LaTeX Math Inline

body	\delta p(t) = p_{wf}(0) - p_{wf}(t)

and pressure log-derivative

LaTeX Math Inline

body	\displaystyle p'(t) = t \, \frac{d p_{wf}}{d t}

(see examples at Fig. 1 – Fig. 3).

Traditionally the pressure drop on pressure log-log plots is denoted by

LaTeX Math Inline

body	p(t)

which is the same as

LaTeX Math Inline

body	\delta p(t)

:

LaTeX Math Inline

body	p(t) = \delta p(t)

but since it's a consistent practise it usually does not create a confusion among well test engineers.

LaTeX Math Inline

body	p'(t)

provides a zoomed insight into the pressure diffusion dynamics at different times which helps identifying the pressure diffusion model behind the pressure variation.

...

Fig. 1. PTA Diagnostic Plot for vertical well in single-layer homogeneous reservoir without boundaries (IARF).

Fig. 2. PTA Diagnostic Plot for vertical well in single-layer homogeneous reservoir with impermeable circle boundary (PSS).

Fig. 3. PTA Diagnostic Plot for vertical well in single-layer homogeneous reservoir with constant pressure boundary (SS).

The usual convention is to split pressure transient response in three major time intervals (see also Fig. 4):

Early Time Response (ETR)	Middle Time Response (MTR)	Late Time Response (LTR)
Wellbore storage and well-reservoir contact effects	Unconstrained reservoir flow	Reservoir boundary effects

Image Added

Fig. 4. PTA Diagnostic Plot with ETR, MTR and LTR time zones.

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