TEM-function

Key takeaways

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

Reference excerpt

In petroleum engineering, true effective mobility (TEM), also called TEM-function is a criterion to characterize dynamic two-phase flow characteristics of rocks (or dynamic rock quality). TEM is a function of relative permeability, porosity, absolute permeability and fluid viscosity, and can be determined for each fluid phase separately. TEM-function has been derived from Darcy's law for multiphase flow.

T E M = k k r ϕ μ {\displaystyle {\mathit {TEM}}={\frac {kk_{\mathit {r}}}{\phi \mu }}}

in which k {\displaystyle k} is the absolute permeability, k r {\displaystyle k_{\mathit {r}}} is the relative permeability, φ is the porosity, and μ is the fluid viscosity. Rocks with better fluid dynamics (i.e., experiencing a lower pressure drop in conducting a fluid phase) have higher TEM versus saturation curves. Rocks with lower TEM versus saturation curves resemble low quality systems. TEM-function in analyzing relative permeability data is analogous with Leverett J-function in analyzing capillary pressure data. Furthermore, TEM-function in two-phase flow systems is an extension of RQI (rock quality index) for single-phase systems. Also, TEM-function can be used for averaging relative permeability curves (for each fluid phase separately, i.e., water, oil, gas, CO2).

Average kr = ∑ i = 1 n T E M i ∑ i = 1 n ( k ϕ μ ) i = ∑ i = 1 n ( k k r ϕ μ ) i ∑ i = 1 n ( k ϕ μ ) i {\displaystyle {\text{Average kr}}={\frac {\sum _{i=1}^{n}{\mathit {TEM}}_{i}}{\sum _{i=1}^{n}\left({\frac {k}{\phi \mu }}\right)_{i}}}={\frac {\sum _{i=1}^{n}\left({\frac {kk_{\mathit {r}}}{\phi \mu }}\right)_{i}}{\sum _{i=1}^{n}\left({\frac {k}{\phi \mu }}\right)_{i}}}}

See also Lak wettability index USBM wettability index

References

Worked examples

Example 1 — a first encounter with TEM-function

Start with the simplest possible case. Write down what TEM-function claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, 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 TEM-function 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 TEM-function 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 TEM-function

In research: TEM-function appears in mathematics 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 TEM-function 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: TEM-function is common in secondary-school and first-year university syllabi. It links to neighbouring topics Fluid dynamics stubs, Petroleum engineering, so understanding it makes those chapters shorter.
In everyday life: Look for TEM-function 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.

How to study TEM-function in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what TEM-function 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 TEM-function out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is TEM-function in simple terms?

In petroleum engineering, true effective mobility (TEM), also called TEM-function is a criterion to characterize dynamic two-phase flow characteristics of rocks (or dynamic rock quality). TEM is a function of relative permeability, porosity, absolute permeability and fluid viscosity, and can be det…

Why does TEM-function matter?

Because it connects several mathematics 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 TEM-function?

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 TEM-function.