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Carbon dioxide gas permeability of coal core samples and estimation of fracture aperture width
International Journal of Coal Geology 83 (2010) 1–10
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International Journal of Coal Geology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i j c o a l g e o
Carbon dioxide gas permeability of coal core samples and estimation of fracture aperture width Phung Quoc Huy ⁎, Kyuro Sasaki, Yuichi Sugai, Satoshi Ichikawa Faculty of Engineering, Kyushu University, Fukuoka, Japan
a r t i c l e
i n f o
Article history: Received 15 November 2009 Received in revised form 15 March 2010 Accepted 16 March 2010 Available online 27 March 2010 Keywords: Permeability Cleats Fractures Homogeneous Heterogeneous Fracture aperture
a b s t r a c t The structure of cleats, or natural fractures in coal seams, is an important factor affecting gas permeability. Coal seam permeabilities have been classified into fracture and matrix flows. However, fractures in coal seams are generally not regular and usually are discontinuous. In addition, it is difficult to definitively distinguish the fracture and matrix permeabilities, and to measure the fracture widths or other necessary properties of fractures for permeability estimation. Typically gas permeability has been determined by using the Darcy equation for incompressible fluid flow and homogeneous porous media, even if the gas flow through fractures has different characteristics with respect to effective stress, which is given by the confined stress minus the gas pressure. In this study, permeability measurements were carried out with a new procedure and methodology to estimate the fracture width in coal core samples. This measurement method is an improvement on conventional permeability measuring methods. In this research, it was identified that fracture permeability can be estimated from measurements of gas flow rates in a limited small area using a pipe attachment on the end of the surface of the core. Finally, a linear equation composed of fracture permeability and matrix permeability is presented. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Gas permeability of coal seams is one of the main parameters used to evaluate CH4 gas emission into working faces, such as heading faces and long wall faces in coal mines. Gas permeability also is important for estimating of the gas drainage rate or gas recovery ratio from coal seams. However, gas permeability is related to many factors, such as the cleat and fracture systems (Harpalani and Chen, 1997; Olson et al., 2009); porosity, gas pressure and mechanical stress (Somerton et al., 1975; Palmer and Mansoori, 1998; Sasaki et al., 2004); fracture orientation (Laubach et al., 2004). Philip et al. (2005) investigated the effect of diagenesis on the initial flow properties of the fracture system, especially with respect to diagenetic effects on the connectivity of the fracture network. In the subsurface, over geologic time, carbonate, quartz, or other cement will precipitate on the fracture walls, often disrupting connected networks. Because permeability and simulation success are commonly limiting factors in gas well performance, knowledge of cleat characteristics and origins is essential for successful exploration and production (Laubach et al., 1998). Owing to the increasing importance of coalbeds as gas reservoirs, geologists are again becoming concerned with the characteristics and
⁎ Corresponding author. E-mail address: [email protected] (P.Q. Huy). 0166-5162/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.coal.2010.03.002
origins of cleat. For coalbed methane (CBM) extraction, knowledge of the properties of natural fractures is essential for planning exploration and development because their influence on recovery of CH4, and the local and regional flow of hydrocarbon and water. New mapping of cleat patterns, guided by recent conceptual advances in the description and theoretical understanding of fracture processes, is beginning to bring these patterns into focus. This, together with more rigorous study of the petrology of cleat development, may resolve uncertainties about causes of cleat that now hinder predictions of interwell-scale patterns of fractures in coal beds (Laubach et al., 1998). Seidle and Huitt (1995) measured deformations of a sample of high volatile C bituminous coal from the San Jan Basin during sorption and desorption of first CH4 then CO2. A pressure cycle was also run with helium, a non-sorbing gas, to determine mechanical compliance of the sample. Observed strain gauge behaviors are discussed and shrinkage coefficients for both gases reported. Matrix shrinkage was found to correlate with gas content rather than pressure, confirming the work of a previous investigator. Shrinkage coefficients varied more among replicate gauges aligned in the same direction than between gauges in different directions. Anisotropic shrinkage effects are discussed. Mazumder and Wolf (2008) noted that the matrix volume of coal swells when CO2/CH4 adsorb on the coal structure. In coalbed gas reservoirs, matrix swelling could cause the fracture aperture width to decrease, causing a considerable reduction in permeability. On a unit concentration basis, CO2 causes greater degree
