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Two phase relative permeabilities for gas and water in selected European coals
Sevket Durucana, Mustafa Ahsanb, Ji-Quan Shia, Amer Syeda, Anna Korrea aDepartment of Earth Science and Engineering, Royal School of Mines, Imperial College London, London SW7 2BP, UK
bSasol Petroleum International Ltd., 6th Floor 101 Wigmore St, London W1U 1QU, UK
Abstract
Gas-water relative permeability behaviour of seven European coals of different ranks was
characterised in order to enhance the scientific understanding of the fundamental processes of
two-phase flow taking place within the macrostructure of coal. Laboratory experiments were
carried out on cylindrical coal samples using the unsteady state method to measure gas-water
relative permeabilities due to its operational simplicity. The impact of factors such as
wettability and overburden pressure on coal relative permeabilities were assessed.
Considerable variation in the shapes of the relative permeability curves for different rank
coals was observed, which was attributed to the heterogeneous nature of coal.
Key words: Relative permeability; coalbed methane; enhanced coalbed methane; laboratory experiments
1. Introduction
Coalbed Methane (CBM) or Enhanced Coalbed Methane (ECBM) production using CO2
injection is initiated through a resource evaluation process involving numerical simulations,
making use of reservoir data that has either been estimated through empirical correlations and
history matching of field data, or derived from laboratory tests on coals from a different basin
altogether. As coal is a highly heterogeneous rock, any discrepancies in its reservoir
characteristics can significantly impact the simulation results for a field site.
When a virgin coalbed methane reservoir is first encountered, the entire cleat network is
normally saturated with water and there are small or insignificant quantities of free gas
present. The presence of water significantly hinders the flow of methane through coal seams
and vice versa. Consequently, the effective permeabilities to both water and methane are
reduced. In order to evaluate the deliverability of coalbed methane wells it is important to
Corresponding author. Tel.: +44-20-7594-7354; fax: +44-20-7594-7444. E-mail address: [email protected]
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determine the effective permeability for the reservoir throughout its production life (when
two-phase flow is prevalent), and this effect is described quantitatively in terms of the coal
relative permeabilities to the gas and water phases. Fluid flow through the cleat system also
depends on the distribution of fluids in the cleats, which is related to capillary pressure. A
clear appreciation of the internal pore structure of coal and its interaction with gas and water
is required if one is to understand the mechanisms of two-phase flow in a complex porous
media such as coal.
Water can exist in coal in a variety of forms, including free water in the cleats, chemically
bound water of hydration, and water adsorbed onto the surface of the matrix blocks. For
water-saturated coals, increases in gas relative permeability help to restrict water production
and improve gas flow as the seam becomes progressively dewatered. During this process
whereby water is withdrawn from the cleats, there is a change from water relative
permeability dominating to gas relative permeability becoming more dominant. At the same
time, coals generally possess high irreducible water saturations in the cleats, which can be up
to 80%. Their relative permeability to gas is therefore quite low, and according to Meaney
and Paterson [1], it can be as low as 10% of the absolute permeability in some coals.
Many coals are described as hydrophilic, where water is the preferred wetting phase in the
cleats. Additionally, some of this water may reside in the larger pores of the matrix, rather
than the micropores which are fully gas saturated. This hinders the migration of gas from the
smaller interstices deep inside the matrix, therefore the gas will not become mobile until the
water saturation has fallen significantly below 100%. This point is referred to as the critical
gas saturation, and underlines the reason why substantial volumes of water may need to be
produced from a well before gas flow is detected.
However, it should be noted that the matrix, particularly the small micropores, are coated
with methane, causing the matrix to be gas wet, despite the cleats being water wet and often
possessing a high irreducible water saturation.
The shape of the relative permeability curves is dependent on whether the coal is wetted
preferentially by water or gas, which in turn is a function of the lithotypes that constitute the
coal. For instance, clarain and vitrain tend to prefer gas, while durain and fusain are more
easily wetted by water. Moreover, in conventional gas reservoirs, the rock surfaces tend to be
water-wet like the cleats in coalbeds, whereas in coal seams, the methane is adsorbed onto the
matrix, therefore it may well be methane wet. Consequently, coals could potentially display a
3
mixture of water wet, methane wet and intermediate wettability behaviour, depending on the
degree of mineralisation. Indeed it is this heterogeneity of coal that is largely responsible for
the variability in relative permeability curves.
