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The generator's flowrate history 

LaTeX Math Inline
bodyq_G(t)
, generator's wellbore pressure history 
LaTeX Math Inline
bodyp_{G,{\rm tr}}(t)
  and receiver's wellbore pressure history 
LaTeX Math Inline
bodyp_{R,{\rm tr}}(t)
  are assumed to be known for the whole period of the test. 

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The pressure trends at generator 

LaTeX Math Inline
bodyp_{G,{\rm tr}}(t)
 and receiver 
LaTeX Math Inline
bodyp_{R,{\rm tr}}(t)
 may have unknown origin but in order for decomposition to work they should have minimum correlation with generating well pressure flowrate variation 
LaTeX Math Inline
body\delta pq_G(t)
. In terms of spectral analysis this means that pressure trend 's spectrum contains minimum overlap with spectrum of pressure flowrate variation 
LaTeX Math Inline
body\delta pq_G(t)
 at generator.

The contamination components of the trends should either have This particularly means that pressure trends at generating and receiving wells may contain:

  • low frequencies (created by monotonous

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  • activities of distant wells), which are lower than frequency range of the generating well flow variation 
    LaTeX Math Inline
    bodyq_G(t)

or

  • high frequencies (created by lift instability at generating/receiving well)

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  • , which are higher than frequency range of the generating well flow variation 
    LaTeX Math Inline
    bodyq_G(t)


If pressure trends contain components correlated with 

LaTeX Math Inline
body\delta pq_G(t)
 (for example receiving well or distant wells have been synchronously varying the rates with generating well) then decomposition is not unique and should not be considered.

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