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of coal-matrix swelling compared to CH4. Much of this difference is attributable to the differing sorption capacity that coal has towards CO2 and CH4 (Kross et al., 2002; Huy et al., 2009). This condition in a coal reservoir would lead to differential swelling. Differential swelling will have consequences in terms of porosity/permeability loss, with serious implication for the performance and implementation of carbon sequestration projects. Coal can be understood as a macromolecular cross-linked polymeric structure. Mazumder and Wolf (2008) have been investigated an experimental effort to measure the differential swelling effect of CO2/CH4 on this macromolecular structure and to theoretically translate that effect in terms of porosity and permeability. A unique feature of this work is that, real time permeability measurements were done to see the true effect of differential strain from CH4 saturated coal core flooding experiments. Using a matchstick geometry model, equations are derived for permeability change due to matrix shrinkage. Coefficients reported here are used in example calculations of absolute permeability and porosity increases during coalbed depletion (Seidle et al., 1992). The behavior of permeability with respect to effective stress is well described using the accepted exponential relationship (Pan et al., in press). As expected the measurements show permeability declines with increasing pore pressure at constant effective stress in response to coal swelling with gas adsorption with the magnitude of the decline depending on the gas type. Simultaneous measurements of coal strain found that the coal sample swells about 2.4% in CO2 at 13.5 MPa and about 1.6% in methane at 12.8 MPa. The swelling strains were modeled by Pan and Connell swelling model with reasonable accuracy and can be explained with empirical Langmuir-like equations too. Coal is known to be a complicated organic carbon material in its packing form and material composition. The characteristics of different coals depend on their coalification processes (Somerton et al., 1975). Some coals are homogeneous porous materials, and others, even in the same coal seam, are heterogeneous materials. Therefore, the determination of gas permeability characteristics is complicated and difficult. Furthermore, gas permeability depends on the sampling location and the same permeability may not be representative for all coal seams, since cleats, or natural fractures in coal seams, are important contributors to gas permeability. The relationship between cleat density and coal rank was first investigated by Ammosov and Eremin (1963). Their results showed that the cleat density increases gradually from brown coal to medium volatile bituminous coal, and then decreases with further rise in coal rank. The gas permeability of a coal core usually is determined by using the Darcy equation, and assuming a laminar gas flow and a homogeneous porous medium. It also is assumed that the gas flows out uniformly through the surface of the core. However, many coal seams have a heterogeneous characteristic for gas permeability. In some cases, the gases only flow through cleats or natural fractures distributed in the coal seam. Thus, the gas permeability measured within coal cores changes greatly and logarithmically, because it has strong sensitivity to the fracture density in the core. In this paper, the use of the Darcy equation to determine gas permeability is referred to as the “conventional method”. Somerton et al. (1975) determined the empirical equation to express the relationship between mean stress and permeability, described as follows: k −3 −0:10 −4 1=3 1=3 = exp −3 × 10 ⋅ σ* ⋅ k0 + 2 × 10 ⋅ σ ⋅ k0 * k0
The simplified relationship between effective stress and permeability for coal cores was presented by Sasaki et al. (2004) as follows: k = exp ð−β ⋅ σe Þ k0
where, σe = effective stress = σ − P, MPa; β = stress attenuation coefficients, MPa− 1. Based on measurements by Somerton et al. (1975), it can be assumed that the second term of the exponential function in Eq. (1) is neglected, which means that β can be calculated by Eq. (3) by converting the units from psi to MPa: −0:10
β = 0:45 ⋅ k0
:
ð3Þ
The permeability (k) can differ among cores, even if the cores are taken from the same position in the coal seam (Fig. 1). This means that the cores are not composed of homogeneous coal matrices, and that they include fractures with different widths, lengths, and distribution densities. Thus, when a higher effective stress is loaded, the gas flow channels within micro-fractures become narrower and some of the micro-fracture may become closed completely. Thus, use of conventional gas permeability equipment may not show the real coal-matrix permeability, since almost all core samples have fractures on their surfaces. For cores containing fractures, the gas flows out through areas that include internal fractures, but not outside these areas. Therefore, if the total flow rate and total cross-section areas of the core sample are used to calculate the fracture permeability, the permeability results will be very low compared with its true value. This is because the flow is divided by total cross-sectional areas of core, even though almost all the area of the core does not contribute to the gas flow. The surface of coal included matrix and fracture areas (Fig. 2). There are two types of fractures — continuous and discontinuous. A discontinuous fracture refers to the lack of gas flow from fracture lines observed in a scanned image of the surface. Somerton et al. (1975) also mentioned the presence of fractures, but they did not carry out investigations on fracture permeability. This study aimed to measure active fractures by an original measurement procedure to determine gas flow from areas with fractures. Based on these data, fracture width, length, and density were estimated. It is expected that the fracture permeability range measured in core samples corresponds to those of their coal seams. Furthermore, these basic permeability data can be applied to numerical simulations on gas flow in coal seams within the double porosity model used in CBM or CO2-ECBM projects. Fracture widths of coal samples might be a valuable parameter to determine the injection or production wells locations.
ð1Þ
where, k = permeability under stress, mD, k0 = permeability under zero stress, mD, σ* = static stress on the core sample, in psi units. In this equation, gas pressure is close to atmospheric pressure, and pressure differences between the two end surfaces (ΔP) is much less than σ*. This means that σ* is almost equal to the effective stress, σe.
