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BUS – Build-up Survey

SPT – Self-Pulse Testing

Conventional single-well testing is based on long-term monitoring of downhole pressure response to the step change in flow rate (usually shut-in or close-in).


The primary hard data deliverables are:
 

  • formation pressure 
    LaTeX Math Inline
    bodyP_i


  • skin-factor S
     
  • average transmissibility in drainage area 
    LaTeX Math Inline
    body\sigma


  • time to reach the reservoir boundary 
    LaTeX Math Inline
    bodyt_e


The conditional deliverables from build-up survey would be:

DeliverablesDescriptionNon-BUS Input ParametersKey Uncertainties


LaTeX Math Block
anchor1
alignmentleft
V_o =  \frac{4 \, \sigma \, t_e \, (1-s_{wi})}{c_t}

where  

LaTeX Math Inline
bodyc_t
 is total compressibility:

LaTeX Math Block
anchor1
alignmentleft
c_t = c_r + (1-s_{wi}) \, c_o + s_{wi} \, c_w

and

LaTeX Math Inline
body\{ c_r, \, c_o \, c_w \}
are rock, oil and water compressibility.



Drainable oil reserves


The rock compressibility

LaTeX Math Inline
bodyc_r(\phi)
is defined from core lab study or empirical porosity correlations

Fluid compressibility

LaTeX Math Inline
body\{ c_o , \, c_w \}
from PVT

Initial water saturation

LaTeX Math Inline
bodys_{wi}
from SCAL


Rock compressibility

LaTeX Math Inline
bodyc_r(\phi)


Initial water saturation

LaTeX Math Inline
bodys_{wi}


LaTeX Math Block
anchor1
alignmentleft
A_e = 4 \, \chi \, t_e

where 

LaTeX Math Inline
body\chi
 is pressure diffusivity:

LaTeX Math Block
anchorchi
alignmentleft
\chi = \Big< \frac{k}{\mu} \Big> \, \frac{1}{\phi \, c_t}

where

LaTeX Math Inline
body\phi
is reservoir porosity,
LaTeX Math Inline
body\big< \frac{k}{\mu} \big>
is fluid mobility:

LaTeX Math Block
anchor0K3BA
alignmentleft
\Big< \frac{k}{\mu} \Big> = k_a \, \bigg[ \frac{k_{rw}}{\mu_w} + \frac{k_{ro}}{\mu_o} \bigg]

LaTeX Math Inline
bodyk_a
is absolute permeability to air,

LaTeX Math Inline
bodyk_{rw}, \, k_{ro}
are relative permeabilities to water and oil,

LaTeX Math Inline
body\mu_w, \mu_o
are water and oil viscosities


Drainage area


Formation porosity

LaTeX Math Inline
body\phi


Absolute permeability to air

LaTeX Math Inline
bodyk_a
from core study


Relative permeabilities

LaTeX Math Inline
body\{ k_{rw}, \, k_{ro} \}
from SCAL

Fluid viscosities

LaTeX Math Inline
body\{ \mu_w, \mu_o \}
from PVT


Absolute permeability to air

LaTeX Math Inline
bodyk_a


Relative permeabilities
LaTeX Math Inline
body\{ k_{rw}, \, k_{ro} \}


LaTeX Math Block
anchorh_PTA
alignmentleft
h = \sigma \, \bigg< \frac{k}{\mu} \bigg>^{-1}



Effective reservoir thickness


Absolute permeability to air

LaTeX Math Inline
bodyk_a
from core study


Relative permeabilities

LaTeX Math Inline
body\{ k_{rw}, \, k_{ro} \}
from SCAL

Fluid viscosities

LaTeX Math Inline
body\{ \mu_w, \mu_o \}
from PVT


Absolute permeability to air

LaTeX Math Inline
bodyk_a


Relative permeabilities

LaTeX Math Inline
body\{ k_{rw}, \, k_{ro} \}


As one can see, the drainage area and the reservoir thickness are conditioned by core data which may not be representative of the whole drainage area.



The single-well self-pulse test is based on long-term monitoring of downhole pressure response to the periodic rate step change (usually shut-in or close-in).

