Rate of decarburization of iron-carbon melts: Part II. a mixed-control model
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I.
GENERAL
SINCE carbon is taken out of the melt in the form of CO by the CO2 of the gas phase flowing past the droplet, the following equation may be used to represent the overall decarburization reaction: CO2+C=
2CO
[1]
This reaction involves the following phenomena: (i) Mass transfer in gas phase. (ii) Mass transfer in liquid phase. (iii) Interracial reaction. The observed rate may be dominated or influenced by one or more of these steps. On the basis of the experimental results presented in Part I, a decarburization mechanism has been formulated. The details are presented in the next sections.
II.
MASS T R A N S F E R IN GAS PHASE
The continuation of the overall decarburization process in a flowing CO-CO2 gas mixture as per Eq. [1] requires counter diffusion of CO2 and CO across a stagnant gas boundary layer that surrounds the levitated droplet. For this binary gas mixture, the steady state flux of CO2 may be expressed by Nco2 =
-
Dcorco
RT]
dPco~ P_~ dz + (Nco2 + Nco)
[2]
where Nco2 and Nco are the fluxes of CO2 and CO, respectively (moles. cm -2. s-l), Dco2-co the binary diffusivity of CO2 and CO (cm 2 9 s-~), R the gas constant (82.06 cm 3 9 atm 9 mole -t 9 K-t), T/ the film temperature (K) which is the arithmetic mean of the bulk gas temperature and the melt surface temperature,l-4 Pco2the partial pressure of CO2 (atm), z the position coordinate in the boundary layer H. G. LEE, Graduate Research Assistant, and Y. K. RAO, Professor, are both with Metallurgical Engineering, FB-10, University of Washington, Seattle, WA 98195. Manuscript submitted August 3, 1981. MEFALLURGICAL TRANSACTIONS B
(cm), and P the total pressure of the gas mixture (atm). From the Eq. [1], it follows thatNco = -2Nco2 since two moles of carbon monoxide are produced when one mole of carbon dioxide is consumed. Substitution into Eq. [2] gives Nc~
-
Dcorco d In (e RTs
+ eco~) e
[3]
dz
Integration of Eq. [3] across the stagnant gas film yields: Ncoz =
Oco~-cq ( P + P/co2) RT~5 in + P~co~/P
[4]
where the superscripts b and i represent the bulk and interfacial quantities, respectively. 8 is the thickness of the stagnant gas film. From the stoichiometry of Eq. [1] it can be seen that each mole of CO2 carried to the gas-metal interface removes an equal number of moles of carbon from the melt. Therefore, the rate of decarburization may be related to the flux of CO2 as follows:
dpct______~C_ (1200 A~ dt \ pV ]
Nco2
_ (1200AP~ ~- p~; ]
(kTi)
In
(P + P~oz~ + pico2/
[5]
where pct C is the carbon concentration in the melt (wt pct), t time (sec), A the surface area of the specimen (cm2), V the volume of the specimen (cm3), p the melt density (g 9 cm-3), and P the total pressure assumed to be 1 atm. Furthermore, k6 (=Dcovco/B) is the average gas-phase mass transfer coefficient (cm 9 s -1) for the levitated droplet. When the rate of decarburization is controlled by gasphase mass transfer, it is reasonable to assume that the is zero. 1'2'3 partial pressure of CO: at the interface, eco2, i Hence, Eq. [5] becomes reduced to
l
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