Effect Of Process Variables On Scales Formation.pdf

Effect Of Process Variables On Scale Formation In Steel Reheating R. C. ORMEROD IV‘, H. A. BECKER‘, E. W. GRANDMAISON’*, A. POLLARD2 and A. SOBIESIAK2 ‘p2Centrefor Advanced Gas Combustion Technology, ‘Department of Chemical Engineering and 2Department of Mechanical Engineering, Queen ’s University, Kingston, ON K7L 3N6, Canada Variables affecting the high temperature oxidation of steel were investigated using an experimental design strategy. The experimental methods included continuous mass-gain measurement to characterize the oxidation kinetics in terms of parabolic rate constants. A Morris and Mitchell (1983) eleven-run experimental design was used to identify main effects and interactions among seven independent variables (oxidation temperature, steel grade, steel surface condition, sample history and gas composition: H,O, O2 and CO,). The levels of these variables were chosen to reflect industrial steel reheat operations. The use of this type of strategy in assessing the effect of variables at an intermediate stage in an experimental program is also demonstrated. On a etudie les variables qui influent sur I’oxydation de I’acier a des temperatures elevees au moyen d’une strategie de conception experimentale. Les methodes experimentales incluent la mesure continu du gain de masse afin de caracteriser la cinetique d’oxydation en termes de constantes de vitesse paraboliques. On a eu recours a une conception expirimentale a onze essais de Morris et Mitchell (1983) afin de determiner les principaux effets et interactions parmi les sept variables independantes(temperature d’oxydation, qualite de I’acier, condition de surface de I’acier, histoire de I’echantillon et composition du gaz: H 2 0 , 0, et CO,). Les niveaux de ces variables ont ete choisis afin de refleter les operations de rechauffement d’acier industrielles. On demontre egalement I’utilisation de ce type de strategie pour evaluer I’effet de variables a un stade intermediaire dans un programme experimental. Keywords: experimental design, steel oxidation. reheat furnaces.

R

eheat furnaces are used to heat steel slabs prior to olling and subsequent processing. These furnaces utilize natural gas, coke-oven gas or oil as fuels in continuous batch heating operations of 4 hours or more to raise slabs to temperatures of 1215- 1300°C. Associated with the heating is the growth of scale (iron oxides) on the surface of the slabs. This scale typically amounts to 1 to 3% of the total steel throughput; it requires removal prior to further processing of the slab and constitutes a direct product loss. Control of scale formation is complicated by the fact that the oxidation reaction is exothermic, with the oxide products acting as a thermally insulating barrier. Hence, a knowledge of the scaling rates is also necessary for accurate energy balances on reheat furnaces. Without the introduction of a permeation barrier for the oxidation reactants, scale formation is inevitable but the kinetics of the oxidation process can be affected by operating variables in the reheating process (Sachs and Tuck, 1968). The objective of the present work was to investigate the effect of process variables on the oxidation rate of low-carbon steel. The steel samples were supplied by the Ferrous lndustry Energy Research Association (FERA) and represent grades and compositions of current industrial interest. The methodology involved the use of an experimental design strategy to reduce the number of runs required for a screening study of the type here undertaken. Seven variables were examined, including the oxidation temperature, the gas and steel compositions, and the surface texture of the steel samples. A Morris and Mitchell (1983) experimental design was chosen for this screening study as it has the ability to

*Author to w h o m correspondence should be addressed. E-mail address: [email protected] 402

identify the presence of interactions at an early stage of experimentation. The use of this experimental design as a tool in assessing the effect of variables at intermediate stages of the experimental program is also demonstrated. The kinetics of scale formation was described in terms of the mass gain and a corresponding parabolic oxidation rate. The effect of the process variables and interactions between variables on the parabolic oxidation rate were assessed from the experiments.

Background The oxidation of metals is of great interest in the nietallurgical, electrochemical and process industries. Research over the past 5 M O years ranges from fundamental studies to ascertain/confirm reaction mechanisms through to methodology for corrosion control. Review articles (Cabrera and Mott, 1949; Smeltzer and Young, 1975; Rapp, 1984) and textbooks by Evans (1960), Kubascgewski and Hopkins (1962), Hauffe (1965) and Kofstad (1965) have resulted. The peculiar problems of high temperature oxidation are addressed in recent texts by Birks and Meier (1 983) and Kofstad (1 988). The oxidation reaction starts with an initial adsorption of oxygen gas on the metal surface, possibly with some dissolution in the metal, to form a thin oxide film. If this film is continuous, it physically separates the reactants and subsequent oxidation occurs by solid-state diffusion through the oxide film. Porosity, cracks and poor adhesion at the scale/metal interface may also lead to phase-boundary control mechanisms as the oxidation proceeds. Models for the oxidation rate of metals and alloys have been developed and validated for many test conditions. These include (Kofstad, 1988) logarithmic, linear and parabolic forms, normally

T H E CANADIAN JOURNAL OF CHEMICAL ENGINEERING, V O L U M E 75, APRIL, 1997

describing the mass gain or scale thickness developed on the metal surface. Investigations of the low-temperature oxidation of iron have included studies of oxide nucleation by Ronnquist and Thomas (1965) and of oxidation rates; Gilroy and Mayne (1965), for example, observed an inverse logarithmic rate. The initial oxidation stages of iron have also been investigated at higher temperatures by means of SEM by Castle and Hunt (1976) and HSESEM by Matson et al. (1 984) and Jungling and Rapp ( 1984). The linear rate equation is used to describe phase-boundary rate controlling steps, while a parabolic form is applicable to cases of solidstate diffusion in scale growth. At temperatures above 57OoC, iron oxidizes to form a multilayer scale of FeO (wustite), Fe30, (magnetite) and Fe203(haematite) with the wustite layer next to the metal surface, magnetite as an intermediate layer, and haematite at the gas-solid interface. The mass ratio of these oxide phases is around 95:4: 1 (Paidassi, 1958). At intermediate temperatures, up to 570°C, only the haematite and magnetite layers form on iron and steel. Wustite is a p-type semiconductor with a metal deficit; typically the stoichiometry approximates Fe,,9,0, but locally the Fe/O atomic ratio may range from 0.95 to 0.88 with the largest iron deficit occurring at the wustite-magnetite interface (Engell, 1958). This level of cation vacancy promotes high mobility of cations and electrons in wustite and the overall mechanism for the oxidation is generally modelled as a cation diffusion through the three scale layers, although some early results suggested that anion diffusion occurs in the haematite layer (several examples of these results are noted in the text of Birks and Meier, 1983). In high-temperature systems, the oxidation to wustite is dominant and the rate is commonly described by a parabolic law relating the cation flux to the metal vacancy concentration in the scale. This approach was first proposed by Tammann ( 1 920) and applied in early studies of iron oxidation by Davies, Simnad and Birchenall (195 1) and Paidassi (1 958) in the form d h -. k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

