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Resistivity Logs Equations

Browse 39 resistivity logs petroleum engineering equations with formulas, inputs, outputs, units, and sources.

Resistivity-log calculations support water saturation, formation factor, resistivity index, flushed-zone diagnostics, and clean-formation petrophysics checks.

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PetrophysicsResistivity Logs

Archie Flushed-Zone Water Saturation from Shallow Resistivity

Sxo=(aRmfϕmRxo)1/nS_{xo}=\left(\frac{aR_{mf}}{\phi^mR_{xo}}\right)^{1/n}
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PetrophysicsResistivity Logs

Archie Water Saturation from Resistivity Logs

Sw=[(aϕm)(RwRt)]1/nS_w = \left[\left(\frac{a}{\phi^m}\right)\left(\frac{R_w}{R_t}\right)\right]^{1/n}
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PetrophysicsResistivity Logs

Arps Formation Water Resistivity Temperature Correction

Rw2=Rw1T1F+6.77T2F+6.77R_{w2}=R_{w1}\frac{T_{1F}+6.77}{T_{2F}+6.77}
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Bulk Volume Water from Porosity and Water Saturation

BVW=ϕSwBVW=\phi S_w
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PetrophysicsResistivity Logs

Carothers Formation Factor - Calcareous Sands

F=1.45ϕ1.70F=\frac{1.45}{\phi^{1.70}}
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Carothers Formation Factor - Shaly Sands

F=1.65ϕ1.33F=\frac{1.65}{\phi^{1.33}}
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Chalky Carbonate Formation Factor from Porosity

Fc=1ϕ2F_c=\frac{1}{\phi^2}
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Chevron Formation Factor from Porosity

F=1.13ϕ1.73F=\frac{1.13}{\phi^{1.73}}
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Compacted Carbonate Formation Factor from Porosity

FcO=1ϕaF_{cO}=\frac{1}{\phi^a}
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Equivalent Formation Water Resistivity from SP

Rwe=Rmfe10−SSP/K,K=61+0.133TFR_{we}=\frac{R_{mfe}}{10^{-SSP/K}},\quad K=61+0.133T_F
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PetrophysicsResistivity Logs

Fertl-Hammack Shaly Sand Water Saturation

Sw=(FRwRt)0.5−VshRw0.4ϕeRshS_w=\left(\frac{FR_w}{R_t}\right)^{0.5}-\frac{V_{sh}R_w}{0.4\phi_eR_{sh}}
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PetrophysicsResistivity Logs

Flushed-Zone Apparent Formation Factor from Apparent Saturation

Fxo=FsSxo2F_{xo}=\frac{F_s}{S_{xo}^2}
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Flushed-Zone Water Saturation from Formation Factor

Sxo=(FRmfRxo)1/nS_{xo}=\left(\frac{FR_{mf}}{R_{xo}}\right)^{1/n}
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Formation Factor - Archie's Equation

F=TϕF = \frac{T}{\phi}
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Formation Resistivity and Permeability - Carothers Limestones

k=4×108F3.65k=\frac{4\times10^8}{F^{3.65}}
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Formation Resistivity and Permeability - Carothers Sandstones

k=7×108F4.5k=\frac{7\times10^8}{F^{4.5}}
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Hingle Crossplot True Resistivity

Rt=[ϕ(SwnaRw)1/m]−mR_t=\left[\phi\left(\frac{S_w^n}{aR_w}\right)^{1/m}\right]^{-m}
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Humble Formation Factor from Porosity

F=0.62ϕ2.15F=\frac{0.62}{\phi^{2.15}}
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Indonesian Water Saturation from Shaly Sand Logs

Sw=[1/RtVsh1−0.5VshRsh+ϕemaRw]2/nS_w=\left[\frac{\sqrt{1/R_t}}{\frac{V_{sh}^{1-0.5V_{sh}}}{\sqrt{R_{sh}}}+\sqrt{\frac{\phi_e^m}{aR_w}}}\right]^{2/n}
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Movable Hydrocarbon Saturation from Flushed Zone