A survey of the literature reveals that very little experimental data has been reported for
coal relative permeability, and there are often large discrepancies between field and
laboratory derived curves. There are still no generally accepted methods in the industry for
laboratory measurement of relative permeability in coal. Similarly, few accepted standards
are available for comparing such data. This is primarily due to the physical properties of coal,
which make it difficult for accurate measurements to be taken. The principal reasons why
relative permeability data are not easily obtainable include: the friable and brittle nature of
coals; the low porosity of the cleat network, which requires the accurate measurement of very
small volumes of water; and the stress dependent nature of coal permeability.
Most of the early work in this field was carried out by Reznik et al. [2] who suggested
laboratory tests for determining the air-water relative permeability behaviour of Pittsburgh
coals. Relative permeabilities were measured at steady state conditions with both increasing
and decreasing water saturations. However, water relative permeability values could not be
measured directly, and had to be inferred from corresponding gas relative permeability data
using Corey’s relationships [3]. Dabbous et al. [4] extended this work by determining gas
relative permeabilities at two different overburden pressures. These techniques were
improved considerably by Puri et al. [5] who formulated a standard procedure for sample
selection, handling, preparation and testing of coals.
In a similar way, Gash [6] conducted both steady state and unsteady state tests using tracer
methods, and found that the two techniques yielded comparable gas-water relative
permeability curves, within the experimental error with which saturations could be
determined. Later on, Gash et al. [7] assessed the effect of cleat orientation and confining
pressure on cleat porosity, permeability and relative permeability for Fruitland coals. An
increase in the confining pressure from 450 psi (3.1 MPa) to 1,000 psi (6.9 MPa) caused the
gas relative permeability to decrease less than the water relative permeability.
Laboratory studies carried out by Meaney and Paterson [1] on coal taken from the Bowen
Basin in Australia indicated that the separation of water and gas in the field due to gravity
resulted in higher effective permeabilities than what was measured in the laboratory. This
suggests that actual relative permeabilities in the field are likely to be higher where there is
4
gravity segregation. For such flow systems it may be more appropriate to use straight-line
relative permeability relationships since capillary effects are considered negligible in
segregated flow. Shen et al. (2011) investigated the relative permeabilities to gas and water in
different rank coals selected from South Qinshui Basin, China under various gas/water
saturations through water replacement with methane using an unsteady-state method.
In this study the gas-water relative permeability behaviour of different coal types is
characterised in order to further our understanding of the fundamental processes of two-phase
flow taking place within the macrostructure of coal. New relative permeability curves for a
range of European coals of varying rank are presented and analysed. This is realised
primarily through laboratory tests, where gas-water relative permeability curves are
determined for coals, and the impact of factors such as wettability, absolute permeability and
overburden pressure, on coal relative permeability, are assessed. It is hoped that the results
will provide characterisation data that would enable CBM and ECBM simulators to better
describe in situ reservoir conditions and evaluate the effect of carbon dioxide injection on gas
productivity.
2. Relative permeability measurement using unsteady state method
The two most common experimental techniques used in determining relative permeability
data are the steady state and unsteady state methods. Laboratory experiments presented here
were carried out using the unsteady state method [9] due to its operational simplicity. In this
method, the core is initially saturated with water, which is subsequently displaced by
continuous injection of a gas. Saturations vary throughout the experiment and therefore
equilibrium is never attained. The pressure differential and flow rates of the produced fluids
are monitored as a function of time, and the corresponding relative permeabilities are
deduced using Buckley-Leverett displacement theory [10]. The unsteady state gas flood
attempts to replicate the displacement of water in the cleats by gas desorbed from the matrix.
2.1. Coal sample collection and preparation
Large coal blocks representative of coal ranks from High Volatile Bituminous to Anthracite
were collected from opencast and underground coal mines in the United Kingdom, France
and Germany as:
- the Schwalbach seam from the Ensdorf underground colliery in Saarland, Germany
5
- the No.1 seam from the Warndt-Luisenthal (W-L) underground colliery in Saarland,
Germany
- the Splint seam from the Watson Head open cast site in Lanarkshire, Scotland
- the Tupton seam from the Carrington Farm open cast site in Derbyshire, UK
- the Dora seam from the Rumeaux underground colliery in Lorraine, France
- the 9ft seam from the Selar open cast site in South Wales, UK
- the 7ft seam from the Tower underground colliery in South Wales, UK
In order to preserve their natural moisture content and prevent oxidation during transport
and storage, the blocks were wrapped in protective plastic sheeting at the mine site and
placed in sealed wooden containers. Samples taken from the coal blocks were later cut to the
appropriate sizes and used in different tests. Before initiating the laboratory relative
permeability measurements the coals were characterised for rank, porosity, absolute
permeability and mechanical/elastic properties as reported in Table 1.