dt

h

(1)

where h is a measure of the scale thickness and t is time. At constant rate coefficient, k, integration gives

h2 = k,,t + C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

where k,, = 2k is the parabolic rate constant and C i s the integration constant. In experimental studies, h is normally expressed in terms either of a measured scale thickness or of the mass gain of the test specimen per unit of its surface. It is implied in these formulations that the scale thickness is typically small compared to the local radius of curvature of the surface. It should also be noted that, because it predicts an infinite rate at t = 0, the parabolic law cannot apply at t + 0. Typical oxidation curves and parabolic rate laws are discussed by Logani and Smeltzer (1971) (e.g., see their Figure 9). The parabolic rate law is also developed in the quantitative theory of Wagner (1933). Assumptions in the theory require that the oxide layer be compact and perfectly adherent to the metal surface, migration of ions or electrons is rate controlling, the scale is thick compared with distances over which space charge effects occur, thermodynamic equilibrium exists locally in the scale at both boundaries, there are only small deviations from stoichiometric composition in the scale, and oxygen solubility in the metal is negligible

(Birks and Meier, 1983). The theory gives for the coefficient of the parabolic oxidation rate

(3) P'

P"

where D is the diffusion coefficient for transport through the scale and p is the chemical potential. The single and double prime superscripts denote the values at the metal-scale and scale-gas interfaces respectively. The subscripts "c" (for cation) and "a" (for anion) refer to metal and nonmetal properties, respectively. Experimental confirmation of Wagner's theory has been found by Himmel et al. (1953) and Engell (1958). Experimental investigations have also demonstrated applicability of the parabolic rate law for oxidation of iron in oxygen (Paidassi, 1958; Davies et al., 195 1; Caplan and Cohen, 1963; Schmahl et al., 1958). Goursat and Smeltzer (1973a,b) have shown that the reaction rate is independent of the oxygen pressure in the range 0.04- 100 kPa. Deviations from the parabolic law occur, for example, when the rate controlling step is a phase boundary reaction (Smeltzer, 1960; Pettit et al., 1960; Surman, 1973), a porous scale is formed (Birchenall, 1956), or when adhesion of the scale to the metal substrate fails (Engell and Wever, 1957; Peters and Engell, 1959; Hussey and Cohen, 1971a,b). The problems of discriminating between different kinetic models are discussed by Smeltzer and Simnard (1957) and Kofstad (1988). From their observations it may be concluded that continuous monitoring of scaling rates is the best route for correct data interpretation. Scale formation in steel reheat furnaces poses a situation where many process variables may have synergistic influences. Sachs and Tuck (1968) review the potential impact based on previous research in the field of high temperature oxidation. Methods of reducing scale formation through favourable control strategies are described by Cook and Rasmussen (1 970). The oxidizing gases in reheat furnaces include oxygen, water vapour and carbon dioxide, presenting a gas composition depending on the fuel type, excess air level and other operating factors such as air infiltration. The effects of gas composition on scaling rates are reported by Rahmel and Tobolski ( 1 965); the presence of water vapour and carbon dioxide was found to increase the rate, with water vapour having a larger effect at higher temperatures. Sachs and Tuck (1970) studied the effect of oxidizing gases on the high-temperature oxidation of iron and steel in an integrated heating strategy for application to reheat furnaces. Kuhn and Oeters (1975) and Selenz and Oeters ( 1 984) examined the effect of several oxidizing species, providing data on coefficients of the linear rate behaviour that occurs in the initial stage of oxidation. Minaev et al. ( 1983) studied the effect of fuel type and temperature on scale formation for five grades of steel. The fuel with the lowest oxidizing potential (as measured by the sum of oxygen, water vapour and carbon dioxide partial pressure) gave the least scale at the higher temperatures, but this effect was less marked at the lower temperatures. Importance of surface preparation on the oxidation rate of metals has been documented in the literature. The effect of cold working on the oxidation of iron was studied by Caplan and Cohen (1966) and Caplan et al. (1970). At temperatures up to 55OoC, cold worked iron exhibits higher oxidation rates than annealed samples; this was partly attributed to poor scale contact for the annealed specimens.

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As noted above, the problem of oxidation of metals, and of iron in particular, has been well researched with mechanisms documented for different experimental and process conditions. The bulk of the previous measurements of scaling rates on iron and steel have been obtained by one-factor at-a-time assessment of the effect of independent variables. While this background serves to suggest useful guidelines for scale control and methodologies to be employed for laboratory and plant investigations, measurements with well planned experimental strategies can also provide useful information for improving scale control for particular steel grades in the process industries. The main objective of the present work was to perform a series of screening experiments to assess the effects of independent variables on the parabolic scale growth coefficient in the high temperature oxidation of steel: log,o(k,,) =f(independent variables) . . . . . . . . . . . . . (4) where kp is assessed in a consistent manner for all experimental runs. The logarithm of k,, is employed as the dependent variable in anticipation of Arrhenius temperature dependence. The steel samples were prepared from slab material supplied by Dofasco Inc. (Hamilton, ON), and the independent variables of interest were chosen to include those most commonly associated with industrial reheat firnaces, namely steel grade/finish, oxidation atmosphere and temperature. The simplest model form for the effects of the independent variables is the linear model

with x, = 1, or, in standard vector notation,

Y = X P + E...............................