Shm=Sxo−SwS_{hm}=S_{xo}-S_w
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Mud Cake Resistivity from Mud and Filtrate Resistivity

Rmc=0.69Rmf(RmRmf)2.65R_{mc}=0.69R_{mf}\left(\frac{R_m}{R_{mf}}\right)^{2.65}
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Mud Filtrate Resistivity from Mud Resistivity

Rmf=KmRm1.07R_{mf}=K_mR_m^{1.07}
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Oil Saturation from IE and CDN Resistivity Logs

So=1−RoRtS_o=1-\sqrt{\frac{R_o}{R_t}}
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Partially Saturated Shaly Sand Resistivity Vsh Model

Rt=1(Vsh/Rsh)Sw+(1/F)Sw2/RwR_t=\frac{1}{(V_{sh}/R_{sh})S_w+(1/F)S_w^2/R_w}
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Phillips Formation Factor - Average Sands

F=1.45ϕ1.54F=\frac{1.45}{\phi^{1.54}}
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Pickett Crossplot Log True Resistivity

log⁡10Rt=−mlog⁡10(ϕ)+log⁡10(Rw)−nlog⁡10(Sw)\log_{10}R_t=-m\log_{10}(\phi)+\log_{10}(R_w)-n\log_{10}(S_w)
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Porter-Carothers Formation Factor - California Pliocene Logs

Fg=2.45ϕ1.08F_g=\frac{2.45}{\phi^{1.08}}
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Porter-Carothers Formation Factor - Gulf Coast Miocene Logs

Fc=1.97ϕ1.29F_c=\frac{1.97}{\phi^{1.29}}
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Residual Hydrocarbon Saturation from Flushed Zone

Shr=1−SxoS_{hr}=1-S_{xo}
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Resistivity Index - Archie's Law

RI=RtRoRI=\frac{R_t}{R_o}
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Sethi Formation Factor - Clean Granular Formations

F=1ϕ2.05−ϕF=\frac{1}{\phi^{2.05-\phi}}
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Shell Formation Factor - Low-Porosity Carbonates

Fl=1ϕ1.87+0.019/ϕF_l=\frac{1}{\phi^{1.87+0.019/\phi}}
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Simandoux Total Shale Equation

Sw=0.4Rwϕe2[−VshRsh+(VshRsh)2+5ϕe2RwRt]S_w=\frac{0.4R_w}{\phi_e^2}\left[-\frac{V_{sh}}{R_{sh}}+\sqrt{\left(\frac{V_{sh}}{R_{sh}}\right)^2+\frac{5\phi_e^2}{R_wR_t}}\right]
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Simandoux Water Saturation from Shaly Sand Logs

Sw=−VshRsh+(VshRsh)2+4FRw(1−Vsh)Rt2FRw(1−Vsh)S_w=\frac{-\frac{V_{sh}}{R_{sh}}+\sqrt{\left(\frac{V_{sh}}{R_{sh}}\right)^2+\frac{4}{F R_w (1-V_{sh}) R_t}}}{\frac{2}{F R_w (1-V_{sh})}}
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Tortuosity from Resistivity Log Path Lengths

T=La2L2T=\frac{L_a^2}{L^2}
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Water Salinity Index Ratio

Sw=CaCS_w=\frac{C_a}{C}
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Water Saturation from IE and CDN Resistivity Logs

Sw=RoRtS_w=\sqrt{\frac{R_o}{R_t}}
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Water Saturation from Neutron Capture Cross Section

Sw=(Σlog−Σma)−ϕ(Σh−Σma)ϕ(Σw−Σh)S_w=\frac{(\Sigma_{log}-\Sigma_{ma})-\phi(\Sigma_h-\Sigma_{ma})}{\phi(\Sigma_w-\Sigma_h)}
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Water-Saturated Shaly Sand Resistivity Vsh Model

Ro=1Vsh/Rsh+1/(FRw)R_o=\frac{1}{V_{sh}/R_{sh}+1/(FR_w)}
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