Fast Pressure-Decay Core Permeability Measurement for Tight Rocks

SPWLA 59th Annual Logging Symposium, June 2-6, 2018
FAST PRESSURE-DECAY CORE PERMEABILITY MEASUREMENT
FOR TIGHT ROCKS
Zheng Gan, Ted Griffin, John Dacy, Harry Xie, Robert Lee
Copyright 2018, held jointly by the Society of Petrophysicists and Well Log
Analysts (SPWLA) and the submitting authors.
This paper was prepared for presentation at the SPWLA 59th Annual Logging
Symposium held in London, UK, June 2-6, 2018.
decay experiment and 20 times faster than the steadystate experiment, and (3) the proposed pressure-decay
experiment can provide the gas-filled pore and fracture
volumes during the permeability measurement, whereas
pulse-decay and steady-state experiments cannot.
ABSTRACT
INTRODUCTION
Matrix permeability is one of the most important factors
used to evaluate long-term production of hydrocarbon
reservoirs. However, for shale reservoirs that have
ultra-low matrix permeability in the range of tens to
hundreds of nano-darcies (nd), the laboratory
measurement of the matrix permeability of intact (nonparticle-ized) samples has remained a challenge. The
widely-used measurement methods such as pulse-decay
and steady-state have two primary limitations: (1)
measurements take hours or even days and (2)
commonly-present sample fractures affect the measured
permeability value. In this study, a new pressure-decay
permeability method is proposed for ultra-tight rocks to
overcome these limitations. The principle of the
pressure-decay experiment is that system gas pressure
is higher than pore pressure of the core sample so that
gas penetrates the core sample and permeability is
derived from the decrease of system gas pressure. In
order to validate the proposed pressure-decay
technique, experiments were conducted on the
following intact rock samples: (1) a set of different
types of rocks including a Marcellus shale plug, (2) a
set of Eagle Ford shale plugs, and (3) a Marcellus shale
plug with open, connected fractures. A series of
comparative studies of the permeability results from
pressure-decay,
pulse-decay,
and
steady-state
experiments on these core samples confirmed that the
proposed pressure-decay experiment can provide
accurate matrix permeability of ultra-tight rocks. Tests
can be completed within one hour and the measurement
range is from 1.0e-01 md to 1.0e-06 md. Further, the
proposed method has the following advantages: (1)
measured matrix permeability by the new pressuredecay method isn’t affected by the open, connected
fractures, whereas these fractures can make the pulsedecay and steady-state permeability results increase by
three orders of magnitude, (2) the new pressure-decay
experiment is around 10 times faster than the pulse-
Successful commercial application of hydraulic
fracturing has unlocked hydrocarbon production from
tight reservoirs such as shales (Gold, 2014). Induced
fractures increase contacting surface area and act as
additional paths for hydrocarbon flow, making
hydrocarbon
production
in
tight
reservoirs
economically feasible. Although fractures (both natural
and induced) dominate hydrocarbon production in the
early life of a well, it is the matrix properties such as
matrix permeability that control long-term performance
of a hydrocarbon well. Matrix permeability is the
fracture-free permeability used to quantify the ability of
a rock to transport hydrocarbons from the rock matrix
to the rock fractures, and is one of the most important
factors in characterization of reservoirs for economic
viability and production management, especially for
long-term production performance.
For conventional cores, matrix permeability is
measured by the steady-state method, which has been
the industry standard for decades because it represents a
laboratory implementation of Darcy’s law (Darcy,
1856). In the steady-state experiment, a core plug
sample is first placed in a core holder with reservoirspecific confining pressure. Experimental gas (or
liquid) is then injected at a constant pressure until flow
rate and pressure stabilize. The pressure difference and
flow rate are recorded for permeability calculation
using the integrated form of Darcy's law. However, for
an ultra-tight core with matrix permeability in the range
of tens to hundreds of nano-darcies, it takes too long
(ten hours or more) for the experimental gas to reach a
constant flow rate. Thus, an unsteady-state experiment
such as pulse-decay is widely-used for ultra-tight cores
(Brace et al., 1968; Gilicz, 1991; Jones, 1997). The
pulse-decay experiment has an upstream reservoir and a
1
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Core Laboratories LP, Houston, TX, USA
SPWLA 59th Annual Logging Symposium, June 2-6, 2018
permeability of an intact core plug sample.
