum pressure was chose n to 2500 mm H 0. At 2 that time the equivalent "normal" blowers in the industry worldwide operated at about 1100-1200 mm H 0 pressure 2 - temperature measurement in the reactor for the control was carefully designed. The number of measureme nt points were greater than normal afld a two-colour pyrometer was fItted to the reactor in order to ascertain the reliability of the measurements. Additionally the temperature control was effected by a derivative mode, by which the amount of feed material was controlled within certain reactor temperature limits. - Special attention was given to the material reaction and in particular, the
12.71
-
133.33
-
-
1 1
3.47
-
----- --- - -
oxidation time, for this purpose a device was designed which well fulfilled the necessary criteria. The method was also patented outside Finland (6). These measures proved successful in production practice. Typical production results are shown in Table I. It was also found that the specific capacity of the reactor could be raised by about 30 % over the nominal value, of comparable reactors worldwide using fluidized bed processes at that time. This increase in capacity did not influence the sulphur content of the calcine product. When the plant was expanded a few years later this also meant that it was possible to reduce the investments considerably. Another important benefit which was achieved was that the coarseness of the fe ed material could significanlty be increased without influencing the fluidized bed process or handling of the calcined product. The control of the reaction zone temperature was as successful as expected and resulted in a steady operational state and high annual availability, 96-97 ~~ wh en tak.ing into account the normal annual three week down time. One of the authors, who was in charge of the research work and planning which lead to construction of the plant, is of the distinct opinion that the research method used for analyzing the test results was of great importance in attaining the outlined good metallurgical and economic results.
Factorial Design and Analysis LITERATURE CITED:
BRIDGING THE GAP BETWEEN THEORY AND PRACTICE Although the factorial design and analysis method has been well documented and known for decades, its application has been very sparse in the world of mining, mineral and metal industry. The reason for this unwarranted circumstance might be the poor cooperation and understanding between the research and operation personnel on one side and the process control engineers and mathematicians on the other.
317
(1)
Developments in mineral processing, Thirteenth International Mineral Processing Congress, Warsaw June 4-9, 1979, Proceedings part A and B, Elsevier Scientific Publishing Company, Amsterdam 1981
(2 )
Worldwide industrial application of mineral processing technology, XIV International Mineral Processing Congress, October 17-23, 1982, Toronto, Canada
For bridging the gap there are institutes and consulting companies which offer their services. This is one way in successfully adopting advanced methods, towards the beneficial utilization of the presently best available technology. This would enable one to run the process at economically optimum operating conditions.
(3)
Vartiainen, Osmo: Factorial Experimentation research method for the analysis of benefication and metallurgical processes, Vuoriteollisuus 1961, p 48-54, (in Finnish)
(4)
The obtained results can be used for the quantitative determination of the relation of the various process variables in a mathematical model of the process.
Davies, Owen L.: The design and analysis of industrial experiments, Oliver & Boyd Ltd., London-Edinburgh 1960
(5)
Lokki, Olli: Ti1astollisista menetelmista, Puukemia, Suomen Paperi-insinoorien Yhdistys 1967, G6, (in Finnish)
(6)
Vartiainen, Osmo: New system for solids removal boosts capacity of roasting furnaces, E/MJ - January 1971, p. 80-83
Copyright :(' IFAC Automation in Mining, Mineral and Metal Processing, Helsinki, Finland, 1983
FACTORIAL DESIGN AND ANALYSIS TO OBTAIN OPTIMUM OPERATION CONDITIONS O. Vartiainen and V. Tinnis Ekono Oy, Helsinki, Hnland
Abstract. It is very astonishing that despite the availability of efficient equipment and well developed methods with more advanced systems a majority of experimental ,,,ork and plant operation management is carried out by using conventional techniques in the mining, mineral processing and metal lur gical industry. It is true that high quality products have been produced for decades without any sophisticated procedures. However, one is not convinced that the processes are run at their optimum performance level. On the con trary, there is an inclination to believe this not be the case. When determining the influence of various process variables and parameters on the results of the production operation a two-dimensional evaluation technique is usually applied. The decisions made on the basis of these results either for control or ope rational instructions purposes are far from optimum. When one variable is changed, it will affect many others. Although the methodology is well documented and efficient modern equipment such as fast analyzers and powerful computers are on the shelf,a yawning gap between theory and practice exists. A special aim of this work is to improve the reliability of the conclusions drawn from test results and indicate the relative significance of dif ferent variables quantitatively. It is also possible to determine the level of stable operation of a process. Emphasis should be placed on these matters now when automation is gaining more and more ground . The paper refers to a previously published article which appeared ai -out twenty years ago and described how Factorial Experiments can practically be utilized when determining the right operating conditions in metallurgical processes. This presentation illustrates the method with a practical example from a pyrometallurgical process and shows how to relate significantly various information data to the qualitative, quantitative and economic results of the production establishment. The purpose of this presentation is to make a contribution towards bridging the gap between theory and practice. Keywords. Multivariable systems; statistics; factorial design; system ana lysis; metallurgy.