ð2Þ
Fig. 1. Gas permeability versus effective stress.
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3. Measurement of gas permeability with the conventional method 3.1. Measurement apparatus A schematic diagram of the gas permeability measurement system is shown in Fig. 3. The system mainly consists of a Hassler core holder to set up tri-axial stresses conditions, with a high-pressure bomb for confining stress on the cylindrical surface, a hydraulic pump for axial stress on the end surfaces, gas cylinders with associated regulators and pressure gauges, relief valves, a differential pressure device, a gas flow meter and flow controller for flow rate measurements, and other necessary valves and tubes. To eliminate the influence of temperature variations on the permeability tests, the apparatus was placed in a temperature-controlled room. The Hassler sleeve permits applications of axial stress independently from the radial stress. CO2 gases were used to measure permeability of the core samples. Gas flow rate was controlled and measured by three kinds of flow meters, which were connected in series. The flow meters included a controller (Ueshima Brooks, Model 5893) with a maximum capacity of 20 cm3-std/min, a CO2 gas accumulated flow meter (KOFLOC, Model ACM-1A) with a maximum capacity of 500 cm3-std/min, and a soap-film flow meter for flow rates less than 5 cm3-std/min. Two pressure transducers (CHINO, Model PD-5119) and a differential pressure transducer (Rosemount, Model 11510P6S12M1B1) were set up in upstream and downstream positions near the end surfaces to measure the gauge pressures and differential pressure across the length of core sample.
Fig. 2. Definition of matrix and fractures.
2. Preparation of core samples Specimens were cored from a large block of coal (Table 1). The blocks were sampled from coal seams of Ha Lam, Maokhe coal mines in Quang Ninh coalfield (Vietnam), Shanxi coal field (China) and Bowen coal basin (Australia). After coring the coal blocks, the cores were covered with silicon rubber and wrapped with a thin rubber sleeve. After the 10 h required for hardening of the silicon rubber the core samples were cut into the required lengths with a diamond saw. To prevent breaking the coal samples under high hydrostatic stress conditions, the ends of the specimens were ground and made parallel to each other.
3.2. Permeability measurement procedure The sample was encapsulated between two stainless steel end caps equipped with perforations to evenly distribute gas flow and permeating pressure over the entire end surfaces. To ensure a leakfree seal, adjoining points between the end caps and the rubber jacket were clean, and a thin layer of grease was used on the seal. To investigate the effect of effective stress on gas permeability, the stress load on the coal core sample was increased from 1 to 6 MPa. A vacuum pump was used to remove air from the tubing lines for
Table 1 Specification of coal core samples. Core no.
Coal site
Weight (g)
Length (cm)
Diameter (cm)
Ash content (%)
Moisture content (%)
Volatile matter (%)
Fixed carbon
Coal rank
HL-11 MK-5 MK-4 MK-3 HL-4 MK-1 AUS-2 AUS-3 AUS-4 AUS-5 AUS-6 AUS-8 AUS-9 AUS-14 CH-4 CH-3 CH-5 CH-6 CH-7 CH-10 CH-11 CH-13
Vietnam Vietnam Vietnam Vietnam Vietnam Vietnam Australia Australia Australia Australia Australia Australia Australia Australia China China China China China China China China
60.29 86.43 79.71 114.17 103.07 121.61 99.10 98.89 98.68 100.27 99.36 99.22 103.75 71.66 74.09 84.49 71.80 80.30 84.40 86.40 87.30 75.00
4.30 5.23 4.82 6.90 3.80 7.35 7.50 7.00 7.00 7.00 7.00 7.00 7.00 5.23 4.30 5.00 4.30 4.40 4.95 5.00 4.80 4.40
3.50 3.80 3.81 3.80 3.50 3.80 3.80 3.80 3.81 3.80 3.80 3.80 3.80 3.80 3.80 3.81 3.80 3.80 3.81 3.80 3.88 3.84
2.5 29.7 30.5 30.8 2.6 28.3 4.2 4.1 4.6 4.3 4.4 4.0 4.5 4.3 15.2 16.2 13.5 15.1 14.8 14.6 15.3 15.5
3.0 4.5 4.6 5.0 4.8 4.1 9.9 8.3 8.9 8.6 9.4 8.2 7.9 8.7 2.3 3.1 2.7 3.0 2.6 2.9 2.7 3.2
6.9 6.5 5.9 5.8 6.2 5.9 36 36 33 25 35 36 35 34 7.2 5.3 6.9 5.9 6.8 5.7 6.4 5.8
87.6 59.3 59.0 58.4 86.4 61.7 50.2 52.0 54.0 61.7 51.3 51.7 52.3 53.3 75.3 75.4 76.9 76.0 75.8 76.8 75.6 75.5
Anthracite Anthracite Anthracite Anthracite Anthracite Anthracite Bituminous Bituminous Bituminous Bituminous Bituminous Bituminous Bituminous Bituminous Anthracite Anthracite Anthracite Anthracite Anthracite Anthracite Anthracite Anthracite
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Fig. 3. Schematic diagram of gas permeability measurement system.
