Synonym: Logarithmic Derivative = Log Derivative

Derivative with respect to the time logarithmthe natural logarithm of the argument (see Fig. 1):

LaTeX Math Block

anchor	LogDer
alignment	left

p' = \frac{dp}{d(\ln t)} = t  \, \frac{dp}{d t}

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Fig. 1.

A sample of typical DTR (pressure P in blue and log-derivative P' in red) presented in log-log coordinates for PTA type-library analysis

Example of log-derivative P' (in red) along with pressure drop P (in blue) for a typical DTR presented on PTA type-library log-log plot

Tip

In Well Testing applications the logarithmic derivative is often denoted as

LaTeX Math Inline

body	p' = t \, \frac{dp}{d t}

which is misnomer as the usual mathematical convention for prime " ' " is the regular Derivative with respect to the argument

LaTeX Math Inline

body	p' = \frac{dp}{d t}

.

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