If flowrate 


The primary hard data deliverables are:

  • formation pressure 
    LaTeX Math Inline
    bodyP_i


  • skin-factor S
     
  • near 
    LaTeX Math Inline
    body\sigma_{near}
     and far 
    LaTeX Math Inline
    body\sigma_{far}
     zone transmissibility 

  • near 
    LaTeX Math Inline
    body\chi_{near}
     and far 
    LaTeX Math Inline
    body\chi_{far}
     zone pressure diffusivity 

  • time to reach the reservoir boundary 
    LaTeX Math Inline
    bodyt_e


The SPT is correlating pressure variation with pre-designed flowrate variation sequence and tracks:

  • pressure response amplitude which depends on formation transmissibility 
    LaTeX Math Inline
    body\sigma
     

and

  • time lag between flowrate variation and pressure response which depends on formation diffusivity 
    LaTeX Math Inline
    body\chi
    .


This allows estimating effective formation thickness 

LaTeX Math Inline
bodyh
 directly from field survey without assumptions on core-based permeability (compare with 
LaTeX Math Block Reference
anchorh_PTA
) and consequently leads to assessing the drainange area 
LaTeX Math Inline
bodyA_e
, fluid mobility 
LaTeX Math Inline
body\bigg< \frac{k}{\mu} \bigg>
 and absolute permeability 
LaTeX Math Inline
bodyk_a
 with lesser uncertainties than in BUS: 


DeliverablesDescriptionNon-BUS Input ParametersKey Uncertainties


LaTeX Math Block
anchor0K3BA
alignmentleft
h = \frac{\sigma}{\phi \, c_t \, \chi}



Effective reservoir thickness


Formation porosity

LaTeX Math Inline
body\phi


Rock compressibility

LaTeX Math Inline
bodyc_r(\phi)


Initial water saturation

LaTeX Math Inline
bodys_{wi}


Fluid compressibility

LaTeX Math Inline
body\{ c_o , \, c_w \}



Rock compressibility

LaTeX Math Inline
bodyc_r(\phi)


LaTeX Math Block
anchor0K3BA
alignmentleft
A_e = \frac{4 \, \sigma \, t_e}{c_t \, h}



Drainage area


Rock compressibility

LaTeX Math Inline
bodyc_r(\phi)


Initial water saturation

LaTeX Math Inline
bodys_{wi}


Fluid compressibility

LaTeX Math Inline
body\{ c_o , \, c_w \}





Rock compressibility

LaTeX Math Inline
bodyc_r(\phi)


LaTeX Math Block
anchorZ1Q09
alignmentleft
\Big< \frac{k}{\mu} \Big>  = \chi \, \phi \, c_t



Fluid mobility


Rock compressibility

LaTeX Math Inline
bodyc_r(\phi)


Initial water saturation

LaTeX Math Inline
bodys_{wi}



Fluid compressibility
LaTeX Math Inline
body\{ c_o , \, c_w \}


Rock compressibility

LaTeX Math Inline
bodyc_r(\phi)


Initial water saturation

LaTeX Math Inline
bodys_{wi}


LaTeX Math Block
anchorHPFMS
alignmentleft
k_a =   \frac{\Big< \frac{k}{\mu} \Big>}{\bigg[ \frac{k_{rw}}{\mu_w} + \frac{k_{ro}}{\mu_o} \bigg]}



Absolute permeability


Rock compressibility

LaTeX Math Inline
bodyc_r(\phi)


Initial water saturation

LaTeX Math Inline
bodys_{wi}


Relative permeabilities

LaTeX Math Inline
body\{ k_{rw}, \, k_{ro} \}


Fluid viscosities

LaTeX Math Inline
body\{ \mu_w, \mu_o \}


Fluid compressibility
LaTeX Math Inline
body\{ c_o , \, c_w \}


Rock compressibility

LaTeX Math Inline
bodyc_r(\phi)


Initial water saturation

LaTeX Math Inline
bodys_{wi}


Relative permeabilities

LaTeX Math Inline
body\{ k_{rw}, \, k_{ro} \}



The absoluite permeability from SPT 

LaTeX Math Inline
body k_a |_{SPT}
 is usually stacked up against core-based permeability 
LaTeX Math Inline
body k_a |_{CORE}
 to validate the core samples and assess the effects of macroscopic features which are overlooked at core-plug size level.


Running SPT in two different cycling frequences allows assessing the near and far resevroir zones spearately.

The usual SPT workflow includes several cycling tests with different frequencies, the lower the frequency the longer the scanning range.

This captures variation of permeability and thickness when moving away from well location.

Together with deconvolution, the SPT is reproducing conventional PTA information and providing additional data on pressure diuffusivity.

This maybe used as estimation of permeability and thickness separately and their variation away from well location.