permeation testing. Pore pressures were applied using CO2 gas, and the desired average and differential gas pressures were controlled by adjusting the regulator and the relief valve. The average gas pressure (pore pressure) changed from 0.1 to 0.7 MPa depending on the effective stress that was applied to the upstream tubing line by the regulator. The flow rate of CO2 gas released from the downstream line was measured with the flow meters. Gas permeability can be defined by Darcy's equation as follows: k=
2Q 0 μLP0 A P12 −P22
ð4Þ
where, k = gas permeability, (m2); Q0 = volumetric rate of flow at reference pressure, (m3/s); μ = gas viscosity, (Pa s); L = length of core sample, (m); P0 = reference pressure, (Pa); A = cross-section area of core sample, (m2); P1 = upstream gas pressure, (Pa); P2 = downstream gas pressure, (Pa). In this paper permeability, k, is defined in SI unit of m2, however unit of [mD] has been commonly used and easy to understand. The conversion factor from m2 to mD is expressed by 1 mD= 10− 15 m2. 4. Measurement of fracture aperture 4.1. Measurement apparatus Gas flow measurements were modified from the conventional method using the relative permeability testing apparatus (Core
Laboratory, USA). It mainly includes a core holder of 38 mm internal diameter, with an adjustable length core holder to measure core samples of various lengths. A synthetic rubber sleeve was used to hold the core sample. The higher pressure end was sealed by a cap, and the other end was open to the atmosphere (Fig. 4). The effective stress was created by a high-pressure bomb of N2, and the gas flow was supplied by a CO2 bomb with accurate pressure transducers. The effective pressure and pore pressure were adjusted independently. A tube of 3.0 mm in diameter and the soap-film gas flow meter were used to check the presence of gas flowing out from the fractures connected to the end surface of the core sample (Fig. 5). 4.2. Measurement procedures The procedure to estimate gas flow rate through fractures included the following steps: Step 1. Specification of fracture positions using a visualization method. In this step, the end surface of the core was opened to the atmosphere. Then, liquid soap was coated on the end surface. Soap bubbles were observed and the position of fractures noted (Fig. 6). Step 2. Measurement of gas flow rate through fractures. A pipe with 5.5 mm in diameter was used to separate gas flow from the surface area, including fractures (Fig. 7), and flow rates were measured with the soap-film flow meter.
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Fig. 4. Schematic diagram of experimental apparatus.
Step 3. Calculation of fracture widths. Fluid flow rates (under laminar flow condition) through narrow channels can be calculated with the following equation:
q=
W 3 ΔPl 12μL
ð5Þ
where, W = fracture width, (m); q = gas flow separated by the pipe at a part of fracture line, (m3/s); ΔP = pressure difference over the core length, (Pa); l = length of the fracture separated by the pipe (roughly equal to the pipe diameter), (m). Thus, fracture width was obtained from following Eq. (6) W=
Fig. 5. Parameters of core and fracture.
rffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 12qμL ΔPl
Fig. 6. Visualization of gas flow with soap liquid.
ð6Þ
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Fig. 8. Gas permeability versus effective stress of Vietnamese coal.
Fig. 7. Positioning of active fractures.
Step 4. Estimation of gas permeability on the fracture area. Darcy's law for incompressible fluid flow was calculated as: q=
kAΔP μL
ð7Þ
From Eqs. (5) and (7), the permeability within fracture areas, Ks, was evaluated with the following equation: Ks =
W3 l 12As
ð8Þ
where, As is the cross section of the flow tube, including fractures, (m2). It was assumed that the diameter of the tube (d) was roughly equal to the length of one fracture on the surface (Fig. 5). As =
π 2 l 4
ð9Þ
By substituting Eq. (9) into Eq. (8), Ks is obtained as follows: Ks =
1 W3 : 3π l
ð10Þ
wide range (0.6 to 1.2), compared with the Chinese and Australian coals. The value of β ranged from 0.8 to 1.2 for low permeability cores of k0 b 1 mD. However, the values decreased to a range of 0.6 to 0.8 for high permeability cores of k0 N 1 mD. It is assumed that the high permeability coal samples included both matrix pores and fractures, but flow rates depend on mainly fractures. Gas flow through the fractures constituted a large share of the total gas flow. For Australian coal (bituminous coal), β was not sensitive to the effective stress. This can be explained by the fact that the structure of bituminous coal has less micro-fractures than anthracite coal. Gas flow through micro-fractures depends on the effective stress, but β is not as sensitive to effective stress. Eq. (2) shows the relationship between gas permeability (k) and effective stress (σe). The behavior of stress-permeability can be modeled if k0 and β are determined. This means that there is an effect by fracture structure on permeability. The k0 range of Vietnamese coal cores was very wide (from 0.14 to 10 mD). Within this range, there are two permeability categories that are low and high permeabilities. Low permeability is considered to be less than 1 mD and high permeability is more than 1 mD. The average value of β for low permeability coals shows higher values than those of high permeability coals. This means that low permeability coals are highly dependent on effective stress. In low permeability coals, gas flow was mainly affected by pore arrangement and pore size. Samples with small pore sizes seemed to be gas-tight and well-packed.