(6)

where Y is an (n x 1) vector of observations, X is the ( n x p ) matrix of independent variables, p is a 0, x 1 ) vector of coefficients to be estimated and E is the 0, x 1) vector of random errors (each having a zero mean and a variance a2). The least squares estimate of p then is

p= (XT X)-1 XT Y. . . . . . . . . . . . . . . . . . . . . . . . . . .

(7)

One criteria for constructing experimental designs, the Doptimality criterion, involves choosing the X matrix such that the determinant of (XTX) is maximized (Smith, 1918). The benefits of this are described by Box and Draper ( 1 97 1). In screening designs, the main objective is often the estimation of the relative importance of independent variables with the assumption that interactions and higher order terms are negligible or can best be explored in later experimentation. Suitable forms of such experimental designs, including those proposed by Plackett and Burman (1946) and fractional factorial designs (Box and Hunter, 1961) have been described in the statistics literature. Applications to industrial problems have been described, for example, by Williams (1963), Stowe and Mayer (1966), Hunter and Hoff (1967), Grandmaison et al. (1984) and Hamada and Wu (1992). These designs require careful analysis to yield information regarding interactions between variables, for example, Hamada and Wu (1992) discuss use of Plackett and Burman designs in this regard. In other cases, additional runs may be 404

TABLE1

Seven-variable Morris and Mitchell (1983) design Variables Run I 2 3 4 5 6 7 8 9

1

2

3

4

5

h

7

-1

-1

-1

+I

-1 +I

-1 +I -1

-1

-I +I +I -I

-1

+I

-I +I -I +I +I

-1

+I

+I

-1 -1 -1 -I +I

-1 +I +I -1

10

+I +I

I1

-1

+I +I

-1

+I +I -1 +1

+I

-1

+I +I -1 -1 -1

+I +I -1

-I +I +I

-1

+I +I I +I -I

-1

+I -I +I

-I

-1

+I

-1

+I -1

-1

+I

-1 -1

~~I

TABLE2 First four runs of Morris and Mitchell (1983) design showing alias structure denoted as A and B arouDings

Variables B

A

Run

1

2

3

1

-1

-1

-1

2 3

+I

+I

+I

4 -I +I

-1

-1

-1

-1

4

+I

+I

+I

+I

5 -I +I +I -I

6

7

-I +I +I

-1

-1

-1

+I +I

required to assess interaction effects, for example, additional runs up to and including a complete fold-over fractional factorial design can be employed (Myers and Montgomery, 1995). The effects of response surface curvature or higher order terms also require additional experimentation, typically at the mid-point level for continuous or quantitative variables. In all the cases mentioned above, it is assumed that additional runs are also performed to obtain an estimate of the system variance; mid-point experiments or replicate runs at design levels are frequently preferred if the variance is a function of the level of the independent variables. Morris and Mitchell (1983) have proposed another method of constructing experimental designs suitable for screening experiments. A feature of these is that they are suitable for detecting the effect of interactions at an early stage of experimentation. If we write the model for Y to include interactions, then

Y = x , p , + X , p , + &. . . . . . . . . . . . . . . . . . . . . . .

(8)

with a corresponding lack-of-fit matrix

L = x,T(I - x l ( x ; XI)-, XT)X,. . . . . . . . . . . . . . . . (9) where pzis a vector consisting of thep@ - 1)/2 interactions and I is the identity matrix. Morris and Mitchell (1983) note that the proposed designs maximize the trace of L and satisfy the D-optimality criterion. In the present study, seven variables were chosen for investigation, as described in detail later. The seven-variable design of Morris and Mitchell (1983, from their Table 6) is shown in Table 1. This type of design permits intermediate analysis of some of the effects under study. In particular, the first four runs can be placed in two groups, A and B, as shown in Table 2. The structure of the first four runs is a 2 , factorial design with variables 1-4 assigned to a set of lev-

THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, VOLUME 75. APRIL, 1997

TABLE 3 First six runs of Morris and Mitchell (1983) design showing decoupling of alias structure from Table 2 A B

~~

~

1

2 3 4

1 -1 +I

2 -1 +1

-1

-1 +1

+I

5

-1

6

+I

-1 +I

3

B2 -

BI

A2

Al

Run

4

5

6 ~~

-1

-1

-1

-1

+I

+1

-1

-1

+I +I -1

+I +I

+I +1 -1

+1 +I -I

-1

-1

-1 +I

+I

7 -1 +I +1 -1 +1 -1

els A and variables >7 assigned to levels B. This subset of experiments provides an estimate of the sum of the main effects due to variables 1, 2, 3 and 4, estimated from PA,and variables 5, 6 and-7, estimated from &. The interaction between A and B, pAB,provides an estimate of the sum of interactions b e p e e n any variable in groups A and B, i.e., p15,p16, . . . . , p47.The interactions betweep va*riableswjthin a group A or B, i.e. R2,R3,.. . ,h4and p45,& . . . , k7, are biased with the overall mean for the model, Runs 5 and 6 in Table 1 provide an additiona decoupling of the alias structure as shown in Table 3. This set of runs provides an estimate of main effects confounded only with one other main effect, plus fractional amounts of all other main effects, except for variable 7. The variables in group A are decoupled into the groups A1 and A2, while those from group B decouple as groups B1 and B2. The estimates of the interactions are biased in three groups of six interactions plus another group consisting of the overall mean aliased with three interactions. The interactions are not biased by any main effect but these groups of interactions are also biased by fractional amounts of all other two-factor interactions. Moms and Mitchell note that this design has an 80% chance of detecting interactions at a 90% confidence level. The full 1 1-run design shown in Table 1 provides estimates of the main effects of each variable biased only by small amounts of other main effects and interactions. This type of design thus offers a compromise with other alternative designs (e.g. a 12-run Plackett and Burman (1946) design or a 2’“ fractional factorial design) with the advantage of indicating the presence of interactions and an intermediate analysis during the course of the experimental programme. Additional runs are required to estimate experimental error; in the present study a total of 20 runs was performed for the complete programme. One of the main objectives in the present work was to demonstrate an experimental design strategy which would permit assessment of the effects of variables/ interactions at an intermediate stage in the experimental program. Such information would be of interest, for example, to industrial users of such statistical methods where progress reports on experimental programs are important.