In the present work we propose a pressure-decay
technique on intact core samples to measure matrix
permeability. We first describe pressure-decay
experiments without and with confining pressure and
their mathematical models. We then conduct
unconfined pressure-decay experiments using different
types of tight rocks including shales. Finally, we
perform a series of comparative studies using matrix
gas permeability results from unconfined pressuredecay, pulse-decay, and steady-state experiments. The
comparative studies confirmed that unconfined
pressure-decay experiment can accurately measure
matrix gas permeability of tight rocks. Further, the
unconfined pressure-decay experiment has these
additional benefits: (1) experimental time is much
shorter; (2) gas-filled pore volume can be provided; and
(3) gas-filled fracture volume can be estimated.
PRESSURE-DECAY EXPERIMENT
In this section, we first describe pressure-decay
experiments and their mathematical models. We then
show an example to describe how to derive matrix
permeability from the experimental data as well as the
gas-filled pore and fracture volumes.
In both steady-state and pulse-decay experiments,
experimental gas passes through a core plug sample
along the axial direction. However, if a core sample has
continuous fractures which connect the end faces of the
core plug sample, the fractures will become conduits
for gas flow and the measured permeability would be
substantially due to the fractures. Shale formations are
laminated and fissile. Shale plug samples may have
fractures induced by coring and sampling. Although a
shale plug sample is placed in a core holder with
specified confining pressure during pulse-decay and
steady-state experiments, coring- and sampling-induced
fractures would likely remain partially open so that the
measured permeability may not represent true matrix
permeability. The Gas Research Institute (GRI)
protocol (Luffel and Curtis, 1996; Luffel et al., 1993)
recommends crushing an intact shale plug into small
particles, 0.5 to 0.85 mm diameter, so that the induced
fractures are eliminated. Also, at such a small size, the
efficient processing for pore liquid removal and
quantification by distillation-extraction can be
accomplished. However, many special core analysis
(SCAL) experiments such as water-flooding and gascycling require core samples to be an intact cylinder of
1 inch (2.54 cm) or 1.5 inch (3.81 cm) diameter.
Therefore, we need to measure the fracture-free matrix
Pressure-Decay Experiment System.
Fig.1 is a
schematic diagram of the unconfined pressure-decay
experiment. Initially, pressure of the reference cell is
around 200 psi. After opening valve B, pressure
immediately decreases to around 100 psi (depending on
the void space volume) due to gas expansion. Pressure
continues to decrease as gas penetrates a core sample.
Permeability is derived from the pressure decrease. If
the matrix cup in Fig.1 is replaced by a core holder and
a short tube is used to connect the upper and bottom
heads of the core holder, the pressure-decay experiment
can be implemented with reservoir-specific confining
pressure.
Mathematical Models. Fig.2 shows gas flow directions
in the pressure-decay experiments without and with
confining pressure. To build mathematical models, we
make the following assumptions: (1) the experimental
gas is ideal (helium is used in the pressure-decay
experiments); (2) the pressure-decay process is
isothermal; and (3) the inertial effect is negligible at
low flow rates. With these assumptions, we can derive
the gas transport equation by combining Darcy’s
equation and the mass balance equation.
2
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downstream reservoir, and a core plug sample is placed
in a core holder with reservoir-specific confining
pressure. Initially, a uniform pressure is obtained in the
sample pore and reservoir volumes. To start the
experiment, a small pressure pulse (e.g., ∆P = 30 psi) is
added to the upstream reservoir. Experimental gas then
starts to flow from the upstream reservoir to the
downstream reservoir by passing through the core
sample, causing pressure decrease of the upstream
reservoir and pressure increase of the downstream
reservoir. The pressure transient data are recorded for
permeability calculation. Since flow rate and pressure
difference in the pulse-decay experiment are not
constant, one cannot directly apply Darcy’s law to
calculate permeability. Therefore, another physics law,
the mass balance law, is needed when analyzing the
pressure transient data of the pulse-decay experiment.
The
pulse-decay
approach
to
permeability
determination has been extensively studied (Hsieh et
al., 1981; Chen and Stagg, 1984; Bourbie and Walls,
1982; Dicker and Smits, 1988; Jannot et al., 2008). This
literature expertly describes how one may analyze the
pulse-decay experimental data to calculate the
permeability value. Since the pulse-decay experiment
doesn’t require steady-state flow, its experimental time
is much shorter than the steady-state experiment.
