Derivative with respect to the natural logarithm of the argument (see Fig. 1):
| (1) | \frac{dp}{d(\ln t)} = t \, \frac{dp}{d t} |
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Fig. 1. 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 |
The calculation algorithm of logarithmic derivative is brought in Logarithmic Derivative @model.
In Well Testing applications the logarithmic derivative is often denoted as 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 p' = \frac{dp}{d t} .
See also
Formal science / Mathematics / Calculus
[ Logarithmic Derivative @model ]
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing / Pressure Testing / Pressure Transient Analysis (PTA) / PTA Diagnostic Plot
[ Well & Reservoir Surveillance ] [ Pressure Diffusion ] [ Pressure log-log plot ]