4

Experimental procedures The variables chosen for investigation were set at two levels according to the experimental design discussed above. The primary dependent variable was the kinetic behaviour of the steel samples undergoing oxidation in a laboratory furnace. From mass-gain data for the samples, the parabolic rate constant, kp, was estimated and the logarithm of kp was used as a dependent variable for statistical analysis.

TABLE 4 Chemical composition (mass%) of steel samples; low CI and low C2 refer to low carbon content, high C I and high C2 refer to high carbon content samples LowCI LowC2 HighCI HighC2 0.003 0.203 0.2 14 Carbon 0.002 0.008 0.005 0.007 0.007 Sulphur Nickel 0.006 0.007 0.006 0.005 0.028 0.056 Aluminum 0.036 0.035 Cobalt

0.022

Titanium Manganese Silicon

0.026

Chromium Molybdenum

Zirconium Phosphorus Copper Tin Vanadium Nitrogen

0.139 0.008 0.018

0.027 0.041 0.157

0.015 0.022

0.003

0.004

0.000

0.001 0.005 0.009 0.005 0.00 1 0.002

0.005 0.008 0.002 0.000

0.002

0.00 1

0.000

0.003 0.356

0.002 0.352

0.008 0.024 0.003 0.001

0.007 0.026 0.003 0.000 0.007 0.005 0.002 0.000 0.004

0.005 0.008 0.003 0.000

0.003

Several properties or attribute variables associated with the steel samples were of interest. These included surface condition, pre-oxidation history and carbon content of the steel. The steel as received was in the form of bars cut from cast slabs, preserving on one face the original cast surface. Two types of samples for study were prepared from these bars. The first were 22.2 x 22.2 x 44.4mm blocks milled and polished on all sides, weighing 160 g. The second type were similar except that one 22.2 mm square face was in the original cast surface, unaltered. It was expected that this contrast would allow a significant gauging of the effects of surface condition, comparing natural cast surfaces with highly machined surfaces. The sample shape and size were chosen to promote good metal/oxide contact (poor contact would tend to occur in cylindrical samples, for example) and to provide a relatively high specific area of 0.031 m2/kg (to reduce the effect of sample superheating due to reaction exothermicity). The elemental analysis of the steel samples is shown in Table 4. The primary component of interest for this work is the carbon content. Those samples with a low carbon content (0.003 mass%) are designated as low C1 and low C2 and those with a high content (0.2 1 mass%) as high C 1 and high C2, where the designation “Cl” and “C2” denote the variations in other components at each carbon level as noted in Table 4. The effect, if any, of pre-oxidation history was gauged by storing the steel samples at either dry or ambient room conditions prior to oxidation tests. For this purpose, samples were stored at room temperature either in a vacuum desiccator as one experimental level or under atmospheric conditions (nominally 50% R.H.) as the other level. This variable was intended to demonstrate any effects like those of substantial time delays between casting and reheating steel in normal plant operation as well as providing guidance for future preparation techniques in our laboratory. The furnace used to oxidize the samples was a Sola Basic Lindberg electrical resistance tube furnace. A schematic diagram of the heating, gas preparation and data acquisition systems is shown in Figure 1. Additional details are given by Ormerod (1991). The firnace housing was 0.6 m x 0.6 m x 0.8 m in outside dimensions. The heating cavity was cylindrical in shape, 80 mm in diameter, 0.7 m long and open at both ends. The temperature within the furnace could

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i

Temperature Controller

Digital Storage Oscilloscope

71

II water Vapourlzer

Gas Supply

Heater

n Balance

supply

be controlled at temperatures up to 1200°C (f 2"C), with three separate heating zones located along the 700 mm heating section. Each heating section was normally set at the desired design temperature for a run, at the low level of 800°C or the high level of 1 150°C. A 57 mm i.d. quartz tube was inserted into the furnace cavity to provide a reaction containment for the oxidizing gas and the steel sample. The gas-feed end of the tube had a contraction terminating in a ground-glass joint through which it was connected to the feed system. The gas discharge end of the tube was open to the atmosphere. The steel sample was introduced through the discharge end, suspended from a quartz rod rigidly attached to the platform of a Mettler PM6100 electronic balance (6 kg range, 10 mg resolution). The gas flow-rate was adjusted to provide a linear velocity of 0.13 m/s at the sample position at 1150°C. A study by Tomlinson and Catchpole (1968) showed no effect of gas velocity on oxidation between 0.002 and 0.9 m/s at temperatures ranging from 600 - 1000°C. The serial output of the balance was connected to a microcomputer for data logging (normal sampling rate of 1 datum per minute). The furnace and balance system were located in a shielded fume hood to minimize external drafts and exhaust the gas discharged from the oxidation process. A thermocouple was placed adjacent to the sample within the furnace to provide an estimate of the sample temperature. This thermocouple did indeed indicate a temperature rise at the onset of the sample oxidation (an exothermic reaction), but these readings could not be used to provide accurate estimates of this phenomena. An additional set of independent variables of interest in this work was defined upon the oxidizing gas atmosphere. In order to simulate conditions present in reheat furnaces, gas mixtures consisting of nitrogen, oxygen, carbon dioxide and water vapour were prepared to simulate combustion products of both natural gas and coke oven gas. Oxygen levels were chosen to simulate relatively low excess air conditions as a low level (nominally 2 mol%) and possible air infiltration situations as a high level (nominally 12 mol%). The corresponding low and high target concentrations for carbon dioxide were 4 and 12 mol%, respectively. The gas streams were prepared from dry oxygen, carbon dioxide and nitrogen mixtures humidified in a gas preparation system. A similar procedure has been described by Miner and Nagarajan ( 1 98 I). The bubbling-gas humidification chamber consisted of a standard pipe tee, 76.2 mm in diameter 406

