A kinetic model of the 60% Mg and 40% CaO injection desulphurization was established. The simulation results from the model were verified by sampling, and it was in accord with the sampling results. By analyzing the model, the desulfurization process of high sulfur molten iron had three stages, incubation stage, rapid desulfurization stage and slow desulfurization stage. In order to improve the dynamic conditions and the utilization rate of the desulfurization agent, for the molten iron of sulfur content ≥0.035%, a new injection desurphurization mode was developed and applied. The smaller injection rate of powder and the larger flow rate of nitrogen were used in the slow desulfurization stage. Compared with the conventional process, the consumption of the desulfurizing agent is reduced by 10–20% by using the two-stage injection method.

Based on the ion and molecule coexistence theory, the calculation model of action concentration for system of CaO–FeO–Fe₂O₃–SiO₂ copper slags was built up in this article. Effects of CaO, reaction temperature and reduction ratio on reduction of copper slag were discussed. Thermogravimetric experiments of the reduction of copper slag were carried out. As a good potential reductant, biomass was injected and it undertook the task of the reduction of copper slag.

The contents of FeO and Fe₂O₃ reflect reduction degree in copper slag. The addition of CaO could change the balance of reaction system and promote the separation of Fe and Si from 2FeO·SiO₂, which was in favor of copper slag reduction. The effects of temperature on mass action concentration were affected by the addition of CaO. High temperature was in favor of the reduction of Fe₃O₄ in copper slag. However, excessive addition of CaO (when the content of CaO was over 28% in calculate conditions) caused excessive insoluble solid in slag, increased the viscosity of copper slag and restricted reduction reactions.

The calculation results achieved high conformity with thermogravimetric experiments. The results obtained in this work indicated that biomass would be a good potential reductant for reduction of copper slag. CaO had promotion effects on the reduction reaction. With the increase of CaO, reduction ratio of copper slag increased firstly and reached a peak when CaO/Slag was 0.3:1 and then it declined due to the changes of slag viscosity.

Aiming to better understand the effect of MgO on sintering process of iron ores, the formation of [Mg_1-x,Fe_x]O·Fe₂O₃ in solid-state reactions between MgO and Fe₂O₃ was studied. Experiment was carried out in air from 873 K to 1573 K by MgO mixing with Fe₂O₃. X-ray diffraction, optical microscope, scanning electron microscopy and energy-dispersive spectroscopy were used to characterize the phase change of the sintered samples. The content of ferrous ion in the sintered samples was determined by potassium dichromate titration for distinguishing the MgO·Fe₂O₃ (x=0) and the Fe₃O₄ (x=1). Thermogravimetric and differential scanning calorimeter test was carried out in air by MgO mixing with Fe₂O₃ to investigate the thermal decomposition of Fe₂O₃. The results show that the reactions between the Fe₂O₃ and MgO in air formed first the magnesium ferrite at 1073 K, subsequently magniferous magnetite appeared at 1173 K, resulting that the thermal decomposition of Fe₂O₃ was carried out at a lower temperature than that of its own self. The following conversion of the magniferous magnetite to the magnesium ferrite was also observed with the temperature increasing to 1482 K. It has been deduced that the [Mg_1-x,Fe_x]O·Fe₂O₃ is formed by the reaction between the prior formed MgO·Fe₂O₃ and the Fe₂O₃ in the heating-up process. It was obtained that amount of ferrous ion formed in sintering process is mainly related by the amount of MgO in raw materials and it’s diffusion rate. Therefore, adding MgO appropriately into raw material can be beneficial to improve the low temperature reduction degradation of iron ore sinter.

In the steel refining process, a metal emulsion in which metal droplets are dispersed in the slag phase plays an important role in improving the reaction efficiency. In a previous study, the formation of metal emulsions was experimentally evaluated using Pb or Al alloys as the metal phase and chloride salt as the slag phase. In this study, the formation of metal emulsions was investigated by using a Sn alloy-salt system, and the influence of the density was clarified. The results revealed that the number, surface area, volume, and mass of emulsified metal droplets were largest in the Al/salt system, while those in the Sn/salt system were similar to those in the Pb/salt system. The formation and sedimentation rates of metal droplets were analyzed based on a mathematical model. The formation rate was also largest in the Al/salt system, while that in the Sn/salt system was similar to that in the Pb/salt system. The bubble rupture frequency showed a similar difference according to the metal phase, and it was shown that the formation rate was strongly influenced by the bubble rupture frequency. In addition, a clear relation between the formation rate by a single gas bubble and the density ratio of the upper and lower phases was found.

