GLOSSARY

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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  P_i

  • skin-factor S
     
  • average transmissibility in drainage area  \sigma

  • time to reach the reservoir boundary  t_e


The conditional deliverables from build-up survey would be:

DeliverablesDescriptionNon-BUS Input ParametersKey Uncertainties
(1) V_o = \frac{4 \, \sigma \, t_e \, (1-s_{wi})}{c_t}

where   c_t is total compressibility:

(2) c_t = c_r + (1-s_{wi}) \, c_o + s_{wi} \, c_w

and \{ c_r, \, c_o \, c_w \} are rock, oil and water compressibility.


Drainable oil reserves


The rock compressibility c_r(\phi) is defined from core lab study or empirical porosity correlations

Fluid compressibility \{ c_o , \, c_w \} from PVT

Initial water saturation s_{wi} from SCAL


Rock compressibility c_r(\phi)


Initial water saturation s_{wi}

(3) A_e = 4 \, \chi \, t_e

where  \chi is pressure diffusivity:

(4) \chi = \Big< \frac{k}{\mu} \Big> \, \frac{1}{\phi \, c_t}

where \phi is reservoir porosity, \big< \frac{k}{\mu} \big> is fluid mobility:

(5) \Big< \frac{k}{\mu} \Big> = k_a \, \bigg[ \frac{k_{rw}}{\mu_w} + \frac{k_{ro}}{\mu_o} \bigg]

k_a is absolute permeability to air,

k_{rw}, \, k_{ro} are relative permeabilities to water and oil,

\mu_w, \mu_o are water and oil viscosities


Drainage area


Formation porosity \phi

Absolute permeability to air k_a from core study


Relative permeabilities \{ k_{rw}, \, k_{ro} \} from SCAL

Fluid viscosities \{ \mu_w, \mu_o \} from PVT


Absolute permeability to air k_a


Relative permeabilities \{ k_{rw}, \, k_{ro} \}
(6) h = \sigma \, \bigg< \frac{k}{\mu} \bigg>^{-1}


Effective reservoir thickness


Absolute permeability to air k_a from core study


Relative permeabilities \{ k_{rw}, \, k_{ro} \} from SCAL

Fluid viscosities \{ \mu_w, \mu_o \} from PVT


Absolute permeability to air k_a


Relative permeabilities \{ 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  P_i

  • skin-factor S
     
  • near  \sigma_{near} and far  \sigma_{far} zone transmissibility 

  • near  \chi_{near} and far  \chi_{far} zone pressure diffusivity 

  • time to reach the reservoir boundary  t_e


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

  • pressure response amplitude which depends on formation transmissibility  \sigma 

and

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


This allows estimating effective formation thickness  h directly from field survey without assumptions on core-based permeability (compare with  (6)) and consequently leads to assessing the drainange area  A_e, fluid mobility  \bigg< \frac{k}{\mu} \bigg>  and absolute permeability  k_a with lesser uncertainties than in BUS: 

DeliverablesDescriptionNon-BUS Input ParametersKey Uncertainties
(7) h = \frac{\sigma}{\phi \, c_t \, \chi}


Effective reservoir thickness


Formation porosity \phi

Rock compressibility c_r(\phi)

Initial water saturation s_{wi}

Fluid compressibility \{ c_o , \, c_w \}


Rock compressibility c_r(\phi)

(8) A_e = \frac{4 \, \sigma \, t_e}{c_t \, h}


Drainage area


Rock compressibility c_r(\phi)

Initial water saturation s_{wi}

Fluid compressibility \{ c_o , \, c_w \}




Rock compressibility c_r(\phi)

(9) \Big< \frac{k}{\mu} \Big> = \chi \, \phi \, c_t


Fluid mobility


Rock compressibility c_r(\phi)


Initial water saturation s_{wi}


Fluid compressibility \{ c_o , \, c_w \}


Rock compressibility c_r(\phi)


Initial water saturation s_{wi}

(10) k_a = \frac{\Big< \frac{k}{\mu} \Big>}{\bigg[ \frac{k_{rw}}{\mu_w} + \frac{k_{ro}}{\mu_o} \bigg]}


Absolute permeability


Rock compressibility c_r(\phi)


Initial water saturation s_{wi}


Relative permeabilities \{ k_{rw}, \, k_{ro} \}

Fluid viscosities \{ \mu_w, \mu_o \}

Fluid compressibility \{ c_o , \, c_w \}


Rock compressibility c_r(\phi)


Initial water saturation s_{wi}


Relative permeabilities \{ k_{rw}, \, k_{ro} \}


The absoluite permeability from SPT  k_a |_{SPT} is usually stacked up against core-based permeability  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.



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