SP BASICS
During the early days of resistivity logging, it was observed that natural potentials existed in boreholes. These are known as spontaneous potentials, or SP. A recording of the changes in SP versus depth gives the SP log. The measurement is very simple: the potential difference between an electrode M on the probe and a reference electrode N placed at the surface is measured with a voltmeter. The voltage is quite small, ranging from +50 to about –200 millivolts.

This is a passive measurement. That is, no energy is provided by the logging tool. There is no SP until the borehole is drilled and filled with conductive muds. This contrasts with telluric currents caused by solar radiation and Northern Lights, and man-made currents from power lines, cathodic protection of pipelines, and welding equipment grounded to the rig while logging proceeds. All these currents can persist without a borehole, but more importantly, can cause anomalies on the SP log, and in some cases rendering it useless.

References:
 1. The SP Log: Theoretical Analysis and Principles of Interpretation,
      H.G. Doll, AIME, 1948.

 2. SP Log in Shaly Sands,
     H.G. Doll, JPT, 1950.

 3.  Natural Potentials in Well Logging
      W.D. Mounce, W. M. Rust, Jr.,  AIME, 1948

SP THEORY
The SP is the result of several electromotive forces: shale membrane potential Em, liquid-junction potential Ej, and electro-kinetic potential Ek. The measured SP is the sum of these three voltages.

Shales are permeable to sodium ions (Na+) but impervious to chloride ions (Cl-). When a shale separates two sodium chloride solutions of different concentration (the mud in the borehole and the water in the formation), sodium ions migrate by diffusion from the higher concentration into the lower concentration. This movement of positive charges builds up a voltage known as shale potential or membrane potential Em.

When two sodium chloride solutions of different concentration are separated by a semi-permeable partition that permits the passage of ions from one side to the other, but prevents bulk mixing of the two solutions, ions migrate by diffusion from the concentrated solution to the dilute solution. This happens at the boundary between the invaded and un-invaded zones. The negative chloride ions have a greater mobility than the positive sodium ions. There is a net transfer of negative electric charges from the more concentrated solution to the less concentrated. The resulting electromotive force is known as the liquid-junction potential Ej.

The passage of an electrolyte through a porous medium also produces an electromotive force, called electro-kinetic potential, Ek, between any two points along the electrolyte flow path. For example, an electro-kinetic potential is developed when mud filtrate passes through a mud cake into the formation. The value of this potential is small and is commonly disregarded in electrical logging.

The current loops shown below circulate between shale, borehole, invaded zone, and un-invaded zone and back to the shale. They represent the sum of membrane and liquid junction potentials, which is known as the electrochemical component of the SP. The curve to the left is the corresponding SP curve as measured by a real tool. The square static SP is the theoretical shape of a perfect SP curve.

Current path is between mud in borehole, formation water and nearest shale. Static SP is
theoretical value; smooth curve shows actual values recorded. High resistivity in any part of
the circuit reduces the SP. Low contrast in the salinity between mud and formation
reduce the SP value.

The numerical values of the electromotive forces depend on the type and quantity of dissolved salts. The electrochemical component of the SP is defined mathematically by:

         1:  Ec = Em + Ej = –K * log(Aw / Amf)

Aw and Amf are the chemical activities of the formation water and mud filtrate, respectively. K is a factor that depends on the temperature. For clean sands and sodium chloride solutions, K ranges from 67 millivolts at 50 F to 123 millivolts at 300 F.

In situations with pure sodium chloride (NaCL) solutions, the SP equation becomes:
           2:  SP = –K * log(Rmf / Rw)

Rw and Rmf are the water and mud filtrate resistivity at formation temperature respectively.

K is reduced when the permeable beds contain dispersed clay, so the SP is sometimes used as  shale indicator.

SP Circuit Diagram. The M electrode is the same electrode as the M on the normal
measurement. N is a separate grounding electrode thrown into the mud pit or clamped
to the casing in dry or frozen territory.