INTRODUCTION
and at the utmost with a parameter as a third variable .
When examining international publications on process studies in the mining industry such as ore- and mineral processing and pyro- and hydrometallurgical processes, one finds that the studies have been designed according to the principle 'one variable at a time'. The determination of the effect of the various factors on the processing results is essentially based on this ap proach. Thus the findings are usually presented as curves in two-dimensional graphs
However, when one process variable is changed many other variables ,,,ill c hang e at the same time so that the eff e ct of the ma nipulated variable alone is overshadowed . This increases the risk for drawing ,,,rong conclusions. The authors have reviewed the publications from th e two latest International Mineral Processing Congresses, i.e. j'Jarsaw - 19 79
AM-K*
311
312
0. Vartiainen and V. Tinnis
and Toronto - 1982 Congresses (1), (2). None of the presented papers at these meetings deal with e.g. at least the effect of the combined main factors in analyzing the various processes. The application of factorial design to a pyrometallurgical process is described in this article. Although the application has been demonstrated by one of the authors (3) already 20 years ago, factorial design has not been used extensively even in Finland. THE FACTORIAL DESIGN METHOD The factorial design and analysis method is well documented in the literature (4), (5). Therefore, the method is only described in this article in brief since the main aim is to describe its application to a pyrometallurgical process (3). Factorial design and analysis for a system of 4 factors (denoted e.g. K, T, H and V) on two levels (1 and 2) can be carried out as 24 -factorial experiment, table no. 11 page 4. The statistical analysis of the measured effect - e.g. the sulphur content in calcine product when roasting iron sulphide matte - will yield both the main effects of the various fa~tors as well as their interactions. An analysis of variance provides also the significance data for the evaluation of the specific effects. In many cases the interactions of the various factors are important. In order to determine the effects more clearly, a 2 3 -factorial analysis can be done separately for the two levels and for some of the most important factors (e.g. T and H).
FACTORIAL DESIGN APPLIED TO A PYROMETALLURGICAL PROCESS Short Process Description Factorial design as applied to a fluidized bed iron matte roasting process has shown very interesting test results. The basic elements of this process are described ~n general terms in the following (6). Roasting of iron sulphide matte, of the grain size distribution as shown in figure no. 1, takes place mainly according to the following chemical reactions: 4FeS + 702 ---> 2Fe 0 + 4S0 2 2 3 4FeO + 02
---> 2F e 0 2 3
Both reactions are exothermal and the amount of heat release is about 5900 kJ per kg of iron sulphide matte. The required completeness is such that the residual sulphur content in the calcine is less than 1 %. Sulphur dioxide is recovered for the production of sulphuric acid. The released heat produces superheated steam (500 °C, 6.5 MPa), which is fed to the power plant. Furthermore steam of 0.5 MPa pressure is produced in the iron calcine cooling process. A cross section of a fluidized bed roasting furnace is shown in figure no. 2. In table no. I. data showing typical process conditions are listed for one of thre e r e actors of the investigated iron sulphide roasting plant.
The experiment in this case is planned according to the standard 23 -factorial design procedure of 8 observations in the following manner:
Obser- K T H KT KH TH KTH I vation J1 J2 J3 J4 J5 J6 J7
J8
+ + + + +
+ + + +
+ + + +
+
+ +
+ + +
+ + +
+ +
+
+ +
+
+ + + + + + + +
Treatment combination (r)
k t kt h kh th kth
The sign + denotes the higher level and the sign - the lower level. An analysis of variance concludes the procedure, which enables a pertinent discussion of the various effects and interactions.
~ 101~+t/:ttti J=t==t==t=W /
:;;; Sf-
~ 6~--vl/--~V~~~--~--~-+-H
l5
~
41 /
~:
0.1
I.
I
2 4 6 a 10 ft'S MATTE PARTICLE SIZE DISTRIBUTlON,mm 02
Figure 1.