Sample selection procedures outlined by Hyman et al. [11], together with
recommendations for measuring relative permeability by Gash et al. [7], were adopted during
the tests,. Efforts were made to select core samples that were as homogeneous as possible so
that the pressure driving force and fluid properties could be maintained at a constant level
throughout the experiment. However, given the anisotropic and highly heterogeneous nature
of coal, this was often difficult to achieve.
Freshly cut core samples of 50 mm diameter were initially placed in a desiccator to help
eliminate any residual gas from the samples. These were then vacuum dried at 60°C to
remove free water in the cleats which could potentially initiate relative permeability effects.
Care was also taken to minimise damage to the coal structure and the formation of artificially
induced fractures, by not using a conventional oven. After about 24 hours of drying, the cores
were weighed. This was followed by full saturation using degassed water and a vacuum
pump. The cores were then re-weighed after 3 days of saturation to establish the pore volume
and macroporosities.
2.2 Experimental set up and test procedure
6
During the measurements, a gas-water separation unit and a backpressure device were
connected in series to the outlet end of the Hassler cell core holder as illustrated in Fig. 1. The
gas-liquid separation tube (Tube 2) was designed especially tall to a height of 1.5 m so as to
accommodate as much gas as possible, yet sufficiently thin to minimise errors whilst reading
fluid levels. The internal diameter and wall thickness of the tubes were 25 mm and 6 mm
respectively. The Hassler cell was designed to withstand stresses of up to 100 MPa. Its end
platens were fitted with seals consisting of Viton O-rings possessing a shore hardness factor
of 90 to minimise deformation due to pressure. The gas-water separator tube was partially
filled with a low density paraffin oil, while the gas and water flow rates were measured by the
main outer tube (Tube 1) and the small upturned syringe respectively.
A single saturated coal specimen was inserted into a rubber core sleeve, which was then
loaded into the oil-filled Hassler cell. A confining pressure of 1,000 psi (6.9 MPa) was
applied to simulate the effect of overburden stress. For a number of coal types, the absolute
and relative permeability tests were repeated at high (6.9 MPa) and low (4.1 MPa) confining
pressures in order to assess the effect of overburden stress on the internal cleat structure and
pore size distribution.
Injection of gas into the Hassler cell causes water to be forced out of the fully saturated
core and simulates a drainage displacement process, as the saturation of the wetting phase
decreases throughout the experiment. As water is produced, it accumulates in the small
syringe forcing the oil column to move upwards. When gas production commences, it pushes
the paraffin oil downwards in the tall tube (Tube 1) and any oil that is displaced is transferred
to the second tube (Tube 2), which serves as an interface across which the backpressure is
transmitted. Due to its non-adsorbing characteristics and smaller molecular size, helium was
used as the injected gas in the experiments.
During the experiments, an overall pressure differential in the range of 50-60 psi (0.34 -
0.41 MPa) was applied across the core, based on an upstream gas injection pressure of 250
psi and a downstream backpressure of approximately 200 psi. The pressure gradient was
selected so as to be large enough to minimise capillary end effects, but also sufficiently small
compared with the total system pressure to render compressibility effects negligible.
Flow measurements were started once the inlet and outlet pressures had ceased to
fluctuate. Data were recorded more frequently just after gas breakthrough when flow rates
began changing more rapidly. Upstream and downstream pressures were also monitored at
7
regular intervals. The use of sensitive Kenmac pressure regulators helped to achieve better
control over the pressures at each end.
Gas flooding was continued until approximately 4 litres of helium gas had been flowed
through the sample. This was done to ensure that the test was terminated only when the water
relative permeability had become negligible and the gas relative permeability was stable.
Once the separation system could no longer hold any more produced gas, the test was
terminated.
If the same core was to be used again for a repeat test, water was pumped through it to
flush out any gas that had accumulated inside. A backpressure was also applied in the
opposite direction to create a surging effect to facilitate the expulsion of this trapped gas. At
the end of each test the cleat porosity was checked by observing the total volume of water
expelled from the core as a result of the gas flood.
