1. Motivation

One of the most important objectives of the well testing is to assess the drainable reservoir volume around tested well.

This particularly becomes important in appraisal drilling.

Conventional pressure build-up survey is normally providing assessment of:

average transmissibility in drainage area
drainage area around the well A_e
formation pressure P_i
skin-factor S

where

(1)	$\begin{array}{l}\displaystyle \sigma = \big< \frac{k}{\mu} \big> \, h\end{array}$

transmissibility

(2)	$\begin{array}{l}\displaystyle \big< \frac{k}{\mu} \big> = k_a \, \bigg[ \frac{k_{rw}}{\mu_w} + \frac{k_{ro}}{\mu_o} \bigg]\end{array}$

mobility

$\begin{array}{l}k_a\end{array}$

absolute permeability

$\begin{array}{l}k_{rw}, \, k_{ro}\end{array}$

relative permeabilities to water and oil

$\begin{array}{l}\mu_w, \mu_o\end{array}$

water and oil viscosities

It is important to notice that drainage area A_e is calculated based on the permeability estimations from core study and compressibility estimation from porosity correlations which may not be representative of the whole drainage area:

(3)	$\begin{array}{l}\displaystyle A_e = 4 \, \chi \, t_e\end{array}$

where $\begin{array}{l}t_e\end{array}$ time to reach the reservoir boundary from BUS log-log plot and $\begin{array}{l}\chi\end{array}$ is pressure diffusivity which is used to translate $\begin{array}{l}t_e\end{array}$ into a drainage area

(4)	$\begin{array}{l}\displaystyle \chi = \big< \frac{k}{\mu} \big> \, \frac{1}{\phi \, c_t}\end{array}$

and $\begin{array}{l}c_t\end{array}$ is total compressibility:

(5)	$\begin{array}{l}\displaystyle c_t = c_r + (1-s_{wi}) \, c_o + s_{wi} \, c_w\end{array}$

In regular workflow one pulls permeability $\begin{array}{l}k\end{array}$ from core studies, then estimates diffusivity $\begin{array}{l}\chi\end{array}$ from (4) and average reservoir thickness in drainage area as

(6)	$\begin{array}{l}\displaystyle h = \phi \, c_t \, \frac{\sigma}{\chi}\end{array}$

and then assess drainable reservoir volume as

(7)	$\begin{array}{l}\displaystyle V_o = (1-s_{wi}) \, \phi \, h \, A_e\end{array}$

This methodology contains a big uncertainty as it is based on

The BUS alone can not assess formation thickness directly and only

instead uses

the ratio of transmissivity (kh) and reservoir permeability (k) where the latter is estimated from core data which may not be representative for the whole drainage area.

The major drawbacks of this approach is that drainable reservoir volume estimation is based on assumption in reservoir thickness which is estimated from OH logs and may not be representative for the whole drainage area.

2. Objectives

Assess reservoir volume around well
Assess reservoir permeability and thickness variation around well

3. Deliverables


V_hc	Potential hydrocarbon reserves
V_e	Drainage volume
A_e	Drainage area
k_s	Permeability of the skin-zone
h_s	Effective thickness of the skin-zone
k_near	Permeability of the near-reservoir zone
h_near	Effective thickness of the near-reservoir zone
k_far	Permeability of the far-reservoir zone
h_far	Effective thickness of the far-reservoir zone
S	Skin-factor
P_u(t)	Deconvolution of the long-term unit-rate response

4. Inputs

Property	Description	Data Source
B_o	Oil Formation Volume Factor	PVT samples
c_o	Oil compressibility	PVT samples
c_w	Water compressibility	PVT samples
c_r	Rock compressibility	PVT samples
s_wi	Initial water saturation	Core samples
$\begin{array}{l}\phi\end{array}$	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
1. Single well with circle boundary
2. High density LGR
3. High density time grid (seconds)
Automated pressure match in PolyGon software

References

$\begin{array}{l}\sigma\end{array}$

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SPT – Self Pulse Test