04
1.0
Screen analysis
Factorial Design and Analysis
313
Amount of steam developed 686 tld = 1.39 tons per ton FeS matte Temperature of feed water 213 °c Iron content of total calcine 67.4 % Sulphur content of total calcine 0.35 % Sulphur content of coarse calcine 0.20 % Sulphur content of fine calcine 0.75 % Total power need 28 kWh per ton FeS matte
·' .iili
Process Technical Requirements
-:;~ o;~
The amount of inert material in the reactor is approximately 30 tons, and the amount of fresh iron sulphide feed about 20 t / h. The gas velocity at 1000 °c is about 3.3 mls against the free-grate area of the reactor. The roasting temperature has to be controlled very closely. This is done so that the air feed is kept constant and the amount of iron sulphide is regulated according to the temperature. The following reaction conditions among others are important:
Figure 2.
Fluidized bed roasting furnace (cross section)
- The reaction time has to be kept constant. - In order to achieve desired chemical results the material has to stay at conditions favorable to the reaction for a specific minimum of time, which among other things is a function of the grain size.
Table I.
Typical roasting conditions of iron sulphide matte
Amount of air
3
38,000 m nlh
Pressure drop in grate and bed total 2,000 mm H 0=20 kPa 2 S02 content of gas after furnace 9.5 % SO content of gas afier electrost~tic precipitator 8.5 % Temperature in reaction zone 1,020 - 1,045 °c Temp e rature before the boiler 965 °c Temperature after the boiler Pressure of superheated steam 6.5 MPa Temperature of superheated steam 495 °c Feed of iron sulphide matte 494 tld Iron content of iron sulphide matte 62 i. Sulphur content of iron sulphide matte 30 % Moisture content of iron sulphide matte 1.4 %
Abnormal particles (grain Size diff e ring greatly from the average) have to be removed from the reaction zone. Thus iron sulphide 'clumps', large pieces of calcine, and pieces dropping from th e walls of the reactor, should not be allowed to accumulate inside the reactor. The removal of the material from the reactor is carri ed out by means of a gas-tight mechanism. Process Variables The variables which characterize the roasting process are mainly the following: Input variables: - Iron sulphide feed rate - Air flow - Fuel flow (at start) - Iron sulphide composition - Feed material grain size distribution Output variables: - Flue gas temperature - Flue gas composition - Dust content in flue gases - Outlet flow rate of roasted material - Roasted material composition and grain
314
O. Vartiainen and V. Tinnis
size distribution - Temperature of roasting material cooling
Table Ill. Reciprocal sulphur content, x 10 b\~fore
H
State variables: - Amount of roasting material in bed - Bed (gas-solid material mixtllre) temperatur.e and distribution - Gas temperature above bed - Geometry of the reactor Mixing condit ions of material - R.esidence time
H2
HI K
T
V
V VI
V
VI
V
Tl
1.91
2.43
4 . 08
2 . 83
T2
2.35
13 . 51
9 . 52
2 1.74
Tl
2.73
3 . 83
6.95
(ZZ .Z9)
T
(9.13)
4.79
( 15.92)
50.00
Kl
KZ
FACTORIAL EXPERI!'1ENTATION AND ANALYSIS
Z
z
z
The result of the statistical analysis are shown in table no. IV
In order to quantitative ly relate these variables factorial design and experimentation are found to be a very powerful tool.
Table IV. Resul ts of Factorial Experimentation
For the determination of the relationship of the most important process variables at steady state conditions a fac torial design procedure has been carried out. The following variables have been included in the experimentation:
Sum of squares
Effect
Degree s Mean of freedom square
Signif icance (X)
Main effect:
-----------
Air £10'01 ratio
- Air flow ratio (actual air/theoretically calkulated air)
change
(K)
Temperature change
(T)
399.10
1.5
Bed he igh t change
( H)
536. 10
( 1
Air velocity change
(V)
296.10
204 .99
Combined effec t:
--------------
- Bed tempera tu re - Bed height (pressure drop of air/reaction time)
Level I
Temperat ur e ,
Bed height, Air veloc ity ,
°c
(T)
mm H O
(H)
2
m/ s (V)
950-
I 989 (TI
I 095-1 470 (HI 2 . 56-2.99
(V I
}
20.36
The changes in bed height and temperature are very significant. On the other hand it can be seen from table no. III that the sulphur co ntent data cor responding to temper~ture T2 are, without exception, better than those for temperature T • Also the figures l are better for a greater amount of material in bed (H) than for a l ess material amount.
2.