3. Relative permeability results and analysis
The Johnson, Bossler and Neumann (JBN) [9] method was used to calculate relative
permeability curves from the unsteady state test data. In order to apply this procedure
successfully, the system was allowed to stabilise over a one-month period prior to the
experiments so as to minimise capillary end effects. Average end points for different coals
are shown in Table 1 (bottom three columns), along with other relevant coal characterisation
data obtained during laboratory work and data analysis. Examples of representative relative
permeability data derived for each of the seven coal types from the laboratory tests are
presented in Fig. 2.
Splint (Fig. 2c) appears to be quite different from the other coals, having an abnormally
high irreducible water saturation and steep relative permeability curves. The samples were
heavily fractured with large visible flow conduits that were responsible for the channelling of
gas and water at high flow rates not ideal for relative permeability experiments. Similar
behaviour has been reported for sub-bituminous coals in the Powder River basin. The fact
that Splint and Selar 9ft (Fig. 2f) have irreducible saturations at opposite ends of the
saturation range typifies the variability that is so common in coals. Selar 9ft is also mildly gas
wet with an average equipotential flow point (cross point saturation) in the range between
0.55 and 0.60, i.e. greater than 0.5. It is the only coal from the set which exhibited this kind of
behaviour as all the others were water wet to differing degrees (Table 1). Nevertheless, such
conclusions are based on empirical correlations and should therefore be treated with caution.
8
Tupton (Fig. 2d), Selar 9ft (Fig. 2f) and Tower 7ft (Fig. 2g) coals generally appear to have
more familiar curve shapes and are comparable to those determined by Gash et al. [7]. In
particular, data from Tower 7ft and Selar 9ft, which have a similar rank and elastic properties,
display a greater coherence than Tupton coal, whose data are moderately dispersed.
Some of the coals, notably Schwalbach (Fig. 2a) Warndt-Luisenthal No.1 (Fig. 2b) and
Dora (Fig.2e) exhibit convex shaped gas relative permeability curves and a relatively flatter
water relative permeability profile. All three coals originate from the Saar/Lorraine Basins
shared by France and Germany. In the case of Schwalbach, the extended water leg could be
attributed to its robust mechanical properties and low permeability, hence the much longer
period over which tests had to be conducted. The breakthrough time for Schwalbach samples
ranged between 12 to15 hours while only 30-45 minutes elapsed in the case of Splint.
The convex shape of the curves suggests that gas flow is not occurring completely through
the main cleat pathways. Instead, part of it is passing through the matrix or other units within
the coal structure. Although water saturation is decreasing, the regions within the structure
from which water is being driven out do not contribute significantly to retarding gas flow. On
the other hand, if the curves are concaved upwards or straight lines, then the gas is able to
drive the water more easily.
Post breakthrough water production was very small in each case, giving rise to generally
low water relative permeabilities. Critical gas saturations (Sgcrit) obtained for the seven
European coals tested appear to be spread out over a broad range of saturations but were
generally found to lie in the 15-35 % band, which sits at the upper end of the range reported
in the literature (Table 2). Irreducible water saturations (Swirr) ranged from 15-40 % for all
coal types except Splint. These values are generally lower than those obtained from previous
work (Table 2).
3.1 Effect of wettability on coal relative permeability
All the coals were found to be water wet to differing degrees by virtue of their cross point gas
saturations being less than 0.50, except Selar 9ft, which displayed moderate gas wettability.
Splint coal was the most water wet with an average cross point saturation of only 0.21. The
composition of a coal in terms of its mineral matter content and the dominant lithotypes
influences the wettability, which in turn affects the relative permeability. The presence of
more clarain and vitrain bands in Selar 9ft coal (Table 3) may explain its gas wetness.
9
Similarly, coal samples from the Lorraine basin are considered to be more gas wet in
comparison to Warndt-Luisenthal No.1 which is strongly water wet. This tendency towards
intermediate gas wettability in the former is characterised by the following features as
demonstrated in Fig. 3.
An increase in gas saturation at the crossover point from 0.35 to 0.42.
An increase in the cross point relative permeability itself from 0.11 to 0.19.
An overall decrease in the gas relative permeability curve and increase in water
relative permeability values.
A decrease in the irreducible water saturation, i.e. the 1-Swirr end point increases from
0.80 to 0.84 on the chart.
