Variables

Expression

Variables

Expression

Dimensionless internal formation pressure

${\psi }_{\text{1D}}=\frac{\text{π}{k}_{01}h{T}_{\text{sc}}}{q_{\text{sc}}{p}_{\text{sc}}T}\left({\psi }_{\text{i}}-{\psi }_1\right)$

Dimensionless outer zone formation pressure

${\psi }_{2\text{D}}=\frac{\text{π}{k}_{01}h{T}_{\text{sc}}}{q_{\text{sc}}{p}_{\text{sc}}T}\left({\psi }_{\text{i}}-{\psi }_2\right)$

Dimensionless bottom pressure

${\psi }_{\text{wD}}=\frac{\text{π}{k}_{01}h{T}_{\text{sc}}}{q_{\text{sc}}{p}_{\text{sc}}T}\left({\psi }_{\text{i}}-{\psi }_{\text{w}}\right)$

Dimensionless time

$t_{\text{D}}=\frac{k_{01}}{{\varphi }_1{\mu }_1{C}_{\text{t}1}{r}_{\text{w}}^{\text{2}}}t$

Dimensionless radius

$r_{\text{D}}=\frac{r}{r_{\text{we}}}=r_{\text{w}}{\text{e}}^{-S},r_{\text{1D}}=\frac{r_1}{r_{\text{we}}}$

Mobility ratio

$M=\frac{k_{01}/{\mu }_1}{k_{02}/{\mu }_2}$

Storage capacity ratio

$\omega =\frac{{\varphi }_1{C}_{\text{t}1}}{{\varphi }_2{C}_{\text{t2}}}$

Dimensionless stress sensitivity coefficient

${\gamma }_{\text{D}}^{*}=\gamma \frac{{\mu }_{\text{i}}{Z}_{\text{i}}}{2p_{\text{i}}}\frac{q_{\text{sc}}{p}_{\text{sc}}T}{\text{π}{k}_{0}h{T}_{\text{sc}}}$

Dimensionless wellbore survival factor

$C_{\text{D}}=\frac{C}{2\text{π}h{\varphi }_0{C}_{\text{t}}{r}_{\text{w}}^2}$