and 254 mm in length, with a capacity of 400 mL of distilled water. The chamber was heated within f 0.4"C with an on/off controller to maintain the desired dew point temperature. The gas stream leaving was heated with a 400 W heating tape to prevent condensation. The temperature in the humidification system was continuously monitored during runs and recorded for later analysis. The average value of the dew point (the total amount of water evaporated during each run was recorded for this purpose) was used for the water vapour content in each run. The dew-point data also allowed estimation of the variation in the water vapour content during each run; the maximum of the standard deviation of this variation about the low level for the water vapour content (a target value of 16 mol% H 2 0 ) was 0.20%, while the worst case for the high level for water vapour (a target value of 26 mol% H 2 0 ) was 0.52%. The steel samples were mounted in the furnace at room temperature with a nitrogen purge and then heated to the desired temperature over a period of 2-3 hours. During the experimental programme, the 1 I-run experimental design discussed above was used with replicates of runs 1 to 7 along with additional replicates of runs 1 and 3, yielding a total of 20 runs. The experimental run conditions are shown in Table 5 with the independent variables shown in natural units and Table 6 with these variables shown in coded units. The coded levels for the quantitative variables (gas compositions and temperature) were calculated from the average low (-1 level) and high ( + I level) values used in each experiment. The independent variables are also denoted with the symbols x , , . . . , x7 corresponding to the seven variables from oxygen level to surface condition in Table 6. The parameter estimates discussed later are denoted by the symbols fi,for the main effects of variable i and for interactions between variables i andj. Experimental results

The gas compositions could not always be set at the precise target levels noted above. This was primarily due to the problem of controlling the water vapour content and to small variations in the original bottled gas supplies. The largest deviations from the design levels occurred for the water vapour content but these errors were not considered large enough to affect the benefits gained from the overall experimental strategy. The furnace temperature was preset to the desired level by a control system which gave consistent temperatures within the furnace to *2"C. Compensation for sample overheating due to reaction exothermicity was not employed (the effect of this phenomena is discussed later). The variable for sample history was set at fixed levels o f f 1 as discussed above and sample grade levels were set to * I based on the carbon content and the steel composition noted in Table 4. For the purposes of statistical analysis, the variable levels were range-scaled and centred with the range being the average upper bound and average lower bound in each variable as shown in Table 5. Runs 1 to 1 1 (original experimental design) and IX to 7X (replicates of runs 1 to 7) were initially performed in a randomized fashion. Additional replicate runs, IXX and 3XX, were performed later to check the previous observations. The mass gain data, expressed in terms of the square of the mass gain per average unit area, are shown in Figure 2. These results were obtained at a sampling rate of one datum per 60 s. To distinguish between the different curves in these

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1

2

TABLE 5 Experimental run conditions expressed in natural units. Independent Variables 3 4 5

co,,

6

7

Grade Low c2 High CI High C I Low C I Low c2 High C2 Low C I High CI Low c 2 High C I Low CI Low CI High CI High C I Low C I Low c2 High C2 Low c 2 Low CI High C2

Surface Smooth Cast Cast Smooth Cast Smooth Smooth Smooth Cast Smooth Smooth Smooth Cast Cast Smooth Cast Smooth Smooth Smooth Cast

Temperature,

mol%

"C

History

800 1150 800 I I50 1 I50 800 1 I50 1150 800 800 800 800 1150 800 1150 1 I50 800 1 I50 800 800

Laboratory Dessiccator Dessiccator Laboratory Laboratory Dessiccator Dessiccator Laboratory Laboratory Laboratory Dessiccator Laboratory Dessiccator Dessiccator Laboratory Laboratory Dessiccator Dessiccator Laboratory Dessiccator

Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Run 1 1 Run I X Run 2X Run 3X Run 4X Run 5X Run 6X Run 7X Run IXX Run 3XX

2.16 12.0 2.20 11.9 2.06 12.0 12.1 1.79 12.0 12.4 1.97 2.2 I 12.1 2.20 12.0 2.05 12.0 12.1 2.19 2.19

17.2 25.7 15.8 26.3 15.4 25.6 15.7 25.7 25.4 16.5 25.3 15.3 25.2 15.9 25.8 15.8 25.5 15.4 16.0 16.2

4.03 11.9 4.09 11.8 11.9 4.05 4.04 4.17 4.06 12.4 12.2 4.12 12.0 4.09 11.9 11.9 4.05 4.05 4.08 4.07

Aver age Low Level Aver age High Level

2.10

15.9

4.08

800

Laboratory

Low

25.6

12.0

1 I50

Dessiccator

High C 1lC2

12.1

c 1lC2

Smooth Cast

TABLE6 Experimental runs conditions expressed in coded units XI

0,

Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Run I 1 Run IX Run 2X Run 3X Run 4X Run 5X Run 6X Run 7X Run IXX Run 3XX

4.988 +0.988 4.980 +0.968 -1.01 +0.988 +1.01

-1.06 +0.988 +1.07 -I .03 4.978 +1.01

4.980 +0.988 -1.01 +0.988 +1.01

4.982 4.982

x2 H2O 4.737 +1.02 -1.03 +1.14 -1.11 +0.998 -1.05 +1.02 +0.956 4.882 +0.936 -1.13 +0.9 15

-1 .o I + I .04

-1.03 +0.977 -1.11 -0.985 4.944

x3

x4 Temperature

-1.01 +0.975

-1

-1

-1 +I +I -1

co2 .oo

+0.950 +0.975 -1.01 -1.01

4.976

-1 .oo +1.10

+1.05 4.989 + I .oo -0.996 +0.975 +0.975 -1.01 -1.01 -0.999 -1

.oo

graphs, appropriate graphical symbols are shown at every 600 s with a continuous line for the intermediate points. Hence the data for the high mass-gain runs (bottom graph in Figure 2) display smoother curves than those from the low gain tests (top graph in Figure 2), due to the mass resolution of the data acquisition system and balance employed. The results in Figures 2 generally exhibit a parabolic behaviour except for the initial stage of run 1. Similar data for the replicate tests are shown in Figure 3. The first replicate of