It is worth noting that Dora coal is semi-anthracitic in terms of rank but also contains a
significant amount of ash,constituting some 36.7% by weight.
Coal wettability can also be affected by monolayers of adsorbed methane or carbon
dioxide, which may act as surface active polar compounds. Thicker organic materials
deposited onto coal could have an impact as well. In coal seams where methane productivity
is hindered by unfavourable gas-water mobility ratios, the gas relative permeability could be
improved by altering the wettability of the coal artificially using particular agents that
increase the gas relative permeability. However, given the highly stress dependent nature of
coal permeability, the feasibility of such processes would need to analysed in depth.
3.2 Effect of confining pressure on coal relative permeability
The only published studies to date that have reported the effect of confining pressure on
coal relative permeability are by Dabbous et al. [4] and Gash et al. [7]. Their results have so
far been inconclusive. Studies by Gash et al [7] found that an increase in confining pressure
from 3.1 MPa to 6.9 MPa caused the gas relative permeability to decrease less than the water
relative permeability. Whilst the converse could also be true, where water relative
permeability increases by a greater extent than the relative permeability to gas, owing to a
reduction in confining pressure, neither effect was clearly observed during these experiments.
Fig. 4 shows comparisons between relative permeability data obtained at two different
confining pressures for Tupton and Tower 7ft coals respectively. The change in stress from
4.1 MPa to 6.9 MPa causes a small but noticeable shift in the curves towards lower relative
permeabilities. The interpreted end point saturations are also reduced, with the irreducible
10
water saturation in particular being higher due to the entrapment of water pockets. There is
also a slight shift towards lower gas saturations, which is confirmed by Dabbous et al. [4]
who measured gas relative permeabilities for Pittsburgh coals at overburden pressures of 1.38
MPa and 4.14 MPa. However, their end points appeared to be independent of confining
pressure and there was even a slight increase in gas relative permeability at the higher
overburden stress level.
Earlier breakthrough was noticed during some of the laboratory tests at higher confining
pressures. However, this behaviour was not observed consistently and may be insignificant
because, although the application of confining stress can cause the cleats to narrow, it might
not be sufficiently large to alter the cleat configuration.
4. Discussion
Research has suggested that when the effect of large cleats dominates, the relative
permeability curves become straighter and narrower, while if the matrix effect is more
predominant then the curves tend to be spread over a wider saturation range and are less
linear. This trend was observed in the results where those samples containing a larger
concentration of fractures parallel to the direction of flow tended to give rise to steeper
curves, resembling straight lines over a narrow saturation range. This was accompanied by an
overall shift towards higher water saturations and corroborates the work of previous
researchers such as Meaney and Paterson [1].
On the other hand, some of the curves obtained so far have displayed a very sharp increase
in gas relative permeability at high gas saturations, while a much shallower decrease in water
relative permeability is observed at lower values. Consequently, the water relative
permeability effectively falls to zero very soon after breakthrough has occurred, confirming a
high irreducible water saturation. This behaviour could represent a possible shift from the
cleat contribution initially dominating to the matrix becoming more prevalent later on.
Further investigation is necessary to establish if it is realistically possible to obtain separate
cleat and matrix relative permeability curves.
It is worth noting that in Fig. 5 the initial productivity index (q/ΔP)i influences variation of
data along the relative permeability axis while pore volume affects variation in the gas
saturation direction.
11
Average relative permeability data for all coals are compared as relative permeability
ratios on the same axes in Fig. 6. Apart from Splint and Selar 9ft, all other lines fall within a
similar range and are bounded by the envelope shown. The gas saturations at which krg/krw =
1, i.e. the equipotential flow point, range between 0.29-0.38 within the envelope. At the same
time, the curves are generally linear for the four UK coals and may be described by a
relationship of the form ln (krg/krw) = aSg + ln b, where a and b are constants. However, coals
from the Saar/Lorraine Basins are more difficult to characterise mathematically due to their
non-linear nature. Whilst the abnormal behaviour of the Splint coal can be accounted for by
its highly fractured nature, the deviation of Selar 9ft is more difficult to explain.
Helium was used during the relative permeability tests and it was assumed that gas did not
adsorb onto the coal during drainage. In reality, however, the presence of adsorptive gases
such as methane and CO2 means that the process would be occurring, albeit much slower and
over a long period, and could therefore affect coal permeability and relative permeability in
the seams.
