physics

Spontaneous potential

Spontaneous potential is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Spontaneous potential rather than just read about it. In short: Spontaneous potentials are often measured down boreholes for formation evaluation in the oil and gas industry, and they can also be measured along the Earth's surface for mineral exploration or groundwater investigation. The phenomenon and its application to geology was first recognized by Conrad Schlumberger, Marcel Schlumberger, and E.G.

Key takeaways

Spontaneous potential belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Spontaneous potential to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Spontaneous potential from memory before moving on to harder problems.

Reference excerpt

Spontaneous potentials are often measured down boreholes for formation evaluation in the oil and gas industry, and they can also be measured along the Earth's surface for mineral exploration or groundwater investigation. The phenomenon and its application to geology was first recognized by Conrad Schlumberger, Marcel Schlumberger, and E.G. Leonardon in 1931, and the first published examples were from Romanian oil fields.

Physics Spontaneous potentials (SP) are usually caused by charge separation in clay or other minerals, due to presence of semi-permeable interface impeding the diffusion of ions through the pore space of rocks, or by natural flow of a conducting fluid through the rocks. The origin of SP across formation can be attributed to two processes involving the movement of ions:

Streaming potential (Ek) Electrochemical potential (Ec) Streaming potential originates from the flow of an electrolyte (water) over naturally charged solids (i.e., surfaces that acquired electrokinetic or zeta potential). The streaming potential appears when mud filtrate is forced into the formation under the differential pressure between mud column and formation. The streaming potential is produced when the flow takes place across mud-cake in front of permeable formations, across permeable formations being invaded, and across shale beds. It is generally accepted that the streaming potential across the mud-cake is compensated by that across the shale. As such, in most cases, the spontaneous potential measured is only related to the electrochemical potential. Electrochemical potential (EC) is the sum of liquid junction or diffusion potential (EJ), and membrane potential (EM)

Liquid junction potential is established at the direct contact of the mud filtrate and formation water at the edge of the invaded formation. Ions Na+ and Cl− diffuse from either solution to the other, but at different rate due to different mobilities. Na+ tends to be less mobile due to its affinity for water molecules.

EJ = K1 log10(aw/amf) where:

K1 = 11.6 mV at 25 °C aw = formation water ionic activity amf = mud filtrate ionic activity Membrane Potential develops when two electrolytes of different ionic concentrations, such as mud and formation water, are separated by shale. The clay minerals in shale are usually made up of atom Al, Si, and O. O2− ions occupy the outer layer and cause a net negative charge. Na+ ions from solution are attracted and allowed to pass through the shale, while Cl− ions are repelled. Na+ ions will migrate between the two solutions, with a net influx from the more saline to the less.

EM = K2 log10(aw/amf) where:

K2 = 2.3 RT/F, where: R = ideal gas constant T = absolute temperature in kelvins F = Faraday constant aw = formation water ionic activity amf = mud filtrate ionic activity The total electrochemical potential is thus summarized as EC = EM + EJ = K log10(aw/amf) Since spontaneous potential is a measure of electrochemical potential and the ionic activity of a solution is inversely proportional to its resistivity, the above equation can be simplified as SP = EC = K log10 (Rmfe/Rwe), where Rmfe and Rwe are equivalent mud filtrate resistivity and equivalent formation water resistivity respectively. The ideal spontaneous potential across clean bed is known as Static SP (SSP), and defined as follow:

SSP = −K log10 (Rmfe/Rwe)

Applications in Boreholes The most useful SP component is the electrochemical potential, since it can cause a significant deflection opposite permeable beds. The magnitude of the deflection depends mainly on the salinity contrast between borehole and formation fluid, and the clay content of the permeable bed. The SP log is therefore useful in detecting permeable beds and to estimate formation water salinity and formation clay content. Due to the nature of the electric current, SP can only be recorded in conductive mud.

Determination of Rw As established earlier, static SP is defined as follow:

SSP = −K log (Rmfe/Rwe) Static SP (SSP) can be obtained directly from the SP curve if the bed is clean, thick, porous, permeable, and only moderately invaded. When these conditions are not met, the recorded SP will need to be corrected. Various correction charts are available for this purpose. To convert the measured mud filtrate resistivity Rmf into an equivalent mud filtrate resistivity Rmfe, the following rules are employed:

If Rmf at 75 °F is greater than 0.1 Ω·m, use Rmfe = 0.85 Rmf at formation temperature. If Rmf at 75 °F is less than 0.1 Ω·m, derive Rmfe from Rmf using Schlumberger Chart SP-2 or equivalent. Schlumberger Chart SP-2 can then be used to convert Rwe to obtain Rw.

Applications on the surface Electrodes can be placed on the ground surface to map relative changes in the SP value (in millivolts, or mV), typically with the goal of identifying the path of groundwater flow in the subsurface, or seepage from an earthen dam. A voltmeter measures the voltage between a fixed liquid-junction electrode and a mobile one (rover), which is moved along a dam face or over an area of investigation to collect multiple readings. Anomalies observed may indicate groundwater movement or seepage.

Interpretation SP can be affected by several factors that complicates the interpretation. Beside petrochemical component, SP is also affected by electrokinetic potential and bimetallism. Besides, SP is also affected by the following factors:

Bed thickness (h); Since SP is a measurement of electrical potential produced by current in the mud, its amplitude approaches the SSP value only when the resistance to current due to formation and adjacent beds is negligible compared with that of the mud. This condition is met only in thick bed. In thin beds, the SP is proportionally reduced. True resistivity (Rt) of permeable bed; As Rt/Rm increases, the SP deflection decreases, and the bed boundaries are less sharply defined. Presence of hydrocarbons also attenuates SP. Resistivity of invaded zone (Rxo) and mud resistivity (Rm); SP increases with increase of Rxo/Rm Diameter of invasion (di); SP decreases as invasion deepens Ratio of mud filtrate to formation water salinities: Rmf/Rw Neighbouring shale resistivity (Rs); SP increases with increase of Rs/Rm Hole diameter (dh); With increasing hole size, the value of SP is reduced

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Spontaneous potential

Start with the simplest possible case. Write down what Spontaneous potential claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Spontaneous potential before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Spontaneous potential ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Spontaneous potential

In research: Spontaneous potential appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Spontaneous potential in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Spontaneous potential is common in secondary-school and first-year university syllabi. It links to neighbouring topics Electrostatics, Geophysics, so understanding it makes those chapters shorter.
In everyday life: Look for Spontaneous potential outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Spontaneous potential in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Spontaneous potential means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Spontaneous potential out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Spontaneous potential in simple terms?

Why does Spontaneous potential matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Spontaneous potential?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Spontaneous potential.