SPWLA 59th Annual Logging Symposium, June 2-6, 2018
𝜙
𝜕𝜌
𝜕𝑡
𝜕𝑃
−
𝑘 𝜕𝜌( 𝜕𝑧 )
𝜇
=0
𝜕𝑧
.
(3)
At isothermal conditions, gas density is linearly
proportional to pressure, so Eq.3 can be written as
𝜕𝑃
𝜕𝑡
𝜕𝑃
−
𝑘 𝜕𝑃( 𝜕𝑧 )
𝜇
=0
𝜕𝑧
.
(4)
Since the pressure decrease is very small due to the
small pore volume of sample, we have
𝑐≈
1
,
𝑃
(5)
where c is the gas compressibility. Therefore, Eq.4
becomes
Fig.1 Schematic diagram of the unconfined pressure-decay
experiment.
𝜙
𝜕𝑃
𝜕𝑡
−
𝑘 𝜕2 𝑃
𝑐𝜇 𝜕𝑧 2
=0
,
(6)
which is the gas transport equation for the confined
pressure-decay experiment.
For the unconfined pressure-decay experiment, gas
flow is two dimensional as shown in Fig.2a. Fig.3
shows cylindrical coordinates used for this twodimensional gas flow. With cylindrical coordinates, the
mass balance equation and Darcy’s equation are as
follows:
𝜕2𝜋𝑟∆𝑟∆𝑧𝜌𝜙
𝜕𝑡
Fig.2 Gas flow directions in pressure-decay experiments
+
𝜕∆𝑧𝜌𝑄1
𝜕𝑧
+
𝜕∆𝑟𝜌𝑄2
𝜕𝑟
=0
,
(7)
without and with confining pressure: (a) gas penetrates a core
sample along both longitudinal and transverse axes for the
unconfined case; (b) while in the confined case, gas penetrates
a core sample from both end faces along the longitudinal axis.
𝑄1 = −
𝑘2𝜋𝑟∆𝑟 𝜕𝑃
𝑄2 = −
𝑘2𝜋𝑟∆𝑧 𝜕𝑃
For the confined pressure-decay experiment, gas flow is
one dimensional as shown in Fig.2b, and Darcy’s
equation and the mass balance equation are as follows:
(1)
where Q1 and Q2 are flow rates along z and r directions,
respectively. Since gas density is linearly proportional
to gas pressure, by combining Eqs.7, 8, and 9 we get
the gas transport equation for this two-dimensional gas
flow:
(2)
𝜙
𝑄=−
𝑘𝐴 𝜕𝑃
𝜕𝜌𝐴𝜙
𝜕𝜌𝑄
𝜕𝑡
+
𝜇 𝜕𝑧
𝜕𝑧
=0
,
,
where Q is flow rate, k is permeability, A is the area of
the end face of the sample equal to 𝜋𝑅2 (𝑅 is the
diameter of the end face), t is time, ɸ is porosity, P is
pressure, 𝜇 is gas viscosity, 𝜌 is gas density, and z is
the axial length with range 0 < z < L/2 (L is the length
of the sample and 0 is the center of the sample).
Combining Eqs.1 and 2, we have
𝜕𝑃
𝜕𝑡
𝜇
𝜕𝑧
𝜇
𝜕𝑟
𝜕𝑃
−
𝑘 𝜕𝑃( 𝜕𝑧 )
𝜇
𝜕𝑧
,
(8)
,
(9)
𝜕𝑃
−
𝑘 1 𝜕𝑃𝑟( 𝜕𝑟 )
𝜇𝑟
𝜕𝑟
=0
.
(10)
Using the gas compressibility c, Eq.10 can be written as
𝜙
𝜕𝑃
𝜕𝑡
−
𝑘 𝜕2 𝑃
𝑐𝜇 𝜕𝑧 2
−
𝑘 1 𝜕𝑃
𝑐𝜇 𝑟 𝜕𝑟
−
𝑘 𝜕2 𝑃
𝑐𝜇 𝜕𝑟 2
=0
,
(11)
which is the gas transport equation for the unconfined
pressure-decay experiment.
3
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𝜙
SPWLA 59th Annual Logging Symposium, June 2-6, 2018
Fig.3 Cylindrical coordinates used for the unconfined pressuredecay experiment on core plug samples.
Further, in the unconfined pressure-decay experiment,
one may use any intact core sample rather than being
limited exclusively to a cylindrically-shaped core plug.