Since coal is a highly heterogeneous material, the standard deviations of data do not
necessarily indicate measurement error, and therefore it would not be appropriate to use this
by examining final results alone.
4.1 Use of empirical correlations
One of the main difficulties experienced during the experiments was the measurement of
water relative permeabilities directly. This was partly due to the low pore volumes of the core
samples, which meant that there was insufficient production of water to be able to determine
krw values over a wide enough saturation range. This was mitigated to some extent by using
regression extrapolation or Brooks-Corey relationships to compute actual values near the end
points. Whether or not the use of such correlations is truly applicable to coal seams is still an
area of contention. The modified Corey equations are based on flow through capillary tubes
of a particular distribution of pore throat radii. However, the cleat system in coals does not
actually have a geometry resembling capillary tubes.
Boatman (1961): 35.1)( wwrw SSk and 5.05.025.0 ])()(1)[1( wwwrg SSSk (2.24)
where krw is the water relative permeability, krg is the gas relative permeability, Sw is the water
saturation and the normalised effective water saturation (Sw*) is given by
12
grwirr
wirrww SS
SSS
1 (2.25)
Brooks & Corey (1964): awrw Sk )( and )1()1( 2 w
bwrg SSk (2.26)
Equations 2.24 to 2.26 were applied to the experimental data for the different coals giving
rise to average values of the modified Corey exponents summarised in Table 4.
4.2 Sources of error in the results
A satisfactory level of consistency was observed between samples tested from the same coal
type as indicated in Fig. 7.
Errors occurred whilst reading the meniscus levels of the gas-liquid separator as well as
due to inaccuracies in pressure readings. The total error involved in measuring the liquid
menisci in the separator tube was approximately 1.0 cm3. Assuming an average volume
measurement of 6 cm3, the percentage error for each test was about 17 %. The error in
reading pressures was of the order of 0.5 psi (3.45 kPa) for both gauges over a pressure
range of 0-600 psi (0-4.14 MPa).
Relative permeability curves for some of the Schwalbach samples were also found to
match remarkably well with curves determined independently using data from the Weiher-1
well, also drilled in the Saar coal Basin [12]. The characteristic convex shape of the gas
relative permeability curve was observed in both cases, thus highlighting a clear resemblance
between the two sets of data as illustrated in Fig. 8. The lines shown for the Schwalbach coal
are only a visual guide and should not be treated as fitted curves.
One of the limitations of the gas-liquid separator is the fact that gas bubbles pass through
the oil-water interface causing it to become irregular and unstable, and therefore resulting in
inaccuracies when reading water volumes. Whilst saturating the cores in water, there was a
tendency for very small pieces of coal to break off; this will have altered the pore volume
calculations. It could also be argued that the relative permeability tests were not truly
representative of reservoir flow conditions because inert gases such as helium or nitrogen
were used instead of methane, which would cause swelling of the coal. However, it was felt
that the gas flow rates were too high for the influence of matrix swelling to be satisfactorily
observable during the time period over which the tests were conducted. Moreover, the need to
isolate the effects of matrix swelling and two-phase flow were considered important at this
stage, so that an initial baseline of results could be generated. Safety issues with regards to
13
handling a methane-water mixture at the downstream end were also taken into account for
this decision.
4.3. Mechanism for two-phase flow in coal
Based on the analysis, it was observed that some two-phase flow is active in the outer regions
of the matrix near the cleat boundary. However, this does not mean that there are relative
permeability effects necessarily taking place within the bulk of the matrix block. Water
particles accumulate in the larger macropores forming a coat of water adjacent to the
cleat/matrix boundary. As a result, gas particles diffusing from the central regions of the
matrix are unable to pass into the cleat network until the concentration of water has dropped
sufficiently to allow gas to find a pathway. This phenomenon is described in Fig. 9.
5. Conclusions
Gas-water relative permeability experiments carried out on different ranks of European
coals using an unsteady state method yielded critical gas saturations in the range of 0.15 to
0.35. Irreducible water saturations ranged between 0.15 and 0.40.
Considerable variability in the shapes of the relative permeability curves was also
observed, which is mainly attributed to the heterogeneous nature of coal, both in terms of
lithotype composition and cleat-matrix configuration. Modified Corey equations were used to
fit some of the experimental data. Although end point saturation values lacked consistency,
the results were generally found to be in keeping with the limited work carried out to date.
