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 $\begin{array}{l}P_i\end{array}$
skin-factor S
average transmissibility in drainage area $\begin{array}{l}\sigma\end{array}$
time to reach the reservoir boundary $\begin{array}{l}t_e\end{array}$

The conditional deliverables from build-up survey would be:

Deliverables

Description

Assumptions

(1)	$\begin{array}{l}\displaystyle V_o = \frac{4 \, \sigma \, t_e \, (1-s_{wi})}{c_t}\end{array}$

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

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

Drainable oil reserves

The rock compressibility $\begin{array}{l}c_r(\phi)\end{array}$ is defined from core lab study or empirical porosity correlations

$\begin{array}{l}s_{wi}\end{array}$ is estimated from SCAL

Conventional pressure build-up survey in a single-well reservoir is normally providing assessment of:

average transmissibility in drainage area $\begin{array}{l}\sigma\end{array}$
drainage area around the well $\begin{array}{l}A_e\end{array}$
formation pressure $\begin{array}{l}P_i\end{array}$
skin-factor S

where

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

transmissibility

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

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 $\begin{array}{l}A_e\end{array}$ 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:

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

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

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

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 (6) and then calculates average reservoir thickness in drainage area as

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

which leads to assessment of drainable oil volume as

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

This methodology is strongly dependent on core-based permeability which may not be representative of the whole drainage area.

The alternative way of

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