The interfacial behavior between sodium polytungstate solution (SPTS) and silicone oil (SO) due to a single rising bubble was directly observed to investigate the influence of the Eötvös number on the flow characteristics. We found that the transient behavior of the jet under the bubble strongly depended on the SPTS density in the range of 1000–3000 kg/m³. Although the SPTS film generated in the SO influenced the detention time of the jet under the bubble, the lifetime of the film did not depend on the SPTS density.

Hot metal Desulfurization kinetics were studied experimentally using CaO–Al₂O₃–SiO₂–MgO–TiO₂–Na₂O slags in the range of 1773 K to 1833 K. The results indicated that the rate of desulfurization increases with the Na₂O and MgO content in slag increase, the slag basicity increase, i.e., the ratio of CaO to SiO₂, Al₂O₃ and TiO₂ content decrease, and the temperature increase. A mathematical model of desulfurization kinetics has been developed, using which the calculated results of the desulfurization of hot metal are in reasonable accord with the experimental data. The activation energy of the apparent rate coefficient was found to be 172.58 kJmol⁻¹, and the mass transfer coefficient of the slag phase hardly changes with temperature. All of these showed that the desulfurization of hot metal using the present slag system is controlled by the slag phase mass transfer.

Recently, low coke rate blast furnace operation has been required in response to the rising cost of coking coal. However, the thickness of the coke layer decreases in low coke rate operation. Since it is known that the gas permeability of the blast furnace deteriorates as the coke layer thickness decreases, it is important to determine the minimum coke layer thickness for stable blast furnace operation. On the other hand, the minimum coke layer thickness has not been clarified due to a lack of equipment capable of measuring the effect of the coke layer thickness on permeability.

In this study, a new experimental device called the cohesive zone simulator was developed to clarify the minimum coke layer thickness. In the cohesive zone, gas flows horizontally along the coke layer. In order to quantify the effect of the coke layer thickness on permeability, this horizontal gas flow should be simulated. Therefore, this simulator simulates a horizontal gas flow.

Next, the effect of the coke layer thickness was quantified by using the cohesive zone simulator. The results showed that melting iron ore penetrated into the coke layer and closed part of the layer. These phenomena caused a deterioration of permeability under thin coke layer thickness conditions.

Finally, a pressure drop estimation model considering penetration of the coke layer by melting ore was developed with the aim of quantifying the minimum coke slit thickness.

Ore-based steelmaking generates a variety of residues including dusts, sludges and slags. Recycling of these residues within the process or via other applications is essential for sustainable production from both environmental and economic aspects. In blast furnace (BF) ironmaking, there are generally two residues leaving the gas cleaning equipment; namely, BF dust and BF sludge. Traditionally, the dust is recycled via the sinter or, in the case of pellet based BF, via cold bonded agglomerates and injection. As the main output of zinc from the BF is the top gas, the sludge has to be dezinced prior to recycling to prevent accumulation of zinc in the furnace. Although dezincing of BF sludge has been successfully accomplished using e.g., hydrocycloning, the studied sludges are generally coarse sized and high in zinc. Furthermore, information is lacking regarding the efficiency of separation of different hydrocyclone setups. In the present work, hydrocycloning of a fine sludge, with low zinc content, generated by a pellet based BF has been studied. The gas cleaning equipment used to produce the sludge was running a primary aerocyclone and a scrubber. A characterization of the sludge has been conducted together with an evaluation of the separation efficiency of the hydrocyclone in order to assess the hydrocyclone performance and limitations. Furthermore, the dezincing using the hydrocyclone has been compared to that of sulfuric acid leaching. The results suggest that 51 to 93% of the sludge can be recycled depending on the demand on zinc removal and the chosen dezincing route.

