1. Motivation

One of the most important objectives of the well testing is to

assess the drainable oil reserves around tested well
assess the reservoir properties

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

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

and $\begin{array}{l}\{ c_r, \, c_o \, c_w \}\end{array}$ are rock, oil and water compressibility.

Drainable oil reserves

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

Fluid compressibility $\begin{array}{l}\{ c_o \, c_w \}\end{array}$ is estimated from PVT study

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

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

where $\begin{array}{l}\chi\end{array}$ is pressure diffusivity:

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

where $\begin{array}{l}\phi\end{array}$ is reservoir porosity, $\begin{array}{l}\big< \frac{k}{\mu} \big>\end{array}$ is fluid mobility:

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

$\begin{array}{l}k_a\end{array}$ is absolute permeability to air,

$\begin{array}{l}k_{rw}, \, k_{ro}\end{array}$ are relative permeabilities to water and oil,

$\begin{array}{l}\mu_w, \mu_o\end{array}$ are water and oil viscosities

Drainage area

Absolute permeability to air $\begin{array}{l}k_a\end{array}$ is estimated from core lab study

Relative permeabilities $\begin{array}{l}k_{rw}, \, k_{ro}\end{array}$ are estimated from SCAL

Fuid viscosities $\begin{array}{l}\mu_w, \mu_o\end{array}$ are estimated from PVT study

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

Effective reservoir thickness

Absolute permeability to air $\begin{array}{l}k_a\end{array}$ is estimated from core lab study

Relative permeabilities $\begin{array}{l}k_{rw}, \, k_{ro}\end{array}$ are estimated from SCAL

Fuid viscosities $\begin{array}{l}\mu_w, \mu_o\end{array}$ 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.

The SPT is a more informative survey than build-up survey.

It monitors pressure response and time lag with flowrate variation which yields transmissibility $\begin{array}{l}\sigma\end{array}$ and diffusivity $\begin{array}{l}\chi\end{array}$ and can estimate effective formaiton thickness separately:

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

This allows asessing the drainange area

(8)	$\begin{array}{l}\displaystyle A_e = \frac{4 \, \sigma \, t_e}{c_t \, h}\end{array}$

mobility:

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

and maxcroscopic absolute permeability:

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

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


V_hc	Potential hydrocarbon reserves
V_e	Drainage volume
A_e	Drainage area
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 period T)
Test 2 = mid freq pulsations (10 pulses with with period 5T)
Test 3 = Low freq pulsations (10 pulses with period 25 T)

So that total duration of the test is 310 T.

Typically T = 3 hrs and total test duration is around 40 days.

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