Convective mass transfer for turbulent flow (acidizing)

Input(s)

\(D_{A}\): Diffusion Coefficient of Component A \(\left(\mathrm{cm}^{2} / \mathrm{s}\right)\)

\(D_{E}\) : Effective Diffusion Coefficient of Component A \(\left(\mathrm{cm}^{2} / \mathrm{s}\right)\)

\(d c_{a} / d Y\) : Concentration Gradient \(\left(\mathrm{mol} / \mathrm{cm}^{4}\right)\)

\(c_{a}\) : Concentration of Flowing Acid \(\left(\mathrm{mol} / \mathrm{cm}^{3}\right)\)

\(<c_{a}>\) : Average Concentration of Flowing Acid \(\left(\mathrm{mol} / \mathrm{cm}^{3}\right)\)

\(<c_{a}(w)>\) : Average Concentration of Flowing Acid \(\left(\mathrm{mol} / \mathrm{cm}^{3}\right)\)

\(V_{N}\) : Fluid Velocity Normal to the Surface \((\mathrm{cm} / \mathrm{s})\)

\(\left\langle V_{N}\right\rangle\) : Average Fluid Velocity Normal to the Surface \((\mathrm{cm} / \mathrm{s})\)

\(K_{g}\) : Effective Mass Transfer Coefficient \((\mathrm{cm} / \mathrm{s})\)

Output(s)

\(U_{a, y}\): Diffusion Flux of a Component A in \(\mathrm{Y}\) direction \(\left(\mathrm{mol} / \mathrm{cm}^{2} \mathrm{~s}\right)\)

\(\left\langle U_{a, y}\right\rangle\) : Average Diffusion Flux of a Component A in Y direction \(\left(\mathrm{mol} / \mathrm{cm}^{2} \mathrm{~s}\right)\)

Formula(s)

\[ \begin{gathered} <U_{a, y}>=-D_{A} \frac{d<c_{a}>}{\partial Y}+<c_{a} V_{N}> \\ <U_{a, y}>=-D_{E} \frac{d<c_{a}>}{d Y}+<c_{a}><V_{N}> \\ <U_{a, y}>=K_{g}\left[<c_{a}>-<c_{a}(w)>\right]+<c_{a}><V_{N}> \end{gathered} \]

Reference(s)

Williams, B. B., Gidley, J. L., & Schechter, R. S. (1979). Acidizing fundamentals. Henry L. Doherty Memorial Fund of AIME, Society of Petroleum Engineers of AIME, Page 23.

Related

Convective mass transfer for laminar flow (acidizing)

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