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Appendix G

# Case for Constant Wellhead Rate (Chapter 8)

Suppose the well flows at a constant wellhead rate qr in the testing period. The wellbore storage of the second layer is negligible. The first layer has wellbore storage coefficient CD. In this case, condition Eq. (F.8) is replaced by

${C}_{D}\frac{d{p}_{wD1}}{d{t}_{D}}-\sum _{j=1}^{2}{w}_{j}{\left({r}_{D}\frac{\partial {p}_{Dj}}{\partial {r}_{D}}\right)}_{{r}_{D}=1}=1$ (G.1)

Its Laplace transform is

${C}_{D}{\sigma }_{D}{\overline{p}}_{wD1}-\sum _{j=1}^{2}{w}_{j}{\left({r}_{D}\frac{d{\overline{p}}_{Dj}}{d{r}_{D}}\right)}_{{r}_{D}=1}=\frac{1}{{\sigma }_{D}}$ (G.2)

or

$\sum _{j=1}^{2}{w}_{j}{\left({r}_{D}\frac{d{\overline{p}}_{Dj}}{d{r}_{D}}\right)}_{{r}_{D}=1}=-\frac{1}{{\sigma }_{D}}\left(1-{C}_{D}{\sigma }_{D}^{2}{\overline{p}}_{wD1}\right)$ ## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

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