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Desulfurization Model Using Solid CaO in Molten Ni-Base Superalloys Containing Al

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Abstract

Details of the desulfurization for molten Ni-base superalloys containing Al using solid CaO have been investigated, and the formula that explains the reaction rate has been developed. A cylindrical CaO rod was inserted into 500 g molten Ni-base superalloy TMS-1700 (MGA1700) containing 200 ppm S and held for a certain period at 1600 °C in each experiment. Sulfur content in the melt decreased with the increasing holding time of the CaO rod. Results of electron probe microanalysis show that Ca, O, S, and Al distribute in the same part of the melt/CaO interface as well as the particle boundaries of the CaO rods. The distribution of these elements suggests that CaO reacted with S in the melt to generate CaS, and Al reacted with O and CaO to form calcium aluminate slag. The desulfurization rate formula was obtained by the assumption that the rate-controlling process of the desulfurization is S diffusion through the generated layer composed of CaS and calcium aluminate slag. This formula expresses the amount of S in the melt by the diffusion term with the effective diffusion coefficient, which was obtained from the experimental results. Moreover, the time required for the desulfurization of 2 kg molten Ni-base superalloy PWA1484 using a CaO crucible, was calculated by this desulfurization rate formula which resulted in fair agreement with the actual result.

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Abbreviations

A :

Area of the melt/CaO interface (m2)

\( c \) :

Content of S in the melt (g/m2)

\( c_{1} \) :

Content of S in the generated layer at the interface with the melt (g/m3)

\( c_{2} \) :

Content of S in the generated layer at the end of the center side (g/m3)

\( C_{\text{S,0}} \) :

Initial S content in the melt (ppm)

\( C_{\text{S,t}} \) :

Content of S in the melt at time t (ppm)

\( C_{\text{S, fin}} \) :

Final content of S in the melt (= target S content) (ppm)

D :

Effective diffusion coefficient (m2/s)

J :

Flux of S (g/m2 s)

l :

Distance of S transfer (m)

\( M_{\text{CaO}} \) :

Chemical formula weight of CaO (g/mol)

M S :

Chemical formula weight of S (g/mol)

t :

Desulfurization time (s)

w :

Amount of transferred S (= amount of desulfurization) (g)

\( W_{\text{Ni}} \) :

Amount of the melt (g)

\( \delta_{\text{t}} \) :

Thickness of the homogeneously generated layer at time t (m)

\( \rho_{\text{CaO}} \) :

Density of CaO (g/m3)

\( \rho_{\text{Ni}} \) :

Density of the melt (g/m3)

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Acknowledgments

The authors are grateful to Mr. D. Kaneko (Meijun Gijutsu Shien) for the designing and development of the induction melting furnace specified for this experiment. I.mecs Co., Ltd is thanked for their precise work on the condition adjustment of the induction heating and for their continuous support. We thank TOUHOKU SOKKI CORP for organizing the development of the experimental apparatus. We also thank Drs. S. Kawada, and A. Iwanade, Materials Analysis Station, NIMS, for chemical analysis. Dr. T. Degawa is thanked for his achievement on the field of desulfurization process and for providing his book that helped the first study of the present research. This research was financially supported by Japan Science and Technology Agency (JST), under the Advanced Low Carbon Technology Research and Development Program (ALCA) project: “Development of Direct and Complete Recycling Method for Superalloy Turbine Aerofoils. (JPMJAL1302)”.

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Correspondence to Yuki Kishimoto.

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Manuscript submitted April 3, 2019.

Appendix

Appendix

Derivation of Desulfurization Rate Formula

The derivation of the desulfurization rate formula [3] is explained as follows. The Fick’s first law is

$$ \begin{array}{*{20}c} {J = - D\frac{{\text{d}c}}{{\text{d}l}}} \\ \end{array} $$
(A1)

The continuous equation can be expressed using flux J, as

$$ \begin{array}{*{20}c} {\frac{{{\text{d}}w}}{{{\text{d}}t}} = {JA}} \\ \end{array} $$
(A2)

Thus,

$$ \begin{array}{*{20}c} {\frac{{{\text{d}}w}}{{{\text{d}}t}} = - {DA}\frac{{{\text{d}}c}}{{{\text{d}}l}}} \\ \end{array} $$
(A3)