References
[1] Meaney K, Paterson L. Relative permeability in coal. In: SPE Asia Pacific Oil & Gas
Conference, Adelaide, Australia;1996; SPE 36986.
[2] Reznik AA, Dabbous MK, Taber JJ, Fulton PF. Air-water relative permeability studies of
Pittsburgh and Pocahontas coals. SPE Trans. AIME 1974; 257:556-61.
[3] Corey AT. The interrelation between gas and oil relative permeabilities. Producers
Monthly 1954; 19 (1): 38-41.
[4] Dabbous MK, Reznik AA, Mody BG, Fulton PF, Taber JJ. Gas-water capillary pressure
in coal at various overburden pressures. SPE Journal 1976; 16 (5): 261-268.
14
[5] Puri R, Evanoff JC, Brugler ML. Measurement of coal cleat porosity and relative
permeability characteristics. In: SPE Gas Technology Symposium, Houston, Texas; 1991;
SPE paper 21491.
[6] Gash BW. Measurement of “rock properties” in coal for coalbed methane production. In:
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pressure on cleat porosity, permeability and relative permeability in coal. In: Proc. Int.
Coalbed Methane Symp. 1993; 9321: 247-55.
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different rank coals. Int. J. Coal Geology 2011; 86: 266-275.
[9] Johnson EF, Bossler DP, Naumann VO. Calculation of relative permeability from
displacement experiments. Trans. AIME 1959; 216:370-72.
[10] Saulsberry JL, Schafer PS, Schraufnagel RA. A guide to coalbed methane reservoir
engineering. Gas Research Institute; 1996.
[11] Hyman LA, Brugler ML, Daneshjou DH, Ohen HA. Advances in laboratory
measurement techniques of relative permeability and capillary pressure for coal seams.
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[12] Lepagney C, Leclercq G. CBM Project COALMET: Simulation of the Coalbed Methane
Production , Gaz de France;2000.
15
Table 1. Coal characterisation data obtained during the laboratory experiments and data analysis.
Coal Seam
Schwalbach W-L No.1 Splint Tupton Dora Selar 9ft Tower 7ft
Volatile Matter (d.a.f) (%)
43.6 41.6 40.2 35.3 16.5 10.2 9.1
Fixed Carbon (d.a.f.) (%)
56.4 58.4 59.8 64.7 83. 5 89.8 90.9
Vitrinite Reflectance (%)
0.79 0.71 0.55 0.49 0.71 2.41 2.28
Moisture Content (%) 1.54 1.39 13.3 15.7 0.83 2.07 0.86
Coal Rank High Vol.
Bituminous B
High Vol. Bituminous
B
High Vol. Bituminous
B
High Vol. Bituminous
A
Semi-anthracite Anthracite Anthracite
Young’s Modulus, E (GPa) 3.20 – 3.90 2.19 – 2.69 1.80 – 2.30 1.10 – 1.62 2.41 – 2.84
1.75 – 2.58
1.82 – 2.26
Poisson’s Ratio, 0.26 0.42 0.34 0.36 0.38 0.40 0.32
Absolute Permeability (mD)
0.90 0.52 0.73 2.15 5.52 9.51 2.93
Porosity (%) 0.63 1.76 1.80 1.35 1.38 0.96 0.12
Average Critical Gas Saturation 0.35 0.32 0.15 0.23 0.33 0.40 0.25
Irreducible Water Saturation 0.22 0.19 0.68 0.36 0.15 0.17 0.34
Average Cross Point Gas Saturation 0.40 0.35 0.21 0.38 0.42 0.58 0.37
Table 2. Summary of end point relative permeability data from previous studies.
Source Swirr Sgcrit Cross-point Sg
Reznik et al. (1974) 0.60 0.07 0.15
Jones et al. (1988) 0.80 0.01 0.05
Young (1989) 0.36 0.04 0.38
Puri et al. (1991) - San Juan 0.38 0.01 0.43
Gash (1991) - Unsteady State 0.35 0.32 0.40
Hyman et al. (1992) 0.40 0.18 0.27
Meaney and Paterson (1996) 0.60 0.11 0.31
Shen et al. (2011) 0.47-0.74 0.02-0.36 0.10-0.27
16
Table 3. Coal petrology data.
