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Partially Saturated Shaly Sand Resistivity Vsh Model Formula

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}

Partially Saturated Shaly Sand Resistivity Vsh Model calculates partially saturated shaly-sand resistivity for resistivity logs workflows in petrophysics.

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How engineers use this formula

Use this formula when the listed inputs (S_w, R_w, V_sh, R_sh, F) are known and the assumptions behind the cited resistivity logs relationship match the engineering case being checked.

Assumptions

  • Input values are representative for the well, reservoir, fluid, or equipment case being evaluated.
  • The declared units match the field-unit constants used in the formula.
  • The cited formula applies to the selected petroleum engineering workflow.

Limitations

  • The calculation does not replace a full engineering model or operating procedure.
  • Accuracy depends on the source correlation, assumptions, input quality, and unit consistency.

Common mistakes

  • Mixing unit systems without converting the inputs.
  • Using default example values as field recommendations.
  • Applying the formula outside the source assumptions.

Default example

Using the default inputs, R_t equals 2.657807 ohm m.

S_wfraction

0.7

R_wohm m

0.08

V_shfraction

0.25

R_shohm m

2.5

Fdimensionless

20

Inputs

S_w

fraction

Water Saturation

R_w

ohm m

Formation Water Resistivity

V_sh

fraction

Bulk Volume Fraction of Shale

R_sh

ohm m

Shale Resistivity

F

dimensionless

Formation Resistivity Factor

Outputs

R_t

ohm m

Partially Saturated Shaly-Sand Resistivity

inv_R_t

1/(ohm m)

Partially Saturated Shaly-Sand Conductivity

Source and review

reviewed

Bassiouni, Z. 1994. Theory, Measurement, and Interpretation of Well Logs. SPE Textbook Series Vol. 4, Chapter 1, Page 16.

Source

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