1. Motivation

One of the most important objectives of the well testing is to assess the drainable oil reserves and reservoir properties around tested well.

This particularly becomes important in appraisal drilling as well testing is the only source of this information.

In conventional well testing which is based on long-term pressure build-up survey 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

Non-BUS Input Parameters

Key Uncertainties

(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 $\begin{array}{l}\{ c_o , \, c_w \}\end{array}$ from PVT

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

Rock compressibility $\begin{array}{l}c_r(\phi)\end{array}$

Initial water saturation $\begin{array}{l}s_{wi}\end{array}$

(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

Formation porosity $\begin{array}{l}\phi\end{array}$

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

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

Fluid viscosities $\begin{array}{l}\{ \mu_w, \mu_o \}\end{array}$ from PVT

Absolute permeability to air $\begin{array}{l}k_a\end{array}$

Relative permeabilities

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

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

Effective reservoir thickness

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

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

Fluid viscosities $\begin{array}{l}\{ \mu_w, \mu_o \}\end{array}$ from PVT

Absolute permeability to air $\begin{array}{l}k_a\end{array}$

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

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 provides more information than build-up survey (BUS).

Expand more on SPT

The BUS correlates pressure decline to change in production rate (usually from constant production rate to shut-in) and it strongly depends on formation transmissibility $\begin{array}{l}\sigma\end{array}$ .

The SPT is doing the same but also tracks the time lag between flowrate variation and pressure response which depends on formation diffusivity $\begin{array}{l}\chi\end{array}$ .

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

Deliverables

Description

Non-BUS Input Parameters

Key Uncertainties

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

Effective reservoir thickness

Formation porosity $\begin{array}{l}\phi\end{array}$

Rock compressibility $\begin{array}{l}c_r(\phi)\end{array}$

Initial water saturation $\begin{array}{l}s_{wi}\end{array}$

Fluid compressibility $\begin{array}{l}\{ c_o , \, c_w \}\end{array}$

Rock compressibility $\begin{array}{l}c_r(\phi)\end{array}$

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

Drainage area

Rock compressibility $\begin{array}{l}c_r(\phi)\end{array}$

Initial water saturation $\begin{array}{l}s_{wi}\end{array}$

Fluid compressibility $\begin{array}{l}\{ c_o , \, c_w \}\end{array}$

Rock compressibility $\begin{array}{l}c_r(\phi)\end{array}$

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

Fluid mobility

Rock compressibility $\begin{array}{l}c_r(\phi)\end{array}$

Initial water saturation $\begin{array}{l}s_{wi}\end{array}$

Fluid compressibility $\begin{array}{l}\{ c_o , \, c_w \}\end{array}$

Rock compressibility $\begin{array}{l}c_r(\phi)\end{array}$

Initial water saturation $\begin{array}{l}s_{wi}\end{array}$

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

Absolute permeability

Rock compressibility $\begin{array}{l}c_r(\phi)\end{array}$

Initial water saturation $\begin{array}{l}s_{wi}\end{array}$

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

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

Fluid compressibility $\begin{array}{l}\{ c_o , \, c_w \}\end{array}$

Rock compressibility $\begin{array}{l}c_r(\phi)\end{array}$

Initial water saturation $\begin{array}{l}s_{wi}\end{array}$

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

The latter is usually stacked up against core-based permeability 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 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

Page tree

1. Motivation

2. Objectives

3. Deliverables

4. Inputs

5. Procedure

6. Interpretation

References

Page tree

SPT – Self Pulse Test

1. Motivation

2. Objectives

3. Deliverables

4. Inputs

5. Procedure

6. Interpretation

References