+I

+I +I -1 -I -1 -1

X5

X6

.r7

History

Grade

Surface

-1 +I +I -I -1 +I +I -1

-1 +I +I -1 -1

-I +I +I

-1 -1

+I -I +I -I +I -1

-1

+I -I

-I -1

+I -1 -1

-1

+I -I +I +I

+I +I

-1 -1

-1

+I +I

+I -I

-1

-1

-1

-1

+I

+I

+I

+I

+I -1 -1

-I +I +I -I -1

-I +I +I -I +I -I

run 1, run IX,shows better parabolic behaviour with sample grade low CI as compared to the low C2 grade used in run I . The observed differences between these two runs prompted an additional replicate, run IXX, using sample grade low CI (there was insufficient sample material to perform an additional test with the low C2 grade). In general, the results in Figures 2 and 3 give a linear relationship, particularly at longer times. The slopes of these curves for the final 6000 s of each run were used for estimates of the par-

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407

TABLE7 Experimental results for the parabolic rate constant Run number I , IX, IXX 2,2x 3,3x, 3 x x 4,4x 5,5x 6, 6X 7, 7 x 8 9

Parabolic rate constant, kp, g2/m4 s 2.83,4.25, 6.17 507,488 4.20, 4.63, 3.98 615,453 248, 198 4.88, 6.28 543,465 423 2.22 2.93 4.55

10 11

log I " kJJ 0.452,0.628,0.790 2.70, 2.69 0.623,0.665,0.600 2.79, 2.66 2.40, 2.30 0.689. 0.798 2.74, 2.67 2.63 0.346 0.467 0.658

t

\

N

m

Y N !

TABLE8 Ranking of factors in descending order after 4 runs

.-c tu

m cn cn

Factor

bo

3

v

+

PI2 ' k 4

+ 656

Effect on log,, k,, 'bI.4

+

+ I .64

6 7 + & 3 + & 4 +&7

+1.10

Pl+&+&+b4

5

0

10

15

Time, ks

bL7

5

10

15

0

5

10

15 0

5

10

Time, ks abolic rate constant. The oxidation rates at longer times, typically up to 15000 s, are of particular interest in applications for reheat furnaces. The estimates of the parabolic rate constants k and log,o are shown in Table 7. As aieady mentioned, a thermocouple was used to monitor the temperature adjacent to the steel samples (thermocouples inserted in the samples were usually destroyed during runs and hence the procedure of placing a thermocouple outside but near the sample was adopted). While this temperature reading is only indicative of the sample temperature, the results show good agreement with estimates from a mathe-

Fp

408

k h

+

P45

615 +&6 ' k 7

Figure 2 - Square of the mass gain as a function of time for the low temperature runs (800°C. top graph) and high temperature runs ( 1 1 5OoC,bottom graph).

0

+

+

617

'pi6

&+p6+&

15

0

5

10

15

+ &5

+ P46 +

-0.0638

+bZS +b47

+0.02 I7

Figure 3 - Square of the mass gain as a function of time for the replicate runs (run 1 -run 7).

matical model (Ormerod, 199 1). The observed temperature rise is typically 10 - 40°C for the high temperature runs and 2 - 8°C for the low temperature runs. The peak temperature values lasted for about 10 minutes before decreasing to the target values for each run. No compensation was made for this exothermic effect and hence in the present work (and many other experiments reported in the literature) the reported temperature represents an under-estimate of the true reaction temperature. The phased approach to estimating the parameters or the influence of variables and interactions can be applied to the

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TABLE 9

Ranking of factors in descending order after 6 runs Factor Effect on log,, k ,

99

m

-

.4--Xl 0 -

0

x2

17 ’‘

XlX2

0 00

10

A+&

4.203

0-

1

TABLE 10

Ranking of factors in descending order after eleven runs

Po

+ 1.569

64

+a734

p15 + 6 2 h + 6 3 7

+0.3 12

616

+

-0.217

625 +647

63

+0.204

614+&3+667

+O. 107

612 + 6 3 4 + A 6

4.104

62 627

+

(336

+0.088 +

-0.084

645

61

+0.078

817 + 6 3 5 +b46

4.074

813 + 6 2 4 + A 7

+0.070

67 66

+0.052 -0.034

ps

+0.004

experiments involving 4, 6 and 11 runs. For this intermediate analysis, it was necessary to employ the target values for the levels of the quantitative variables to maintain the required number of degrees of freedom for such an analysis. The results after four runs are summarized in Table 8 as estimates of four pieces of information: (I)

6,+~2+A4+A6+P]4+b23+P57+~3+8?4+PS7.

(2)

PI + b2 +

(3)

b 2 7 + ~ 6 + b 4 ~ + ~ 7 + ~ ~ + 8 4 6 + 8 ] 5 + ~ 6 + ~ 7

+ 64’

k5+ b47,and (4) ps +& +I$ +

as shown in the “factor” column in Table 8. These results show that the factors in ( I ) and (2) have the largest effect; i.e.,

x5

I

I

I

0

5

10

15

Normalized effect

Effect on log,, k,

Factor

----X7

Figure 4 - Normal probability plot of the normalized effects. Interaction effects are identified by one term from biased groups of three terms noted in Table 10.