If one wants to use a spherical shape for an intact core
sample, the gas flow becomes one dimensional along
the radial direction. Therefore, the gas transport
equation has the following form:
𝜙
𝜕𝑃
𝜕𝑡
−
2 𝜕𝑃
𝑘 1 𝜕𝑟 ( 𝜕𝑟 )
𝑐𝜇 𝑟 2
𝜕𝑟
=0
.
(12)
Analysis of Experimental Data. In this subsection, we
show how to analyze unconfined pressure-decay
experimental data. Fig.4a shows the unconfined
pressure-decay experimental data for an as-received
shale plug sample with 1.5 inch diameter and 1.5 inch
length. The left y-axis is the recorded pressure, and the
right y-axis is the gas-filled porosity calculated by
Boyle’s law. The “star” mark at top left is the
theoretical initial pressure when no gas penetrates the
sample (that is, zero gas-filled porosity). The theoretical
initial pressure is calculated by incorporating initial
reference cell pressure, void volume of the whole
system, and sample bulk volume. Pressure decline stops
after 2000 seconds, and the gas-filled total porosity is
1.88%. The gas transport equation (Eq.11) is solved to
get the pressure solution P(r, z, t) by using the finite
difference method. P(r=R, z=L/2, t) is the pressure
function of time at the sample surface. We extract the
permeability value which minimizes the square
difference between the pressure solution P(r=R, z=L/2,
t) and the experimental data. Fig.4b shows the pressure
solution curve with permeability value 7.3e-06 md,
which matches the experimental data best. In Fig.4b,
we also notice that there is a gap between the
theoretical initial pressure and the solution pressure,
which equals to 0.13 psi and 0.56% gas-filled porosity.
Therefore, the pressure-decay process of this shale
sample has two stages. There is a rapid pressure decay
before 1 second and a slower pressure decay which
(a)
(b)
Fig.4 (a) The blue curve is the unconfined pressure-decay
experimental data for the shale plug sample; (b) the brown
curve is the pressure solution curve corresponding to
permeability 7.3e-06 md. The “star” mark at top left is the
theoretical initial pressure when no gas penetrates the sample.
4
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takes 2000 seconds. The rapid pressure decay
corresponds to 0.56% gas-filled porosity, which is
controlled by fractures or very large pores. The slower
pressure decay corresponds to (1.88% − 0.56% =)
1.32% gas-filled porosity, which is controlled by gasfilled matrix pores. In summary, from the unconfined
pressure-decay experiment, we can obtain the following
results for this as-received, unconfined shale sample:
(1) gas-filled total porosity = 1.88%; (2) gas-filled
fracture porosity = 0.56%; (3) gas-filled matrix
porosity = 1.32%; and (4) matrix permeability =
7.3×10−6 md. The fracture permeability is at least
three orders of magnitude larger than the matrix
permeability since the first-stage pressure decay is three
orders of magnitude faster than the second-stage
pressure decay.
SPWLA 59th Annual Logging Symposium, June 2-6, 2018
In this section we describe a series of comparative
studies on two sets of core plug samples using
permeability results from unconfined pressure-decay,
steady-state, and pulse-decay experiments (the gas used
in all the experiments is helium). We also show the
impact of connected sample fractures on permeability
measurements.
Different Types of Plug Samples.
We compare
permeability results between unconfined pressure-decay
and steady-state experiments on different types of plug
samples. Fig.5 shows the plug samples used in this
comparison: (1) steel plug; (2) shale plug; (3) chert
plug; and (4) sandstone plug. The steel plug represents
a sample with zero permeability, and the shale sample
comes from the Marcellus formation without cleaning.
All the plugs have 1.5 inch (3.81 cm) diameter and 2
inch (5.08 cm) length. The unconfined pressure-decay
experiment was conducted on these samples using
exactly the same experimental conditions, as was the
case in the steady-state experiment.
(1)
(2)
(3)
(a)
(4)
Fig.5 Plug samples used in the comparison: (1) steel plug; (2)
shale plug; (3) chert plug; (4) sandstone plug.
(b)
Fig.6 (a) The unconfined pressure-decay experimental data for
Fig.6a displays the unconfined pressure-decay
experimental data for these plugs. The y-axis is the gasfilled porosity calculated by Boyle’s law. By converting
the pressure value to the gas-filled porosity value, we
can put all the sample data in a single graph for a fair
comparison. The purple symbols represent data from
the steel plug, which shows zero gas-filled porosity.
