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LogPressure log-log plot of unit-rate drawdown surveypressure variationdrop 

LaTeX Math Inline
body\Delta delta p(t) = p_{wf}(0) - p_{wf}(t)
 and pressure log-derivative 
LaTeX Math Inline
body\Delta displaystyle p'(t) = t \, \frac{d \Delta p_{wf}}{d \, \ln t}
 (see examples at Fig. 1 – Fig. 2 for example).3).

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

LaTeX Math Inline
bodyp(t)
 which is the same as 
LaTeX Math Inline
body\delta p(t)
:  
LaTeX Math Inline
bodyp(t) = \delta p(t)
 but since it's a consistent practise it usually does not create a confusion among well test engineers. 


The pressure log-derivative 

LaTeX Math Inline
body\Delta p'(t)
 provides a zoomed insight into the pressure diffusion dynamics at different times which helps identifying the pressure diffusion model behind the pressure evolutionvariation.

See PTA Type Library for a wide range of typical PTA Diagnostic Plots.


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

Pressure drop is in blue and log-derivative is in red.

Fig. 2. PTA Diagnostic Plot for vertical well in single-layer homogeneous

reservoir without boundaries. Pressure

reservoir with impermeable circle boundary (PSS).

Pressure drop is in blue and log-derivative is in red.

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

Pressure drop is in blue and log-derivative is in red.



See PTA Type Library for a wide range of typical PTA Diagnostic Plots.


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 effectsUnconstrained reservoir flowReservoir boundary effects


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

Pressure drop is in blue and log-derivative is in red.



See Also

...

Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing / Pressure Testing / Pressure Transient Analysis (PTA) 

[ Well & Reservoir Surveillance ] [ Pressure Diffusion ] [ PTA Type Library ]