1. Motivation
One of the most important objectives of the well testing is to assess the drainable oil reserves around tested well.
This particularly becomes important in appraisal drilling.
In conventional pressure build-up survey in a single-well reservoir 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:
Deliverables | Description | Assumptions | ||||||
---|---|---|---|---|---|---|---|---|
where c_t is total compressibility:
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 \} is estimated from PVT study Initial water saturation s_{wi} is estimated from SCAL | ||||||
where \chi is pressure diffusivity:
where \phi is reservoir porosity, \big< \frac{k}{\mu} \big> is fluid mobility:
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 | Absolute permeability to air k_a is estimated from core lab study
Fuid viscosities \mu_w, \mu_o are estimated from PVT study | ||||||
| Effective reservoir thickness | Absolute permeability to air k_a is estimated from core lab study
Fuid viscosities \mu_w, \mu_o are estimated from PVT study |
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.
Unlike BUS the SPT is a more informative survey than build-up survey.
It monitors pressure response and time lag with flowarate variation which yields transmissibility \sigma and diffusivity \chi and can estimate effective formaiton thickness separately:
(7) | h = \frac{\sigma}{\phi \, c_t \, \chi} |
This allows asessing the drainange area
(8) | A_e = \frac{4 \, \sigma \, t_e}{c_t \, h} |
mobility:
(9) | \bigg< \frac{k}{\mu} \bigg> = \chi \, \phi \, c_t |
and maxcroscopic absolute permeability:
(10) | k_a = \frac{\bigg< \frac{k}{\mu} \bigg>}{\bigg[ \frac{k_{rw}}{\mu_w} + \frac{k_{ro}}{\mu_o} \bigg]} |
Running SPT in two different cycling frequences SPT can assess the near and far resevroir zones spearately.
2. Objectives
- Assess reservoir volume around well
- Assess reservoir permeability and thickness variation around well
3. Deliverables
Vhc | Potential hydrocarbon reserves |
Ve | Drainage volume |
Ae | Drainage area |
knear | Permeability of the near-reservoir zone |
hnear | Effective thickness of the near-reservoir zone |
kfar | Permeability of the far-reservoir zone |
hfar | Effective thickness of the far-reservoir zone |
S | Skin-factor |
Pu(t) | Deconvolution of the long-term unit-rate response |
4. Inputs
Property | Description | Data Source |
---|---|---|
Bo | Oil Formation Volume Factor | PVT samples |
co | Oil compressibility | PVT samples |
cw | Water compressibility | PVT samples |
cr | Rock compressibility | PVT samples |
swi | Initial water saturation | Core samples |
\phi | Porosity | Core samples |
5. Procedure
- Test = Test 1 + Test 2 + Test 3
- Test 1 = high freq pulsations (10 pulses with 0.3 day)
- Test 2 = mid freq pulsations (10 pulses with 1.5 day)
- Test 3 = Low freq pulsations (5 pulses with 5.5 day)
6. Interpretation
- Numerical model
- Single well with circle boundary
- High density LGR
- High density time grid (seconds)
- Single well with circle boundary
- Automated pressure match in PolyGon software
References
\sigma