Fig.6b shows the pressure solution fitting that estimates
permeability values: (1) 3.6e-06 md for the shale plug;
(2) 4.5e-03 md for the chert plug; (3) 8.0e-02 md for
the sandstone plug. We can also interpret Fig.6b in the
following way. In order to fill 2% porosity, the shale,
chert, and sandstone plugs take around 5000 seconds, 2
seconds, and 0.1 second, respectively. Therefore, it is
understood that permeability of the chert plug is about
three orders of magnitude larger than the shale plug,
and permeability of the sandstone plug is about one
order of magnitude larger than the chert plug. Further,
different types of samples: steel plug, shale plug, chert plug,
and sandstone plug; (b) the pressure solution fitting that
provides the permeability results: 3.6e-06 md for the shale plug,
4.5e-03 md for the chert plug, and 8.0e-02 md for the sandstone
plug.
Fig.7 Unconfined pressure-decay experimental data and
pressure solution fitting for the shale plug.
5
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from Fig.6b, it’s shown that for the sandstone and chert
plugs, the pressure solution curves can extend back to
zero gas-filled porosity. However, this is not the case
for the shale plug. Fig.7 contains the shale plug data
and analysis with an expanded y-axis and shows there is
around 0.6% gas-filled fracture porosity. The
unconfined pressure-decay results for these three plugs
are summarized in Table 1 along with fracture, matrix,
and total porosities (ɸf, ɸm, ɸt).
COMPARATIVE STUDIES
SPWLA 59th Annual Logging Symposium, June 2-6, 2018
results.
Samples
ɸt(%)
ɸm(%)
ɸf(%)
k(md)
Sandstone
13.8
13.8
0
8.0e-02
Chert
7.3
7.3
0
4.5e-03
Shale
2.1
1.5
0.6
3.6e-06
Steady-state permeability experiments were conducted
on these plugs with 1500 psi confining pressure,
Pmean≈30 psi, and ∆P≈30 psi. Table 2 shows the
permeability result comparison between unconfined
pressure-decay and steady-state experiments. The two
results are very close and the largest difference ratio, a
factor of 1.5, comes from the shale plug. The difference
in results may be caused by: (1) confining pressure
applied in the steady-state experiment; (2) differences
in flow direction; (3) slippage effect. The slippage
effect was initially studied by Klinkenberg (1941). The
slippage effect is due to collision between gas
molecules and the pore wall, which causes a higher
flow rate. The slippage effect is stronger when the pore
radii are smaller and the pore pressure is lower. Table 2
also shows the steady-state permeability results are
consistently larger than the unconfined pressure-decay
results. In the steady-state experiment, the mean pore
pressure was around 30 psi, and in the unconfined
pressure-decay experiment it was around 90 psi.
Therefore, the steady-state experiment suffers a
stronger slippage effect which would cause the
measured permeability to be larger. Since the shale plug
has a smaller pore-radius network than the other two
plugs, the shale plug suffers the strongest slippage
effect, which may explain why the difference ratio of
the shale plug is largest. Further, from this test on rock
samples with different permeability values, we can
reasonably conclude that the measurement range of this
unconfined pressure-decay experiment system is from
1.0e-06 md to 1.0e-01 md.
Fig.8 Eagle Ford shale plugs used in the comparative tests:
Sh1, Sh2, Sh3 and Sh4.
Steady-state and pulse-decay experiments were also
conducted on these Eagle Ford shale plugs. Steady-state
experiments were conducted with 1500 psi confining
pressure, Pmean≈30 psi, and ∆P≈30 psi, and pulse-decay
experiments were operated with 1500 psi confining
pressure, Pmean≈1000 psi, and ∆P≈30 psi. The results
are summarized in Table 4. For all the samples, the
difference in the permeability results is less than a
factor of 4. Fig.10 shows the permeability results in a
column chart format. The pulse-decay experiment has
the highest mean pore pressure and the steady-state
experiment has the lowest mean pore pressure.
Therefore, the pulse-decay experiment has the weakest
slippage effect, while the steady-state experiment
suffers the strongest slippage effect. This may explain
why the pulse-decay permeability is smallest and the
steady-state permeability is largest.
Table 2. Permeability comparison between unconfined
pressure-decay (UPD) and steady-state experiments (SS).
