Shut-in formation pressure estimate based on a wellbore sandface pressure after a given well is shut-in for

p_e = p_{wf}(t_e) \bigg|_{q = 0}

Well intervention

This definition is based on the practical observation of wellbore pressure in shut-in wells for well intervention purposes.

It is the simplest and the most popular definition of formation pressure and is widely used in all upstream industry applications.

The definition of shut-in time

Some conventions are to pick

Drain-boundary formation pressure estimate along the boundary of drainage area

p_e = \frac{1}{L_e} \int_0^{L_e} p(x,y,z) dl

where

Pressure Testing

This definition is based on the idea that there is a boundary line

The advantage of this method over

• it provides more accurate estimate of the pressure away from a given well
• it is not dependent on a single value 

  LaTeX Math Inline
  body t_e

  , and accounts for varying 

  LaTeX Math Inline
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   depending of drainage area

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  body A_e(t)

  of a given well at a given moment of time

Drain-area formation pressure estimate within the drainage area

p_r = \frac{1}{A_e} \iint_{A_e} p(x,y,z) dS

Well Flow Performance Analysis

This definition is based on the productivity index estimate and assumption that it stays constant

Historically this definition is using a specific symbol

9-cell formation pressure estimate from reservoir flow simulation model

p_{e9, \ i,j} = \frac{1}{9} \sum_{k=i-1}^{i+1} \sum_{l=j-1}^{j+1} p_{k,l}

Dynamic Modelling

It defines formation pressure as an arithmetic average of reservoir pressure values in all cells of reservoir flow simulation model adjacent to the cells containing a well-reservoir contact. 

In a particular case of vertical well the adjacent cells will be 9 cells around a cell with vertical well which raised the term 9-cell formation pressure. 

It provides a very rough and often inaccurate estimate of formation pressure and often used in history matching.

It should be used with caution when planning new wells, workovers, well performance analysis and testing existing dynamic model against other estimates.

A more accurate model estimate of formation pressure can be retrieved from a proper well shut-in in reservoir flow simulation model.