5. Results and discussion 5.1. Conventional gas permeability and stress attenuation coefficient Results of CO2 permeability (k) versus effective stress (σe) for Vietnamese, Australian and Chinese coal cores are shown in Figs. 8–10. The graphs show that permeability of the cores was different from core to core even though they had been taken from the same coal block. Low permeability coals have low distribution densities of pores and microfractures, and they are very sensitive to σe. In the high effective stress range, the permeability decreased exponentially with σe, because the micro-pores and fractures were closed with increasing σe. The average permeability of coal core samples at σe = 0 is denoted as k0, and shows relative incidence of existing pores and fractures in the core samples. The stress attenuation coefficient (β) is the power constant of exponentially decreasing permeability against σe, which is not constant for the same kind of coal seams. Fig. 11 shows the relationship between k0 and β. For Vietnamese coal cores, β had a
Fig. 9. Gas permeability versus effective stress of Australian coal.
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Using measurements of gas flow at the outlet fracture area, the fracture width can be evaluated (see Fig. 14). The stress reduction exponent for the fracture width (ζ), and average fracture width, W (μm), are roughly expressed by an equation as follows: −1
W≈γ0 exp ð−ζσe Þ; γ0 = 7:7 e 20 μm and ζ = 0:11 e 0:14 MPa
Fig. 10. Gas permeability versus effective stress of Chinese coal.
A large reduction in low permeability coals may be attributed to the small size of pores. Somerton et al. (1975) showed that permeability is a function of four power of the pore radius. The low permeability coals normally include pores and a few micro-fractures. Thus, when the effective stress increases, the flow channels within micro-fractures become narrower, and some may close completely. Consequently, the permeability decreases dramatically at high effective stress levels, and gas permeability may even become zero when the effective stress is more than 5 MPa (MK-1 sample).
5.2. Fracture width and permeability Fig. 12 showed the gas flow distribution on the surface of core samples by using a new measurement method. Based on this method, active and inactive fractures can be clarified. The cross-section photo of core showed that many areas seem to be fractures, but in fact there is no any gas flow out. Permeability measurements on the fracture areas within Australian cores (see Fig. 13) are referred to as the average fracture permeability. The cores showed a wide range of fracture permeabilities from 14 to 230 mD. (1 mD = 10− 15 m2). When conventional permeability measurement methods were applied, the average core permeability was evaluated as less than 10 mD. Thus, the permeability range differed between the conventional evaluation and the one derived from the new method. The stress attenuation coefficient (β) of fracture cores are from 0.27 to 0.38, and this range is not as great as the one obtained with the average permeability (conventional method). This means that fracture permeability was reduced gradually with increasing effective stress.
ð11Þ
where, γo(μm) is average fracture at zero stress (σe = 0). This result is in agreement with research by Paul et al. (1993), who determined the fracture width (5.0 to 20 μm) for Bowen coal using scanning electron microscopy (SEM). This comparison demonstrates that even using simple measuring equipment, fracture width can be obtained with confidence. This method was confirmed to be an easy and simple way to identify the active fractures. In this study, the downstream end surface of the core was opened to the atmosphere. To safely measure at high pressure, a core stopper was attached. The core stopper was an empty cylinder with a smaller diameter than the core diameter. For the safety reason, this measurement was carried out with pressure range from 0 to 2 MPa. In this pressure range, stress reduction exponent (ζ) was not so high (ζ = 0.11–0.14). This result showed that fracture wide is not depended much on effective stress at low pressure range (less than 2 MPa). Measurement of fracture permeability by using high-pressure range will be a challenge for the future work. The contact between tube or straw and core surface is very important. To prevent leakage from the contacting surface area, a silicon rubber was used at the head of tube or straw. Fig. 15 shows the stress attenuation coefficient for several types of coal. The stress attenuation coefficient for the averaged permeabilities increased with decreasing permeability. Conversely, the stress attenuation coefficient of fracture permeabilities changed only slightly with changing permeability. Those result points out the fact that fracture permeability is not affected strongly by effective stress. 5.3. Overall permeability As described above, coal is not homogeneous. Many coal samples usually have more cleats or fractures. For cores with fractures, a revised measurement system and methodology was employed to evaluate the overall permeability. This methodology considered both fracturing and matrix areas on the surface of core samples. Overall permeability (k) was assumed to consist of two types of permeability, as illustrated with the following equation: n
k = a ∑ Kfi + ð1−aÞKm
ð12Þ
i=1
where: Km = matrix permeability, (m2); Kfi = permeability within the fracture area number i (i = 1 to n), (m2); n = number of fracture or number of investigating point using a tube; a = area contribution coefficient. The area contribution coefficient (a) was calculated considering the ratio of core area, A, and fracture area Af as follows: n
∑ Afi
a=
i=1
A
=
nd2 D2
ð13Þ
where: Afi is each area separated by a pipe, (m2), d = diameter of pipe which is roughly equal to length of fracture l, (m); D = diameter of core sample, (m). Eq. (13) was then substituted into Eq. (12), and the k was obtained as follows: k= Fig. 11. Permeability and average stress attenuation coefficients of various coals.