Vitrinite Liptinite Inertinite Minerals
Schwalbach 75.4 17.4 5.0 2.2
Warndt-Luisenthal No.1 74.4 15.6 9.0 1.0
Splint NA NA NA NA
Tupton 59.4 14 25.8 0.8
Dora 31.4 0 0 68.6
Selar 9ft 85.6 0 14.2 0.2
Tower 7ft 84.6 0 15.2 0.2
Table 4. Corey exponents for coals of different rank.
Coal Type Water Exponent Gas Exponent
Schwalbach 1.23 2.21
Warndt-Luisenthal No.1 4.15 1.73
Splint 3.71 2.12
Tupton 4.90 1.50
Lorraine 3.19 2.79
Selar 9ft 5.10 2.79
Tower 7ft 3.15 1.51
17
Fig. 1. The experimental set-up for the relative permeability tests.
18
(a) Schwalbach – Sample 4 (b) Warndt-Luisenthal No.1 – Sample 5
(c) Splint – Sample 2 (d) Tupton – Sample 6
(e) Dora – Sample 10 (f) Selar 9ft – Sample 5
(g) Tower 7ft – Sample 7
Fig. 2. Examples of relative permeability curves for the seven coals tested.
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Gas Saturation
Rel
ativ
e P
erm
eabi
lity
krgkrw
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Gas Saturation
Rel
ativ
e P
erm
eabi
lity
krgkrw
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Gas Saturation
Rel
ativ
e P
erm
eabi
lity
krgkrw
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Gas Saturation
Rel
ativ
e P
erm
eabi
lity
krgkrw
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Gas Saturation
Rel
ativ
e P
erm
eabi
lity
krgkrw
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Gas Saturation
Rel
ativ
e P
erm
eabi
lity
krgkrw
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Gas Saturation
Rel
ativ
e P
erm
eabi
lity
krgkrw
19
Fig. 3. Effect of wettability on relative permeability curves.
Fig. 4 Effect of confining pressure on relative permeability for Tower 7ft and Tupton coal samples.
Fig.5. Cleat and matrix effects on relative permeability behaviour.
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Gas Saturation
Rel
ativ
e P
erm
eabi
lity
krg (Warndt No.1)
krw (Warndt No.1)
krg (Lorraine)
krw (Lorraine)
Tower 7ft (Sample 4)
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Gas Saturation
Rel
ativ
e P
erm
eabi
lity
krg (4.1 MPa)
krw (4.1 MPa)
krg (6.9 MPa)
krw (6.9 MPa)
Tupton (Sample 2)
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Gas Saturation
Rel
ativ
e P
erm
eabi
lity
krg (4.1 MPa)
krw (4.1 MPa)
krg (6.9 MPa)
krw (6.9 MPa)
0.45 0.85Gas Saturation
Rel
ativ
e P
erm
eabi
lity
All gas produced here through the
main cleat system
All gas produced from smaller cleats
or even matrix
0.0
1.0
1.0
20
Fig. 6. Relative permeability ratios for the averaged curves determined in the laboratory.
(a) Splint (b) Schwalbach
Fig.7. Relative permeability curves for different samples from the same coal seam.
0.001
0.01
0.1
1
10
100
1000
0.0 0.2 0.4 0.6 0.8 1.0Sg
krg /kr
w
krg (Schwalbach) krg (Lorraine) krg (Tower 7ft)krg (Tupton) krg (Splint) krg (Warndt)krg (Selar 9ft)
Splint (Samples 2 and 3)
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0Gas Saturation
Rel
ativ
e P
erm
eabi
lity
krg (Sample 2)
krw (Sample 2)
krg (Sample 3)
krw (Sample 3)
Schwalbach (Samples 1 and 4)
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Gas Saturation
Rel
ativ
e P
erm
eabi
lity
krg (Sample 1)
krw (Sample 1)
krg (Sample 4)
krw (Sample 4)
21
(a) Weiher‐1 (b) Schwalbach
Fig. 8. Relative permeability curves for different coals from the Saar Basin.
Fig. 9. Schematic description of the two-phase flow near the boundary between cleat and matrix.
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Water Saturation
Rel
ativ
e P
erm
eabi
lity
Gas
Water
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Water SaturationR
ela
tive
Pe
rme
ab
ility
Gas
Water
Gas particles in bulk of matrix
Coat of water along cleat/matrix
boundary
Cleat
Matrix Block
Gas particles unable to leave matrix until
water saturation has decreased