Relationship between SSP and Rw for water containing salts (non-NaCl predominant)

Input(s)

$a_{N a}$ : Activity of $\mathrm{Na}$ Ions in Water (dimensionless)

$\mathrm{K}$ : Equilibrium Constant $(\mathrm{mV})$

$a_{C a}$ : Activity of $\mathrm{Ca}$ Ions in Water (dimensionless)

$a_{M g}$ : Activity of $\mathrm{Mg}$ Ions in Water (dimensionless)

$a_{\text {Nam }}$ : Activity of $\mathrm{Na}$ Ions in Mud Filtrate (dimensionless)

$a_{\text {Cam }}$ : Activity of $\mathrm{Ca}$ Ions in Mud Filtrate (dimensionless)

$a_{M g m}$ : Activity of $\mathrm{Mg}$ Ions in Mud Filtrate (dimensionless)

$E_{s p p}$ : Static Self Potential (V)

E_{s s p}=-K * \log \left(\frac{\left(a_{N a}+\left(a_{C a}+a_{M g}\right)^{0.5}\right)}{\left(a_{N a m}+\left(a_{C a m}+a_{M g m}\right)^{0.5}\right)}\right)

Bassiouni, Z., 1994, Theory, Measurement, and Interpretation of Well Logs. SPE Textbook Series Vol. 4. Chapter 6, Page: 135.