The objective of this paper is to develop a prediction tool for burden distribution of a blast furnace (BF) by using Discrete Element Method (DEM). The high-speed video recording in an actual blast furnace process was tried to capture the particle behavior in Nagoya No.3 BF, and the particle trajectory discharged from a rotating chute was also measured by using a pressure sensitive sheet. The modeling of particle behavior was conducted by DEM, and the simulated behavior was compared with the measured results. The particle discharging behavior was recorded from a large manhole during a shutdown, and an individual particle was able to be seen in the images. It was observed that the particles were pressed up against the chute side wall due to the centrifugal force of chute rotation. The particle discharging velocity was analyzed by Particle Image Velocimetry (PIV). It is found that the velocity of coke particle is larger than that of sinter because of the particle size. This difference affects the particle discharging trajectory, and the one for coke particle is shifted toward the BF wall by comparing to that for sinter. The simulated particle behavior using DEM has a good agreement with the observations, both by the high-speed recording and the trajectory measurement. Therefore, it can be concluded that this particle simulation has high reliability for prediction of the particle trajectory in the actual blast furnace operation.

The extent of coal combustion within the tuyere and raceway region is one key factor affecting the maximum pulverized coal injection (PCI) rate. Oxygen enrichment, especially local oxygen enrichment, is the most effective way to increase the PCI rate. In this study, a three-dimensional numerical model was developed to simulate the lance-blowpipe-tuyere-raceway of a blast furnace. In the study, the characteristics of oxygen-coal combustion are investigated under the single oxygen-coal and oxygen-coal double lances. Under local oxygen enrichment ways, the oxygen content around the coal particles increases significantly, benefiting coal combustion. However, the cooling effect of room-temperature oxygen delays coal combustion. Therefore, the way by which the oxygen flows should not be neglected. The results indicate that the increase in the burnout is quite different under different lance patterns. The burnout had the maximum increase of 2.17% under the coaxial oxygen-coal lance. The burnout had the highest increase of 12.84% under the oxygen-coal double lance.

Experiments were carried out to measure mixing time and slag eye area in two different water model ladles with gas injection nozzle located at the mid bath radius position. Within the range of experimental conditions studied, the following correlations (in SI unit), for 95% mixing time and slag eye area, were found to work satisfactorily:

In the above equations, Q is the gas flow rate (corrected to mean height and temperature of the liquid)(m³/s), L is the liquid depth (m), R is the vessel radius (m), ΔL is the slag layer thickness (m), υ_s is the kinematic viscosity (m²/s) of the upper phase, ρ_L is the bulk liquid density (kg/m³), τ_mix,95% is the mixing time (s), A_es is the slag eye area (m²), U_P is the average plume rise velocity (m/s), g is the gravitational acceleration (m/s²) and Δρ is the metal-slag density differential (kg/m³). Based on the above and a set of four different bounds on (i) specific energy input rate, (ii) ladle aspect ratio, (iii) amount of liquid in ladle and (iv) slag layer thickness, a multi-objective, constrained optimization problem was formulated to investigate inert gas injection in steelmaking ladles. To this end, a Genetic Algorithm based optimisation procedure embodied in MATLAB™ was applied. Due to the conflicting nature of the objective functions, a Pareto optimal front, comprising many optimal solutions resulted from which the desirable range of operating parameters was identified. Present study has also indicated that desirable optimal operating conditions are likely to be a function of the location of the porous plug in a ladle. Finally, for the sake of validation, three arbitrarily chosen experimental conditions were evaluated against the relevant Pareto front and it is shown that the chosen conditions are, by and large, sub-optimal.

In this study, a calculation procedure of gas/liquid mass transfer capacity coefficients based on liquid/liquid ones was developed and cold model studies on benzoic acid transfer between water and liquid paraffin, and oxygen transfer among water, liquid paraffin and air was carried out under various top/bottom blowing rates and liquid/liquid volume ratios. The liquid/liquid mass transfer rate increased with the increase in a top blowing rate, but the increasing rate of a larger vessel diameter to the top blowing rate was lower than that of a smaller one. The gas/liquid mass transfer rate increased with the increase in both of top and bottom blowing rates, but the difference became reduced with the increase in the top blowing rate. The bottom blowing rate to minimize the sum of the top and bottom gas flow rates was almost constant for a given gas/liquid or liquid/liquid mass transfer rate. The liquid/liquid mass transfer rate increased and the gas/liquid one decreased with the increase in liquid paraffin volume ratio to water. There was a roughly positive correlation between the liquid/liquid and gas/liquid mass transfer rates throughout a wide range of top and bottom blowing rates, but the tendency was the opposite under the condition of the same paraffin volume and total blowing rate.

