Appendix G

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

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

(G.1)

Its Laplace transform is

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

(G.2)

or

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

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