The changes in air velocity and air flow ratio as well as the combined effects KH and HV are significant on a 5 % level. According to table no. III one can conclude that a higher air velocity (V ) is better than a lower 2 velocity (V ) and that a higher air L flow ratio lK ) results in better product quality than a lower ratio (K ). The latter is, however, uncerl tain because the result is based on the calculated data rather than measured.
1. 400-1.650 (K ) 2 990-1 025 (T ) Z I 471 -1 850 (H ) 2 3.00-3.53 (V )
The su l phur content in the calcine product has been chosen as the criterion for the anal ysis, being the most important output variable. In order to facilitate the calculations the reciprocal value of the sulphur content has been taken as a basis for the analysis. This data is shown in table no. Ill. The figures in parenthesis have been calculated according to the Yate's method because the corresponding test data were not available.
28.49
1. Level 2
1 . 152-1.399 (K
KTHV
The following conclusions can be drawn from table no. TV:
Table 11. Experimentation levels
(K)
THV
17.00 7. 30 178.08 45.66
8 10 4.5
(Co1'llbined effect· int e raction)
These variahles have been manipulated at two experimentation levels according to table no. 11.
Variable
201.00 34 .60 110.93 87.47 168.68
KTH KTV KMV
- Air velocity in the bed (calculated for the free cross section of furnace above the grate)
Air flow ra tio
4.17
KT KM KV TH TV HV
z
Factorial Design and Analysis 3.
The combined effects of TH and TV are significant on a 10 % level.
In order to obtain the effect of the various 3 process conditions a 2 -Factorial Experimentation analysis has been done such, that the calculation has been carried out separately for two temperature levels: Tl and T . This enables on to eliminate the effect 2 of the temperature.
315
It can be seen from Table no. VI that a a higher bed (H ) and greater air velocity (V ) in combination provide better results. 2 As shown also in Table no. III a higher bed yields better results. In order ~o get clearer picture of the situation a 2 -Factorial Experimentation analysis has been carried out separately for the H - and 1 H -1evel. The results are presented in 2 Tab le no. VII.
Table no. V shows the obtained results. 2 3 -Factorial Experimentation.
Table V.
Statistical analysis, separately for T - and T -level. 2 1 T2
Tl
Influence Sum of squares
Degrees of freedom
Mean
Signifi-
square
cance (%)
Sum of squares
Degrees of freedom
Mean
square
Significance (%)
Main effect: ------------
Air flow ratio change
(K)
75.34
2
> 10
133.83
-
-
Bed height change(H)
79.69
2
> 10
567.85
1
6
Air velocity change
30.85
1
-
352.72
2
(V)
Combined effect: ----------------
KV HV KHV
50.55 36.85 19.44 32.04
Sum
47.05
!CH
10
-
i}3
35.61
-
-
-
n
167.45 5.06 194.83 174.47
4
126.96
-
93.59
-
It can be concluded that:
1.
The conditions are more stable at Tl -temperature level than at T . 2
2.
The changes in bed height and air flow ratio are significant on the Tl -temperature level. As shown in Table no. III H~ and K? give better product quality tlan the-corresponding RI and K . l
3.
4.
On the T2 -temperature level the bed height and air velocity are significant. H2 and V give better results than the 2 corresponding HI and VI' as shown in Table no. HI.
The results indicate the following: 1.
2.
3.
The combined HV-effect is relatively high. This effect is further analysed in Table no. VI on the T2 -temperature level.
On the HI-level the temperature change is statistically the most important. The T -condition provides better results 2 tfian T , as shown in Table no. Ill. 1 On the H -1evel the air flow ratio and 2 air velocity changes are very significant. A higher air flow ratio gives better results than a lower one. The same applies for a higher air velocity. On the H -1evel the significance of the 2 change in temperature, air flow ratio and air velocity is of the same order. However, it should be taken into account that the degree of freedom for the temperature change is zero.
Combined RV-effect at temperature T2
Table VI.
CONCLUSIONS The following general conclusions can be drawn from the analyses:
H
V
*
Hl
H2
V 1
11.48
25.44
36.92
V 2
18.30
71 .74
90.04
29.78
97.18
The best results are obtained under the level 2 conditions, i.e.: -
bed height temperature air velocity air flow ratio
1470 990 3.00 1.40
-
1850 mm H 0 2 1025 °c 3.53 m/s 1.65
316
0. Vartiainen and V. Tinnis
Table VII.