The kinetics of lime dissolution containing different amounts of magnesium oxide (4.3–7.6%) in steelmaking slags has been studied in a non-stationary diffusion, at temperatures ranging from 1300–1600°C, directly in the hot process. The decrease in solubility of lime with the increasing content of magnesium oxide is due to the formation of high temperature solid chemical compounds (Ca₂SiO₄, (Mg,Fe)₂SiO₄) and solutions based on MgO like ((Mg,Fe) O) in the volume of lime samples. Formed slightly soluble phases hinder the process of CaO dissolution and slow down the rate of dissolution of lime samples. Based on differential equations of mass balance of the dissolving substance and taking into account its transition into the melt phase, and accumulation in the consistently dissolving layers of solid, values of mass transfer coefficients and diffusion coefficients were calculated. Mass transfer coefficients, despite a decrease in the concentration gradient, increase in the process of slag saturation with lime. Activation energy has been calculated under conditions of non-stationary linear and spatial semi-infinite diffusion. Based on the dependency of the logarithm of diffusion coefficients on the inverse temperature derived value of the activation energy of diffusion is 230.2±14.0 kJ/mol.

Experiments with different titanium addition were carried out in alumina crucible without slag at 1873 K to investigate the variation of inclusion composition, size and morphology in Al–Ti–Ca complex deoxidized steel. The samples exacted from the experimental steels were analyzed by field emission scanning electron microscopy (FE-SEM) and energy dispersive spectroscopy (EDS). Titanium influence significantly on the morphology, size distribution and composition of oxide inclusions in Al–Ca deoxidized steels, and the inclusions characteristics vary with titanium content. Liquid oxide inclusions are promptly modified by titanium. On the other hand, titanium can also change solid calcium aluminate inclusions into spherical ones in the melts similarly, but there are a number of inhomogeneous inclusions in molten steel at the initial stage. Therefore, to modify inclusions better, the content of titanium and calcium in molten steel should be controlled simultaneously during the production process.

Freckles severely affect the quality of high-carbon chromium bearing steel ingots produced by electro-slag remelting (ESR). With conventional slags, reducing the melt rate of the electrode can prevent freckle formation, but severe surface defects can still occur. In order to design an appropriate slag for control of segregation and also improve the surface quality of the ingots, the melting temperature, heat transfer properties, and viscosity of several synthetic slags based on the system CaF₂–CaO–Al₂O₃–MgO were evaluated. As a consequence of the laboratory investigation, a slag with 50% CaF₂ and a CaO/Al₂O₃ ratio of 1.5, was selected as a candidate for validation on ESR production facilities based on the following package of attractive properties: low melting temperature, low break temperature, low viscosity and high thermal conductivity. Following evaluation of the selected slag formulation on full-scale plant trials, HSLA steel ingots were produced that were free from freckles and exhibited good surface quality.

A transient three-dimensional (3D) mathematical model has been established to study the effect of the current on the desulfurization in the electroslag remelting process using direct current (DC). The solutions of the mass, momentum, energy, and species conservation equations were simultaneously calculated by the finite volume method. The movement of the metal droplet was described by the volume of fluid (VOF) approach. In order to include the influences of the slag composition and the current on the desulfurization, a dynamic module of was introduced. Three experiments have been carried out to validate the model. The volume-average temperature of the slag increases from 1940 K to 2019 K, while the current ranges from 1200 A to 2400 A. The sulfur transfer caused by the slag treatment is promoted by the stronger current because of the higher temperature. The value of the negative transfer rate induced by DC also becomes larger with the increasing of the current. The overall transfer rate at the metal droplet-slag interface is decided by the competition of these two transfer rates. The removal ratio of sulfur increases from 82% to 88% when the current changes from 1200 A to 1500 A, and then drops to 65% if the current continuously increases to 2400 A.

The effect of an axial magnetic field on the dendrite morphology in directionally solidified Ni-based superalloy was investigated experimentally. Results show that an application of the magnetic field modified the morphology of the dendrite remarkably. Under a relatively weak magnetic field (B<0.5 T), the primary dendrite spacing decreases with the increase of magnetic field intensity. However, under a relatively high magnetic field (B≥2 T), the primary dendrite spacing increases with the increase of magnetic field intensity. Moreover, it was found that the strong magnetic field is capable of inducing the fracture of the dendrite and the columnar to equiaxed transition (CET). With the increase of the magnetic field and the decrease of the growth speed, the fracture of the dendrite and the CET under the magnetic field is enhanced. The above results may be attributed to the TE magnetic convection in the liquid and the TE magnetic force acting on the dendrite.