the overall average biased with a group of interactions and the main effects associated with the gas compositions and temperature. On the other hand, the effect of steel history, grade and surface condition along with the group of two-factor interactions in (3) above are relatively small. The signs associated with the effects in these results indicate whether an increase in a variablehnteraction increases (positive effect) or decreases (negative effect) the dependent variable. The results after the first six runs are shown in Table 9 with the relative ranking of the factors affecting the dependent variables. These effects were estimated by applying a singular value decomposition (SVD) to Equation ( 7 ) to solve for eight factors in the vector p shown in Table 9. At this point the influence of temperature and interactions between variables are more evident. After eleven runs the results, Table 10. obtained by SVD for fifteen factors, show that the highest-ranking main effect is temperature with other main effects and groups of interactions interspersed through the remaining rankings. An interaction effect is strongly indicated. The data for the full twenty experiments were analyzed using unweighted, weighted and stepwise regression procedures. Model adequacy was checked by comparing the ratio, F,, of the mean square lack of fit and the mean square pure error to the appropriate Fa. ,,2 value with a significance level of a = 0.05. The mean square pure error, estimated from the replicate runs, was 0.00902 with 9 degrees of freedom. Additional tools in this analysis included assessment of normal probability plots of the residuals, 0,- j ) , and plots of the residuals as a function of? and the independent variables and interactions. A normal probability plot of the normalized effects is +shown 8 ~ 6 in Figure 4. These effects are the average of the “low” and “high” values of each effect divided by their respective standard deviations. Those effects that are negligible fall along a straight line while significant factors or interactions (or groups of interactions in this case) will deviate from the straight line. The results shown in Figure 4 include the fourteen main effects and interactions (shown in

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409

Table 10) with the latter denoted by one interaction member from an aliased group, for example, x I 5denotes an effect from the group x , +~ x2, + x37. These results, as expected, clearly indicate the importance of temperature (x,) and the relatively minor influence of other factors. In many experimental design studies, it is assumed that only a small number of effects are important; this has been called effect spursity by Hamada and Wu ( 1 992). These authors have also noted that when a two-factor interaction is significant, it is highly likely that at least one of the corresponding main effects is also significant; Hamada and Wu (1992) refer to this as effect heredity. A model based only on temperature as a main effect gives = 1.62 and p4= 1.OO.This model exhibits lack of fit with F, = 3.98 compared with F,,,, 9, = 3.18. Stepwise regression procedures indicate that the significant effects include temperature (x4), a positive interaction from the group (x,, + x2, + x ~ ~grade ) , (x,) and surface condition (x7). It is likely that only one term from the interaction group (xI4+ x2, + x67) is important in this analysis. The interaction between water vapour (x2) and carbon dioxide (x,) concentrations is an unlikely candidate because neither main effect is significant. A positive interaction between oxygen concentration (xI)and temperature (x,) would imply that (i) at the low temperature, the oxidation rate is higher at the low oxygen concentration and (ii) at high temperatures the oxidation rate is higher at high oxygen concentrations. Both of these conditions make this interaction term unlikely on physical grounds. This leaves the interaction term between grade (x6) and surface condition (x7) as the most plausible candidate among these interaction terms. This conclusion is also supported by the significant main effect of each variable in this interaction term. A positive interaction between grade and surface condition implies that at the +I grade level, surface condition has little effect on the oxidation rate but at the -1 grade level, the cast surface has a lower oxidation rate. This conclusion leads to the model,

103

h

- - -C102

6

j = 1.58 + 1.03x4 + 0 . 0 8 3 8 + ~ 0~ .~0 ~7 6 3 ~ ~ - 0 . 0 8 2 8 ~ ~. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(10)

and this model is statistically adequate with F, = 1.1 1 compared with Fo,05,, ? = 3.37. The effect of grade and surface condition on the oxidation rate at low and high temperature conditions is shown in Figure 5. There are other variables and interactions that might appear more important or rank higher than the interaction term x6x7 in Table 10 and Figure 4. For example, the variables x,, x2 and x3 and interactions x,xs and x,x7 are the next higher ranking effects in Figure 4 following the inclusion of temperature (x,) in the model. However, each of these variables had a small to moderate correlation with the large effect of temperature in the regression analysis. Interactions from the group (xIx4+ xp3 + x,x7), on the other hand, had a very low correlation with temperature and from this group, the interaction x,x7 appears to offer the most plausible explanation. The residuals from the model in Equation (10) exhibited a larger dispersion at the low surface condition and hence a weighted least squares procedure was also examined. Pooled estimates of the pure error variance at the two surface conditions for the replicate runs were obtained and used in estimating weights for all the experimental test conditions. The results of this analysis gave improved residual 410

I

L

I

I

Temperature = 115OoC

- - -1 Grade

1

I

I

I

I

I

Temperature = 8OO0C

I--+--

-1 Grade

4

1

I

I

1

1

-1

0

1

I

Surface condition Scatter plots showing the effect of the interaction between grade and surface condition; top graph is for 1 150°C and bottom graph is for 800°C. Figure 5

-

behaviour with only modest changes in the parameter-estimates noted in Equation (lo), p0 = + I .58, f3, = + I .02, ph7 = +0.0838, pS = +0.0757 and = 4 . 0 8 2 4 . The parabolic rate constants obtained here can be compared to values found by others. For example, Davies et al. (1951) and Schmahl et al. (1958) studied the oxidation of iron in pure oxygen over a wide temperature range. Rahmel and Engell (1959) studied the oxidation rate of iron in atmospheres with oxygen concentrations in the range 1 to 100% for three temperatures that overlap the results obtained in the present work. Sachs and Tuck ( 1 970) also report parabolic oxidation rates for iron in pure oxygen, air and synthetic gases simulating combustion products. Data from these investigations and the present data are shown in the left graph of Figure 6 in an Arrhenius plot in the temperature range of 600 to 1200°C. Sachs and Tuck ( 1 970) also studied the high-temperature oxidation of mild steel in oxygen, air and synthetic combustion product gases. These results and data from the present study are shown in the right graph of Figure 6.

a

Discussion The present work demonstrates an experimental screening study of a problem with important industrial applications. The variables chosen for investigation are consistent with those of interest for industrial control of scale, namely the oxidizing gas composition, temperature, and steel composition. The oxidation tests were performed with an exposure time of 4 hours, a time scale typical of that employed in steel reheat furnaces for the batch heating of steel slabs. The phased approach suggested in this work, based on the experimental design strategy of Moms and Mitchell (1983), func-