n 1 3 ∑ li Wi + 2 3πD i = 1
1−
nd2 D2
!
2Q 0 μLP0 A P12 −P22
ð14Þ
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Fig. 12. Gas flow from the surface of core samples.
where: k = total gas permeability of core, (m2); Wi = width of fracture number i, (m); li = length of fracture number i on the surface (roughly equal to the pipe diameter, d), (m); Q0 = the volumetric flow rate at reference pressure, (m3/s); μ = fluid viscosity, (Pa s); L = the length of core sample, (m); P0 = the reference pressure, (Pa); P1 = upstream gas pressure, (Pa); P2 = downstream gas pressure, (Pa). Based on Eq. (14), maximum and minimum permeabilities of coal core samples can be estimated from the fracture and matrix permeabilities, respectively. This means that if both of the permeabilities can be measured with one coal core sample, almost the entire range of permeabilities in the core samples can be estimated. The coefficient (a) depends on the fracture structure of the core. Even if a is a small value, the overall permeability results in a large value, since permeability at the fracture area is one order of magnitude higher than the matrix permeability. Fig. 13. Average fracture permeability versus effective stress of Australian coal.
Fig. 14. Average fracture width versus effective stress of Australian coal.
Fig. 15. Stress attenuation coefficient for several coals.
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Fig. 16. Contribution of fracture length, width to permeability.
In the fracture system, both the fracture length and width contributes to the permeability of core samples. But according to the results of these experiments, the fracture length does not contribute to the gas permeability. In Fig. 16, the total fracture lengths over the diameter of core samples (the secondary vertical axis) expressed the contribution of fracture length compared with diameter of the core. The permeability is small when this ratio is N1 and the permeability is high in case of that ratio less than 1. This result shows that, in some cases, the permeability of fracture areas does not depend on the fracture length. In contrast, fracture width has much to contribute to gas permeability. The permeability is increased with increase with the total of W3 over the diameter of core samples. The Fig. 8 indicates that fracture width is the main factor in the first component of Eq. (14). The value of total fracture length was evaluated as (0.6 to 1.4)D. In average, this ratio is equal to 1. In that case, the second component (matrix component) of Eq. (14) will become zero. This result pointed out that overall permeability of fracture cores were dominated by the fracture width more than fracture length, Σl. Because the second term of Eq. (14) is much smaller than the first term, the Eq. (14) can be rewritten as follows:
k=
n n 1 d 3 3 ∑ Wi li ≈ ∑ Wi 2 2 3πD i = 1 3πD i = 1
ð15Þ
6. Conclusions Permeability of core samples of coal from Vietnam, Australia and China were investigated using a conventional and a revised method to evaluate fracture width. The results of the present study are summarized below: (1) The relationship of permeability against effective stress, σe, was roughly expressed by Eq. (2), and stress attenuation coefficient, β, has been presented against permeability at zero effective stress for each coal sample in Fig. 15 with comparisons to previous measurements by Somerton et al. (1975) and Sasaki et al. (2004). It was shown clearly; especially for Vietnamese coal core samples, that the stress attenuation coefficient for low permeability cores has larger values than those of high permeability cores. (2) The typical permeability measurement method of fracture width in coal core samples was improved with a new method. This work demonstrated that fracture permeability can be estimated from measurements of gas flow rates within small areas using a pipe attached to the end surface of the core. The
fracture widths of Australian core samples were determined to be from 7.7 to 20 μm with this method. (3) Gas permeabilities that considered a contribution by fractures and matrix were calculated with Eq. (14). For the coal samples, Eq. (14) can be shortening using with fracture width of each fracture, Wi, which is the dominant parameter to estimate coal core permeability as Eq. (15). Thus, the fracture length of core samples does not contribute to the permeability but fracture aperture width contributes strongly to the permeability. Especially, fracture permeability of Australian coals had a wide range from 14 to 230 mD. These results may provide fracture and matrix permeabilities to simulate the gas flow with a dual permeability model for CBM and ECBM projects.