In hot rolling, lubrication oil plays an important role in reducing rolling force and protecting the work roll surface. However, the oil behavior in hot rolling has not been clarified sufficiently. In this work, a numerical analysis of the introduced oil film was attempted. There are no previous reports on numerical analysis of hot rolling lubrication. The analytical results of the introduced oil film thickness showed a good correlation with the experimental results. The numerical analysis of hot rolling lubrication clarified the following points: The introduced oil film did not become saturated even if the oil film thickness increased. The reason for this phenomenon is thought to be because the oil viscosity remains high on the work roll side. It was also found that the gradient of the oil velocity in the thickness direction is not constant and changes greatly on the strip side.

In this study, we have simulated the electro-cleaning process considering the actual surface topography of steel sheet to determine the final topography and roughness of the steel surface (R_z, distance between the surface peak and the valley) after different duration of electro-cleaning. COMSOL Multi-Physics^® simulation module with moving mesh technique was used for the electro-cleaning simulation. The effect of applied current density (A/m²), electrolyte concentration (H₂SO₄, g/l) and temperature (°C) on the change in roughness (ΔR_z, µm) of steel surface was evaluated by the simulation. Simulation results show that the current density has the highest effect towards the change in roughness of steel surface. The change in roughness increases with increase in current density. The current density of 500–700 A/m² is required for appreciable electro-cleaning roughness in this study. An electrolyte concentration of 40–60 g/l would provide the maximum change in roughness for any fixed applied current density. The change in roughness also increases with increasing the electrolyte temperature. Lab scale experimentation showed good agreement with the simulated results. Finally, it was determined that 600 A/m² of applied current density and 4.75 µm of steel surface final roughness (R_z,f) would provide the maximum adhesion strength of 110 N between the steel and rubber.

The coaxing effect has been recognized as a phenomenon that enhances the fatigue resistance associated with work hardening and strain-age hardening. To uncover the intrinsic factors that affect the degree of coaxing effect, rotating bending fatigue tests including a process of stepwise stress increases every 10⁷ cycles were carried out at ambient temperature in interstitial free steel and binary Fe–C ferritic alloys. The effects of the work hardening capacity, aging time, stress amplitude increment, and carbon concentration were examined in this simple alloy system. The work hardening capacity was changed by controlling carbon state in a Fe-0.017C (wt%) steel. However, the degree of coaxing effect did not show a significant correlation with work hardening capacity. For the effect of aging time, a fatigue test at a high stress amplitude was interrupted, aged for 2 weeks, and subsequently restarted. Although this process is sufficient to induce strain-age hardening in terms of aging time and plastic strain, a fatigue life of the aged steel was not comparable to that with the coaxing effect. Moreover, an increase in stress increment for each step deteriorated a degree of coaxing effect. It was concluded that the effect of work hardening is minor, and the other factors affecting strain-age hardening must be optimized simultaneously to show a coaxing effect. In addition, the degree of coaxing effect of smooth steel specimens was predominantly controlled by the intergranular fatigue crack initiation behavior. Consequently, a considerable amount of solute carbon and an alternate process for the stress amplitude increment and aging time are required for strain-age hardening that suppresses intergranular fatigue crack initiation.

This study presents investigations of the micro-crack formation in pearlite microstructure as a trigger of unstable cleavage crack propagation in ferrite-pearlite steel. In order to clarify the micro-crack formation mechanism, a trace analysis was conducted to compare the direction of crack surface with those of cleavage and slip planes of ferrite in pearlite. It is found that any directions of crack surface were not coincident with those of {100} planes. On the other hand, all of the directions of crack surfaces showed good agreement with those of {110} planes. The result showed a probability that the micro-cracks in pearlite are formed by the shear fracture on slip planes in ferrite. The condition of unstable propagation from a micro-crack in pearlite into a neighbor ferrite grain was investigated. Effective surface energy was estimated by the crack length obtained by SEM observation and the local stress calculated by finite element analysis. The result showed the estimated effective surface energy of a propagation from micro-crack in pearlite into ferrite matrix is larger than that of cleavage crack propagation across boundary between ferrite grains. A probability of the micro-crack formation in pearlite was quantified by the measurement of micro-cracks in steels having various ferrite-pearlite microstructures and finite element analysis. As a result, the probability of micro-crack formation could be effectively estimated as a function of only the equivalent plastic strain, independently from temperature, volume fraction of pearlite and loading condition.

