\frac{1}{R_t} = \frac{\phi_e^m \, s_w^n }{A R_w} \quad \Rightarrow \quad s_w = \Big (  \frac{A}{\phi_e^m} \; \frac{R_w}{R_t} \Big) ^{1/n}

\frac{1}{R_t} = \frac{\phi_e^m \, s_w^n }{A R_w} \quad \Rightarrow \quad s_w = \Big (  \frac{A}{\phi_e^m} \; \frac{R_w}{R_t} \Big) ^{1/n}

\frac{1}{A} = 1 + \Big( \frac{V_{sh}^{2-V_{sh}}}{\phi_e} \, \frac{R_w}{R_{sh}}  \Big)^{1/2}  

\frac{1}{R_t} =   \frac{\phi_e^m \, s_w^n}{A R_w (1-V_{sh})}    + \frac{V_{sh}}{R_{sh}} s_w^{n/2}
 
 \quad \Rightarrow \quad s_w^{n/2} = \frac{A R_w (1-V_{sh})}{2 \phi_e^m} \, \Big( \sqrt{ \Big( \frac{V_{sh}}{R_{sh}} \Big)^2 + \frac{4\phi_e^m}{a R_t R_w (1-V_{sh}) } }   - \frac{V_{sh}}{R_{sh}} \Big)

\phi_t = \phi_e  + \phi_t s_{wb} 

s_w = \frac{s_{wt} - s_{wb}}{ 1 - s_{wb}}

V = V_m + V_t = (1-\phi_t) V + \phi_t V

\phi_t = \frac{V_t}{V}

V_t = \phi_t V = V_e + V_{wb} = \phi_e V + s_{wb} V_t

V_e = V_t  (1 - s_{wb})

\phi_e = \phi_t  (1 - s_{wb})

V_{wt} = V_{wb} + V_{wf}

s_{wt} V_t = s_{wb} V_t + s_w V_e = s_{wb} V_t + s_w V_t  (1 - s_{wb})

s_{wt} = s_{wb} + s_w (1 - s_{wb})

s_w = \frac{s_{wt} - s_{wb}}{ 1 - s_{wb}}

\frac{1}{R_t} = \phi_t^m s_{wt}^n \, \Big[ \frac{1}{R_w} + \frac{s_{wb}}{s_{wt}} \Big( \frac{1}{R_{wb}} - \frac{1}{R_w} \Big)  \Big] \quad \Rightarrow \quad s_w = \frac{s_{wt} - s_{wb}}{ 1 - s_{wb}}

s_{wb} = \zeta_{wb} V_{sh}

\frac{1}{R_t} = \phi_t^m s_{wt}^n \, \Big[ \frac{1}{R_w} +\frac{B Q_V}{s_{wt}}  
 \Big]

B Q_V = s_{wb} \Big( \frac{1}{R_{wb}} - \frac{1}{R_w} \Big)

Коррекция на промывку бурового раствора

\xi_{mud} = \frac{V_{mud}}{V_{drain}}

\xi_{mud} = \frac{1}{1 + \exp(k_{mud}/k-k/k_{mud})}

s_{mud} = \frac{V_{mud}}{V_{pore}} =(1-s_{wi}-s_{or}) \, \xi_{mud}

\frac{1}{R_{fl}} = \frac{s_{mud}}{R_{mud}} +  \frac{1 - \xi_{mud} (1-s_{wi})}{R_w}