Acknowledgments This study was carried out as a part of a project entitled “Technology Development for Carbon Dioxide Sequestration in Coal Seams” and G-COE “Novel Carbon Science”, Kyushu University.
References Ammosov, Eremin, 1963. Fracturing in Coal. IZDAT Publishers, Office of Technical Services, Washington, DC. 109 pp. Harpalani, S., Chen, G., 1997. Influence of gas production induced volumetric strain on permeability of coal. International Journal of Geotechnical and Geological Engineering 15, 303–325. Huy, P.Q., Sasaki, K., Sugai, Y., Kiga, T., Fujioka, M., Adachi, T., 2009. Effects of SO2 and pH concentration on CO2 adsorption capacity in coal seams for CO2 sequestration with considerations for flue gas from coal-fired power plants. Journal of Canadian Petroleum and Technology 48 (10), 58–63. Kross, B.M., Van Bergen, F., Gensterblum, Y., Siemons, N., Pagnier, H.J.M., David, P., 2002. High-pressure methane and carbon dioxide adsorption on dry and moistureequilibrated Pennsylvanian coals. International Journal of Coal Geology 51, 69–92. Laubach, S.E., Marrett, R., Olson, J., Scott, A.R., 1998. Characteristics and origins of coal cleat: a review. International Journal of Coal Geology 35, 175–207. Laubach, S.E., Olson, J.E., Gale, J., 2004. Are open fractures necessarily aligned with maximum horizontal stress. Earth and Planetary Science Letters 222 (1), 191–195. Mazumder, S., Wolf, K.H., 2008. Differential swelling and permeability change of coal in response to CO2 injection for ECBM. International Journal of Coal Geology 74, 123–138. Olson, J.E., Laubach, S.E., Lander, R.H., 2009. Natural fracture characterization in tight gas sandstones: integrating mechanics and diagenesis. AAPG Bulletin 93 (11), 1535–1549. Palmer, I., Mansoori, J., 1998. How permeability depends on stress and pore pressure in coal beds—a new model. SPE Reservoir Evaluation & Engineering 1 (6), 539–544. Pan, Z., Connell, L.D., Camilleri, M., in press. Laboratory characterisation of coal reservoir permeability for primary and enhanced coalbed methane recovery. International Journal of Coal Geology. doi:10.1016/j.coal.2009.10.019. Paul, D., Gamson, B., Basil, B., David, P.J., 1993. Coal microstructure and micro permeability and their effects on natural gas recovery. Fuel 72, 87–99.
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Philip, Z.G., Jennings Jr., J.W., Olson, J.E., Laubach, S.E., Holder, J., 2005. Modeling coupled fracture–matrix fluid flow in geomechanically simulated fracture networks. SPE Reservoir Evaluation & Engineering 8 (4), 300–309. Sasaki, K., Fujii, K., Yamaguchi, S., Ohga, K., Hattori, K., Kishi, Y., 2004. CO2 gas permeability and adsorption of coal samples in consideration of CO2 sequestration into coal seams. Journal of the Mining and Materials Processing Institute of Japan 120 (8), 461–468. Seidle, J.P., Huitt, L.G., 1995. Experimental measurement of coal matrix shrinkage due to gas desorption and implications for cleat permeability increase. SPE International Meeting on Petroleum Engineering, Beijing, China, 14–17 November. SPE 30010.
Seidle, J.P., Jeansonne, M.W., Erickson, D.J., 1992. Application of matchstick geometry to stress dependent permeability in coals. SPE Rocky Mountain Regional Meeting, SPE 24361, Casper, Wyoming. Somerton, W.H., Soylemezoglu, I.M., Dudley, R.C., 1975. Effect of stress on permeability of coal. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 12, 129–145.