Samples
UPD
k(md)
SS
k(md)
Diff. Ratio
(SS/UPD)
Sandstone
8.0e-02
9.0e-02
1.1
Chert
4.5e-03
6.5e-03
1.4
Shale
3.6e-06
5.3e-06
1.5
6
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Eagle Ford Shale Plugs. In this subsection we
compare permeability results of unconfined pressuredecay, steady-state, and pulse-decay experiments on
four as-received Eagle Ford shale plugs. Fig.8 shows
the four Eagle Ford shale plugs used in the comparative
test: Sh1, Sh2, Sh3, and Sh4. These plugs have 1 inch
(2.54 cm) diameter and 1.8 to 2 inch (4.5 to 5 cm)
length. Fig.9 shows the unconfined pressure-decay
experimental data and pressure solution fitting for these
Eagle Ford shale plugs. The pressure solution curves
match the experimental data very well. From Fig.9, it’s
seen that the pressure solution curve can extend back to
the point which is very close to the theoretical initial
pressure. It shows the gas-filled fracture porosity is
pretty small for these Eagle Ford shale plugs. Table 3
summarizes unconfined pressure-decay results for these
Eagle Ford plugs. The gas-filled fracture porosities are
0.17%, 0.04%, 0.28%, and 0.14% for Sh1, Sh2, Sh3,
and Sh4, respectively. The gas-filled fracture porosity is
so small that the pulse-decay and steady-state results
shouldn’t be significantly affected by fractures.
Table 1. Summary of unconfined pressure-decay experiment
SPWLA 59th Annual Logging Symposium, June 2-6, 2018
Table 3. Summary of unconfined pressure-decay experiment
results.
ɸt(%)
ɸm(%)
ɸf(%)
k(md)
Sh1
4.55
4.38
0.17
8.4e-05
Sh2
4.12
4.08
0.04
5.5e-05
Sh3
5.16
4.88
0.28
4.1e-04
Sh4
4.46
4.32
0.14
9.8e-05
Table 4. Summary of permeability results from unconfined
pressure-decay (UPD), steady-state (SS), and pulse-decay
(PDP) experiments for the Eagle Ford shale plugs.
Samples
UPD
k(md)
SS
k(md)
PDP
k(md)
Diff.
Diff.
Ratio
Ratio
(UPD/SS) (UPD/PDP)
Sh1
8.4e-05
1.3e-04
3.3e-05
0.65
2.5
Sh2
5.5e-05
1.1e-04
4.4e-05
0.50
1.3
Sh3
4.1e-04
9.5e-04
1.8e-04
0.43
2.3
Sh4
9.8e-05
3.9e-04
5.4e-05
0.25
1.8
Fig.10 Permeability results for Eagle Ford shale plugs.
Next we compare experimental time for these
experiments. For the unconfined pressure-decay
experiment, it took less than 2000 seconds to reach the
equilibrium state in every case. However, experimental
time was 5 hours and 10 hours for the pulse-decay and
steady-state experiments, respectively. Therefore, the
unconfined pressure-decay experiment is around 10
times faster than the pulse-decay experiment and 20
times faster than the steady-state experiment. The short
experimental time is one of the greatest advantages of
the unconfined pressure-decay experiment.
Impact of Connected Fractures on Permeability
Measurements. Fig.11a is a white-light photograph of
an as-received Marcellus shale plug, M2 which contains
visible fractures and has overall dimensions of 1.5 inch
(3.81 cm) diameter and 1.7 inch (4.3 cm) length.
Fig.9 Unconfined pressure-decay experimental data and
pressure solution fitting for Eagle Ford plugs: Sh1, Sh2, Sh3,
and Sh4.
However, in Fig.11a it is difficult to see whether or not
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Samples
SPWLA 59th Annual Logging Symposium, June 2-6, 2018
Fig.12 Unconfined pressure-decay experimental data and
pressure solution fitting for shale plug M2.
Table 5. Unconfined pressure-decay (UPD) and steady-state
(SS) results for M2.