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10-2 Schmahl et al (1958) A Rahmel and Engell(l959) C

10.3

'? i0-4 E

P

w '

0

10-5

Y

Y"

10-7 108

'

0.6

I

0.8

1

1.o

in,K - ~ X I O - ~

1.2

0.6

0.8

1.o

in,K - ~ X I O - ~

tions well in providing significant intermediate information about possible effects of interactions during the study. This approach thus has merit in allowing for an interim reporting and/or assessment of project objectives at an intermediate stage. It should also be noted that the effects of the qualitative variables (steel history, grade and surface condition) were small in the initial stage of experimentation and the potential significance of some of these variables only became apparent after the completion of the full programme. Hence, one should also be aware of the potential need for changes in conclusions drawn from early stages of experimentation. While a significant temperature effect might have been anticipated in this work, based on the levels chosen for this variable, the fact that interactions could also be ranked high in relative importance demonstrates the utility of the experimental strategy. The parabolic oxidation mechanism here employed is consistent with the observations for all runs except the early stages of the low-temperature runs. The results for run 1, in particular, did not indicate a parabolic behaviour for the first 6000 s. However, the parabolic rate constants were estimated from the present data based on results for the last 6000 s where a distinct parabolic form was evident. This also corresponds to the time when a larger scale growth develops on steel slabs in the soak zone of reheat furnaces. Within this region a parabolic model provides an adequate description of the data for all test conditions, including those for run 1. The effect of temperature is shown to be of greatest importance in the present study while a two-factor interaction between surface condition and grade is also important at a 5% significance level. The effect of temperature is an expected result. The interaction term between surface condition and grade coupled with the main effects of these variables indicates that for the low carbon grade, the cast surface has a lower oxidation rate or a more protective coating against oxidation than the machined surface condition. This observation is important for experimental tests and indicates the importance of surface preparation in studies of oxidation kinetics. The parabolic rate constants in the present work are similar in magnitude to those observed in previous studies of high temperature oxidation of iron and steel. A comparison between the present data and previous results for the oxidation of iron indicates that the parabolic rate constant is typically lower for mild steel, as shown in Figure 6. The scatter in the data sets shown in Figure 6 is attributable to the effect

1.2

Figure 6 - Arrhenius graphs of the parabolic rate constant for scale formation on mild steel (present work) and iron (other references) on the left graph and for scale formation on mild steel on the right graph.

of other variables (for example, the oxygen or gas concentration for the work of Rahmel and Engell(l959) and Sachs and Tuck (1 970) and the significant variables found in the present work) and experimental error. The fact that other variables/interactions appeared to rank higher than the interaction between grade and surface condition was due to the biased nature of the results from this Morris and Mitchell design (1983). Traditional alternatives for the investigation of seven variables include the 27-3 fractional factorial design involving 16 runs (plus replicates). This design will provide unbiased estimates of main effects (an improvement over the present case) plus interactions in seven groups of three (similar to the present case). Hence, there is a penalty incurred in our implementation of the Morris and Mitchell design ( 1 983). but in the present work, plausible results have been obtained and hrther tests could be performed to confirm or reject these hypotheses. Computer generated experimental designs (Myers and Montgomery, 1995) could be used for this task and with better hindsight might have been used at the outset in the present work, but it was felt that the Morris and Mitchell design (1983) would indicate the presence of significant effects at an early stage in the experimental program. The present results do indicate these benefits and also point out some of the problems that can arise in the final analysis of the results.

Conclusion Variables affecting the high temperature oxidation of low carbon steel samples have been examined in a laboratoryscale apparatus using a Morris and Mitchell ( 1 983) experimental screening design. The experimental program included eleven runs for the basic design and nine replicate runs to obtain an estimate of the pure error variance. This type of design allows for an assessment of the effect of variables and interactions between variables at an intermediate stage of the experimental program. The independent variables investigated included those commonly encountered in reheat furnace operation: gas composition, temperature, steel grade and surface preparation. The dependent variable was the parabolic rate constant estimated from the mass gained by the steel samples during the oxidation process. From the results, the following conclusions can be drawn: I . The phased approach using the Morris and Mitchell (1983) screening design performed well in this study. The intermediate results after four and six runs indicated

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41 I

the importance of both main effects and two-factor interactions between variables. The early knowledge gained from this information served to guide the development of the process model. 2 . The complete eleven run design confirmed that within the range o f the variables examined, the most significant factor was the oxidation temperature. The relative importance of this variable was indicated at the intermediate stages of the experimental program. An interaction between the qualitative variables, surface condition and steel grade, w a s also significant. For the lower carbon grade, a lower scaling rate was observed on samples having a partially cast surface while a machined surface gave higher rates.

Acknowledgements We acknowledge financial support by the Natural Sciences and Engineering Research Council of Canada in the form of a CRD grant. The cooperation of the Ferrous Industry Energy Research Association (FERA), the assistance of Sue Olynyk and Ted Kerr of Dofasco, Inc. and useful suggestions by Dr. D.W. Bacon and Dr. P.J. McLellan of Queen’s University in the project are gratefully noted.

Nomenclature integration constant, g2/m4 diffusivity, m2/s ratio of mean square lack of fit to mean square pure error test statistic with a level of significance a and degrees of freedom vI and v2 identity matrix 112 kp, g2/m4.s parabolic rate constant, g2/m4.s lack of fit matrix gas constant, 8.3 144 J/mol.s time, s temperature, K independent variable vector of independent variables dependent variable predicted value of dependent variable vector of observations

Greek letters significance level regression parameter parameter estimate vector of regression parameters random error vector of random errors scale thickness (mass), g chemical potential, J/mol degrees of freedom

reference to variable i reference to interaction between variables i a n d j

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Manuscript received May 16, 1995; revised manuscript received January 13, 1997; accepted for publication January 20, 1997.

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