The content gradient d\( c \)/dx can be assumed by the equation:

$$ \begin{array}{*{20}c} {\frac{{{\text{d}}c}}{{{\text{d}}l}} = \frac{{c_{ 1} - c_{ 2} }}{{\delta_{\text{t}} }}} \\ \end{array} $$
(A4)

Using the amount of S in the melt at time t, \( w_{\text{t}} \) and the initial amount of S in the melt \( w_{ 0} \), the amount of transferred S can be written in the equation of the content gradient dc/dl, as

$$ \begin{array}{*{20}c} {\frac{\text{d}}{{{\text{d}}t}}\left( {w_{\text{t}} - w_{ 0} } \right) = - {DA}\frac{{c_{ 1} - c_{ 2} }}{{\delta_{\text{t}} }}} \\ \end{array} $$
(A5)

It can be assumed that the content of S \( c_{ 1} \) = constant and \( c_{ 2} \) = 0.

The thickness of the generated layer \( \delta_{\text{t}} \) can be expressed using content of S in the melt at time t by forming the molar amount of CaO and S reacted (when x = 3) as

$$ \begin{array}{*{20}c} {\frac{{\rho_{\text{CaO}} \delta_{\text{t}} A}}{{M_{\text{CaO}} }} = 2\frac{{W_{\text{Ni}} \left( {C_{\text{S,0}} - C_{\text{S,t}} } \right) \times 1 0^{ - 6} }}{{M_{\text{S}} }}} \\ \end{array} $$
(A6)

and solving for \( \delta_{\text{t}} \) gives

$$ \begin{array}{*{20}c} {\delta_{\text{t}} = \frac{{ 2M_{\text{CaO}} W_{\text{Ni}} }}{{\rho_{\text{CaO}} M_{\text{S}} A}}\left( {C_{\text{S,0}} - C_{\text{S,t}} } \right) \times 1 0^{ - 6} } \\ \end{array} $$
(A7)

The amount of S \( w_{t} \) and \( w_{ 0} \) can be rewritten using the content of sulfur \( C_{\text{S, t}} \), as

$$ \begin{array}{*{20}c} {w_{\text{t}} = W_{\text{Ni}} C_{\text{S,t}} \times 1 0^{ - 6} } \\ \end{array} $$
(A8)
$$ \begin{array}{*{20}c} {w_{ 0} = W_{\text{Ni}} C_{\text{S,0}} \times 1 0^{ - 6} } \\ \end{array} $$
(A9)

Furthermore, it can be assumed that the content of S \( c_{ 1} \) was equal to the finally remaining content of S in the melt, as

$$ \begin{array}{*{20}c} {c_{ 1} = \rho_{\text{Ni}} C_{\text{S,fin }} \times 1 0^{ - 6} } \\ \end{array} $$
(A10)

Rewriting Eq. [A5] gives

$$ \begin{array}{*{20}c} {\frac{{{\text{d}}C_{\text{s,t}} }}{{{\text{d}}t}} = - \frac{ 1}{ 2}\frac{{\rho_{\text{CaO}} \rho_{\text{Ni }} M_{\text{S }} A^{ 2} C_{\text{S, fin }} D}}{{W_{\text{Ni}}^{ 2} M_{\text{CaO}} \left( {C_{\text{S,0}} - C_{\text{S,t}} } \right)}} \times 1 0^{ 6} } \\ \end{array} $$
(A11)

Thus, the content of S in the melt \( C_{\text{S,t}} \) can be expressed as

$$ \begin{array}{*{20}c} {C_{\text{S,t}} = C_{\text{S,0}} - \sqrt {\frac{{\rho_{\text{CaO}} \rho_{\text{Ni}} M_{\text{S }} A^{ 2} C_{\text{S, fin }} D t }}{{W_{\text{Ni}}^{ 2} M_{\text{CaO}} }} \times 1 0^{ 6} } } \\ \end{array} $$
(A12)

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Kishimoto, Y., Utada, S., Iguchi, T. et al. Desulfurization Model Using Solid CaO in Molten Ni-Base Superalloys Containing Al. Metall and Materi Trans B 51, 293–305 (2020). https://doi.org/10.1007/s11663-019-01716-8

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