Samples
ɸt(%)
ɸm(%)
ɸf(%)
UPD
k(md)
SS
k(md)
M2
1.18
0.54
0.64
1.5e-06
2.0e-03
CONCLUSIONS
Conventional methods for ultra-tight rock permeability
measurement, such as steady-state and pulse-decay,
have the following limitations: (1) measurement times
are excessive; (2) measurement results could be
affected by open, connected fractures, despite
application of confining pressure. A new, unconfined
pressure-decay technique has been described and shown
to provide matrix gas permeability of ultra-tight rocks
compatible with the conventional methods when open
fractures are absent. When open fractures are present in
a test plug, the new method will provide matrix
permeability independent of fracture artifacts. By
means of a thorough comparative study, it has been
demonstrated that for all the tested rock samples, the
largest difference ratio between the new method and
steady-state results is 4, while the largest difference
ratio between the new method and pulse-decay results
is 2.5. These resultant differences are mainly caused by
the slippage effect confirming the unconfined pressuredecay experiments can provide accurate matrix gas
permeability at laboratory conditions. Additional
advantages of the new method over conventional
methods include: (1) it is 10 times faster than the pulsedecay method and 20 times faster than the steady-state
method; (2) it can provide the gas-filled pore volume;
and (3) an estimate of fracture volume. From tests on
rock samples with permeability values, the
measurement range of the unconfined pressure-decay
method is from 1.0e-06 md to 1.0e-01 md. At last, we
(a)
(b)
Fig.11 Marcellus shale plug M2: (a) white-light photo; (b) 25 µm
resolution Micro-CT image of plug cross-section.
8
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the surface-visible fractures are connected. Fig.11b
shows a 25 µm resolution Micro-CT image of the
cross-section of this shale plug, wherein one can clearly
confirm the existence of open, connected fractures
inside the sample. Both unconfined pressure-decay and
steady-state experiments were conducted on this
sample. The steady-state experiment has 1500 psi
confining pressure, Pmean≈30 psi, and ∆P≈30 psi.
Fig.12 shows the unconfined pressure-decay
experimental data and pressure solution fitting for this
sample. The unconfined pressure-decay and steadystate results for this shale plug are summarized in Table
5. The gas-filled total porosity of this sample is 1.18%
and the gas-filled fracture porosity is 0.64%. The
steady-state permeability is significantly affected by the
open, connected fractures which are visible in Fig.11b.
The steady-state permeability is 2.0e-03 md, while the
unconfined pressure-decay permeability is only 1.5e-06
md. Therefore, the unconfined pressure-decay
experiment provides more accurate matrix permeability
for this sample than the steady-state experiment.
SPWLA 59th Annual Logging Symposium, June 2-6, 2018
technique, SPE Annual Technical Conference and
Exhibition, Dallas, Texas, USA, October 6-9, 1991,
SPE-22688-MS
LIST OF SYMBOLS
Gold, R., 2014, The boom: how fracking ignited the
American energy revolution and changed the world,
New York: Simon & Schuster
c
k
L
P
Q
R
t
ρ
ɸ
µ
Gas compressibility (psi-1)
Permeability (md)
Sample length (cm)
Pressure (psi)
Gas flow rate (cm3/s)
Sample diameter (cm)
Time (s)
Gas density (g/cm3)
Porosity (%)
Gas viscosity (cp)
Hsieh, P.A., Tracy, J.V., Neuzil C.E., Bredehoeft J.D.,
and Silliman S.E., 1981, A transient laboratory method
for determining the hydraulic properties of tight rockstheory, International Journal of Rock Mechanics and
Mining Sciences & Geomechanics Abstracts, 18(3),
245-252
Jannot, Y., Lasseux, D., Delottier, L. and Hamon, G.,
2008, A simultaneous determination of permeability
and klinkenberg coefficient from an unsteady-state
pulse-decay experiment, International Symposium of
the Society of Core Analysts, Abu Dhabi, October 29November 2, 2008.
ACKNOWLEDGEMENTS
We want to thank the management of Core Laboratories
for the approval of this publication. We also would like
to thank our colleagues Derek Beckett, Art Curby, Kory
Holmes, Craig Merritt, Craig Whitney, AJ Kumar,
Tommy Williams, Daniel Burch, Aaron Congdon, Tuan
Vo, Amanda Patterson, Omar Reffell, Phillip Lim, and
Lucien Morales, for guiding discussions and laboratory
support.