In metallurgy, there are many factors influencing the quality of gray iron. These are especially the charge material, chemical composition (content of C, Si, Mn, P, S), metallurgical treatment until the final casting process. Charge materials, in particular the steel scrap ratio exerts notable effect on the quality of gray cast iron, which is increasingly being used for economic reasons, especially in the melting of cast iron in electric furnaces. The use of majority amounts of steel scrap in the charge, instead of pig iron necessitates modifying the chemical composition (increase of C and Si content), and improved metallurgical processes. The experimental melts with different ratio of raw materials were realized in laboratory conditions. The paper is aimed to investigate the effects of different composition of charge materials in relation to specific technological conditions of the microstructure, mechanical properties and performance of gray iron.

The effects of partitioning of Mn and Si during intercritical annealing on the transformation behavior and mechanical properties of low alloyed TRIP-assisted steel sheets were investigated by using 0.17%C-1.5%Si-1.7%Mn steel. During intercritical annealing, Mn and Si concentrated in austenite and ferrite by partitioning, respectively. This partitioning of Mn and Si suppressed the bainite transformation during austempering and decreased the volume fraction of retained austenite and its C content. This is considered to be mainly because partitioning of Mn and Si shifted the T₀’ curve to the lower C concentration region and stopped the bainite transformation at a lower C concentration in residual austenite. The decrease in the volume fraction of retained austenite and its C content deteriorated the ductility of the low alloyed TRIP-assisted steel sheets. Although proper intercritical annealing is necessary in order to increase the C content in retained austenite, it should be noted that excessive intercritical annealing can deteriorate the ductility of low alloyed TRIP-assisted steel sheets by causing excessive partitioning of Mn and Si.

The Graduate Institute of Ferrous Technology (GIFT) under the umbrella of Pohang University of Science and Technology (POSTECH) in Korea was established in 2005, aiming at education and research in all that is steel. It is currently run with three centers which have eleven laboratories in all, each of which focuses on a particular aspect of ferrous technology. GIFT offers both master’s and PhD programs, both specialized in ferrous technology. It covers process, product and application of steels and steel-related materials. It also keeps developing close links with steel producers, users and supporters. The interaction happens via many mechanisms including collaborative projects, workshops, participation in teaching, employment of highly trained graduates, secondments from industry to conduct research at GIFT, etc. Such interactions are considered vital in the two-way transfer of knowledge, ideas and direction. In this report, the educational performance of GIFT is briefly summarized. The research emphasis of each center and focal research areas of each laboratory are also outlined. An example out of recent research outcomes of GIFT, which is about a novel approach to the development of light-weight steels, is elaborated in some detail.

Steel is one of the most recyclable materials, and thus it is recycled repeatedly. When steel is recovered from end-of-life products, some materials containing tramp elements besides carbon steel are mixed into the scrap. Therefore, we must prevent contamination by tramp elements during repeated recycling. Meanwhile, there is little knowledge on tramp element contents in carbon steel. This study aims to quantify tramp element contents in carbon steel produced in Japan. The tramp element contents of more than 500 samples of carbon steel were analyzed. The specimens were classified by steel product forms because the tolerance for tramp element contents differs by form. The average contents and confidence intervals for populations were calculated and then multiplied by the annual carbon steel production in Japan. The amounts of Ni and Mo impurities associated with carbon steel produced annually accounted for more than 15% of the annual consumption of these metals in Japan. In addition, the consumptions for plating were considered. The results were confirmed by a comparison with the contents in carbon steel produced from steel scrap generated in Japan after non-ferrous metals were separated from the scrap, which was performed in Vietnam. It is hypothesized that the tramp element contents in the Vietnamese steel are equal to the weighted average contents of carbon steels consumed in Japan. The comparison for Cu and Sn showed good agreement. We conclude that tramp element contents in carbon steel obtained in this study are representative values, even though the number of samples was limited.