Question 3 of 12: Sources of Spontaneous Potential
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
National Exams, 98-Pet-B1, Well Logging and Formation Evaluation — May 2014, 3 hours, closed book (calculators permitted), 12 questions, all marked, 100 marks total.
Reference texts: Bassiouni, Theory, Measurement, and Interpretation of Well Logs (SPE Textbook Series Vol. 4); Asquith & Krygowski, Basic Well Log Analysis, 2nd ed. (AAPG); Ellis & Singer, Well Logging for Earth Scientists, 2nd ed.; Schlumberger, Log Interpretation Charts / Log Interpretation Principles and Applications.
Question 3: Sources of Spontaneous Potential (4 marks)
The static SP is the algebraic sum of four component EMFs, generated wherever fluids of differing salinity are in contact across a semi-permeable or free interface:
Membrane (electrochemical) potential, Em. Generated across the adjacent SHALE bed, which behaves as an ion-selective (cation-permeable) membrane between the mud filtrate and the undisturbed formation water — the dominant component, and the one the ESSP equation of Question 12 models directly.
Liquid-junction (diffusion) potential, Ej. Generated at the boundary between mud filtrate and formation water WITHIN the permeable bed itself (at the front of the invaded zone), where the two electrolytes mix freely with no membrane — roughly one-fifth the magnitude of Em and of opposite mechanism (free ionic mobility, not selective exclusion).
Electrokinetic (streaming) potential across the mudcake, Ekmc. Produced by mud filtrate flowing under the differential (mud-column minus formation) pressure through the mudcake lining a permeable bed.
Electrokinetic (streaming) potential across the shale, Eksh. Produced the same way, but by filtrate flowing through the low-permeability shale itself; normally negligible except in underbalanced or very low-permeability shale sections.