2
3
- Factorial Experimentation
Statistical analysis separately for H - and H -level. 1 2 HI
Influence
Sum of squares
H2
Degrees of
Mean
freedom
square
Significance (%)
Sum of
squares
Degrees of freedom
Mean
Signifi-
square
cance (%)
Main effect : ------------
Air flow ratio change
-
(K
0.01
2
405.98
1
Tempera tu re change (T
44.56
1
> 10
465.58
-
-
Air velocity change (V
8.90
1
-
455 . 87
1
6
-
19.00 184 . 80 129.69 3 . 47
-
KTV
2.16 27 . 83 3 . 38 32.32
Sum
40.68
6
Combined effect :
---------------KT KV
TV
Hs
On the other hand it has been found that a lower temperature 950-990 °c provides more stable conditions than a higher one.
*
*
At lower bed height (1095-1470 mm H 0) 2 the effect of the temperature is more significant in comparison with the other variables. This indicates that the process is sensitive to temperature variations. At a higher bed (1470-1350 mm H20) the effect of the temperature, air flow ratio and air velocity are about equally significant. This also means that the roasting process is more stable at a higher bed level.
Achieved results and their utilization in prac tice The above research work was originally carried out in connection with the pilot tests and repeated after three years when the practical siz e mill with two reactor lines was ready. Based on analysis of the pilot test results - the reactor main air blower maximum pressure was chose n to 2500 mm H 0. At 2 that time the equivalent "normal" blowers in the industry worldwide operated at about 1100-1200 mm H 0 pressure 2 - temperature measurement in the reactor for the control was carefully designed. The number of measureme nt points were greater than normal afld a two-colour pyrometer was fItted to the reactor in order to ascertain the reliability of the measurements. Additionally the temperature control was effected by a derivative mode, by which the amount of feed material was controlled within certain reactor temperature limits. - Special attention was given to the material reaction and in particular, the
12.71
-
133.33
-
-
1 1
3.47
-
----- --- - -
oxidation time, for this purpose a device was designed which well fulfilled the necessary criteria. The method was also patented outside Finland (6). These measures proved successful in production practice. Typical production results are shown in Table I. It was also found that the specific capacity of the reactor could be raised by about 30 % over the nominal value, of comparable reactors worldwide using fluidized bed processes at that time. This increase in capacity did not influence the sulphur content of the calcine product. When the plant was expanded a few years later this also meant that it was possible to reduce the investments considerably. Another important benefit which was achieved was that the coarseness of the fe ed material could significanlty be increased without influencing the fluidized bed process or handling of the calcined product. The control of the reaction zone temperature was as successful as expected and resulted in a steady operational state and high annual availability, 96-97 ~~ wh en tak.ing into account the normal annual three week down time. One of the authors, who was in charge of the research work and planning which lead to construction of the plant, is of the distinct opinion that the research method used for analyzing the test results was of great importance in attaining the outlined good metallurgical and economic results.
Factorial Design and Analysis LITERATURE CITED:
BRIDGING THE GAP BETWEEN THEORY AND PRACTICE Although the factorial design and analysis method has been well documented and known for decades, its application has been very sparse in the world of mining, mineral and metal industry. The reason for this unwarranted circumstance might be the poor cooperation and understanding between the research and operation personnel on one side and the process control engineers and mathematicians on the other.
317
(1)
Developments in mineral processing, Thirteenth International Mineral Processing Congress, Warsaw June 4-9, 1979, Proceedings part A and B, Elsevier Scientific Publishing Company, Amsterdam 1981
(2 )
Worldwide industrial application of mineral processing technology, XIV International Mineral Processing Congress, October 17-23, 1982, Toronto, Canada
For bridging the gap there are institutes and consulting companies which offer their services. This is one way in successfully adopting advanced methods, towards the beneficial utilization of the presently best available technology. This would enable one to run the process at economically optimum operating conditions.
(3)
Vartiainen, Osmo: Factorial Experimentation research method for the analysis of benefication and metallurgical processes, Vuoriteollisuus 1961, p 48-54, (in Finnish)
(4)
The obtained results can be used for the quantitative determination of the relation of the various process variables in a mathematical model of the process.
Davies, Owen L.: The design and analysis of industrial experiments, Oliver & Boyd Ltd., London-Edinburgh 1960
(5)
Lokki, Olli: Ti1astollisista menetelmista, Puukemia, Suomen Paperi-insinoorien Yhdistys 1967, G6, (in Finnish)
(6)
Vartiainen, Osmo: New system for solids removal boosts capacity of roasting furnaces, E/MJ - January 1971, p. 80-83