Jones, S.C., 1997, A technique for fast pulse-decay
permeability measurements in tight rocks, SPE
Formation Evaluation, 12(01), 19-26
Klinkenberg, L. J., 1941, The permeability of porous
media to liquids and gases, Drilling and Production
Practice, New York, New York, USA, January 1, API41-200
REFERENCES
Bourbie, T. and Walls, J., 1982, Pulse decay
permeability: analytical solution and experimental test,
SPE Journal, 22(05), 719-721
Luffel, D.L. and Curtis, J.B., 1996, Development of
laboratory and petrophysical techniques for evaluating
shale reservoirs, Gas Research Institute Technical
Report, GRI-95/0496
Brace, W.F., Walsh, J.B., and Frangos, W.T., 1968,
Permeability of granite under high pressure, Journal of
Geophysical Research, 73(06), 2225-2236
Luffel, D.L., Hopkins, C.W., Holditch, S.A., and
Schettleer,
P.D.,
1993,
Matrix
permeability
measurement of gas productive shales, SPE Annual
Technical Conference and Exhibition, Houston, Texas,
USA, October 3-6, 1993, SPE-26633
Chen, T. and Stagg, P.W., 1984, Semilog analysis of
the
pulse-decay
technique
of
permeability
measurement, SPE Journal, 24(06), 639-642
ABOUT THE AUTHORS
Darcy, H., 1856, Les fontaines publiques de la ville de
dijon, Victor Dalmont, Paris
Zheng Gan is Mathematical Advisor for the Petroleum
Services division of Core Laboratories in Houston, TX.
He received a B.S. degree in mathematics from
University of Science and Technology of China in
2007, and a PhD degree in mathematics from Rice
University in 2012. Dr. Gan joined Core Lab in 2013,
and as Mathematical Advisor he works on statistical
analysis, mathematical modeling, numerical simulation,
and software development for various core analysis
Dicker, A. and Smits, R., 1988, A practical approach
for determining permeability from laboratory pressurepulse decay measurements, International Meeting on
Petroleum Engineering, Tianjin, China, November 1-4,
1988, SPE-17578-MS
Gilicz A., 1991, Application of the pulse decay
9
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would like to mention that we’ve already done a few
confined pressure-decay experiments and the result
comparison and analysis will be presented in our next
study.
SPWLA 59th Annual Logging Symposium, June 2-6, 2018
projects such as Unconventional Core Measurements,
Digital Rocks, NMR, and EOR. He focuses on
improving Core Lab’s existing core analysis services
and developing new core analysis technologies.
He is a 1987 graduate of Texas Tech University and
joined Core Laboratories in 1990 as a Core Analyst in
Midland, Texas. He later transferred to the gulf coast
region of Texas to acquire experience in the
unconsolidated sand formations found along the gulf.
Downloaded from http://onepetro.org/SPWLAALS/proceedings-pdf/SPWLA18/4-SPWLA18/D043S010R002/1185000/spwla-2018-dd.pdf/1 by Hugo Luna on 29 January 2025
Ted Griffin is Vice President of the Petroleum Services
Division of Core Lab. In this capacity, Ted is
responsible for technology development for rock
properties, reservoir fluids services and laboratory
instrument manufacturing. Ted has 44 years of rock
petrophysics experience and has published a number of
technical papers on the engineering and petrophysical
applications of core properties data. Ted is a member
of SPWLA, the Society of Core Analysts and SPE.
John Dacy is Technical Director for the Petroleum
Services division of Core Laboratories and is based in
their Houston, Texas office. He graduated with a B.S.
degree in geology from the University of Texas at
Arlington in 1972 and began his career with Core Lab
the same year working in their Dallas Special Core
Analysis lab. In his 45 years at Core he has held a
variety of technical and administrative positions. As
Technical Director he provides training and other
support to Core Lab's worldwide network of rock
properties laboratories on issues of technology transfer,
testing protocols, data applications, and quality
assurance. He is a member of SPWLA, SPE, AAPG,
and the Society of Core Analysts.
Harry Xie is NMR Senior Advisor at Core
Laboratories. He received his PhD in Physics from the
University of Kent at Canterbury, UK, in 1994 and
worked as a research fellow for both the University of
Surrey and the University of Kent on an industrial
project to build an on-line NMR system for quality
control purposes. Dr. Xie has spent several years
working as Product Specialist to develop and support
laboratory NMR products (MARAN product line) at
Resonance Instruments Ltd. He has also spent time at
Bruker as Senior Applications Scientist in the Time
Domain NMR division, Technical Director of the Time
Domain products for Asia Pacific, and General
Manager of Bruker Optics China. Dr. Xie has been
focusing on developing new NMR techniques for
unconventional mudstones since he joined Core Lab in
November 2012.
Robert Lee is currently the General Manager for the
Petroleum
Services
Division
Core
Analysis
Laboratories located within the United States. He is
past Area Manager for Core Laboratories’ Advanced
Rock Properties laboratory located in Houston, Texas.
10