Contents lists available at ScienceDirect
International Journal of Coal Geology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i j c o a l g e o
Carbon dioxide gas permeability of coal core samples and estimation of fracture aperture width Phung Quoc Huy ⁎, Kyuro Sasaki, Yuichi Sugai, Satoshi Ichikawa Faculty of Engineering, Kyushu University, Fukuoka, Japan
a r t i c l e
i n f o
Article history: Received 15 November 2009 Received in revised form 15 March 2010 Accepted 16 March 2010 Available online 27 March 2010 Keywords: Permeability Cleats Fractures Homogeneous Heterogeneous Fracture aperture
a b s t r a c t The structure of cleats, or natural fractures in coal seams, is an important factor affecting gas permeability. Coal seam permeabilities have been classified into fracture and matrix flows. However, fractures in coal seams are generally not regular and usually are discontinuous. In addition, it is difficult to definitively distinguish the fracture and matrix permeabilities, and to measure the fracture widths or other necessary properties of fractures for permeability estimation. Typically gas permeability has been determined by using the Darcy equation for incompressible fluid flow and homogeneous porous media, even if the gas flow through fractures has different characteristics with respect to effective stress, which is given by the confined stress minus the gas pressure. In this study, permeability measurements were carried out with a new procedure and methodology to estimate the fracture width in coal core samples. This measurement method is an improvement on conventional permeability measuring methods. In this research, it was identified that fracture permeability can be estimated from measurements of gas flow rates in a limited small area using a pipe attachment on the end of the surface of the core. Finally, a linear equation composed of fracture permeability and matrix permeability is presented. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Gas permeability of coal seams is one of the main parameters used to evaluate CH4 gas emission into working faces, such as heading faces and long wall faces in coal mines. Gas permeability also is important for estimating of the gas drainage rate or gas recovery ratio from coal seams. However, gas permeability is related to many factors, such as the cleat and fracture systems (Harpalani and Chen, 1997; Olson et al., 2009); porosity, gas pressure and mechanical stress (Somerton et al., 1975; Palmer and Mansoori, 1998; Sasaki et al., 2004); fracture orientation (Laubach et al., 2004). Philip et al. (2005) investigated the effect of diagenesis on the initial flow properties of the fracture system, especially with respect to diagenetic effects on the connectivity of the fracture network. In the subsurface, over geologic time, carbonate, quartz, or other cement will precipitate on the fracture walls, often disrupting connected networks. Because permeability and simulation success are commonly limiting factors in gas well performance, knowledge of cleat characteristics and origins is essential for successful exploration and production (Laubach et al., 1998). Owing to the increasing importance of coalbeds as gas reservoirs, geologists are again becoming concerned with the characteristics and
⁎ Corresponding author. E-mail address: [email protected] (P.Q. Huy). 0166-5162/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.coal.2010.03.002
origins of cleat. For coalbed methane (CBM) extraction, knowledge of the properties of natural fractures is essential for planning exploration and development because their influence on recovery of CH4, and the local and regional flow of hydrocarbon and water. New mapping of cleat patterns, guided by recent conceptual advances in the description and theoretical understanding of fracture processes, is beginning to bring these patterns into focus. This, together with more rigorous study of the petrology of cleat development, may resolve uncertainties about causes of cleat that now hinder predictions of interwell-scale patterns of fractures in coal beds (Laubach et al., 1998). Seidle and Huitt (1995) measured deformations of a sample of high volatile C bituminous coal from the San Jan Basin during sorption and desorption of first CH4 then CO2. A pressure cycle was also run with helium, a non-sorbing gas, to determine mechanical compliance of the sample. Observed strain gauge behaviors are discussed and shrinkage coefficients for both gases reported. Matrix shrinkage was found to correlate with gas content rather than pressure, confirming the work of a previous investigator. Shrinkage coefficients varied more among replicate gauges aligned in the same direction than between gauges in different directions. Anisotropic shrinkage effects are discussed. Mazumder and Wolf (2008) noted that the matrix volume of coal swells when CO2/CH4 adsorb on the coal structure. In coalbed gas reservoirs, matrix swelling could cause the fracture aperture width to decrease, causing a considerable reduction in permeability. On a unit concentration basis, CO2 causes greater degree
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of coal-matrix swelling compared to CH4. Much of this difference is attributable to the differing sorption capacity that coal has towards CO2 and CH4 (Kross et al., 2002; Huy et al., 2009). This condition in a coal reservoir would lead to differential swelling. Differential swelling will have consequences in terms of porosity/permeability loss, with serious implication for the performance and implementation of carbon sequestration projects. Coal can be understood as a macromolecular cross-linked polymeric structure. Mazumder and Wolf (2008) have been investigated an experimental effort to measure the differential swelling effect of CO2/CH4 on this macromolecular structure and to theoretically translate that effect in terms of porosity and permeability. A unique feature of this work is that, real time permeability measurements were done to see the true effect of differential strain from CH4 saturated coal core flooding experiments. Using a matchstick geometry model, equations are derived for permeability change due to matrix shrinkage. Coefficients reported here are used in example calculations of absolute permeability and porosity increases during coalbed depletion (Seidle et al., 1992). The behavior of permeability with respect to effective stress is well described using the accepted exponential relationship (Pan et al., in press). As expected the measurements show permeability declines with increasing pore pressure at constant effective stress in response to coal swelling with gas adsorption with the magnitude of the decline depending on the gas type. Simultaneous measurements of coal strain found that the coal sample swells about 2.4% in CO2 at 13.5 MPa and about 1.6% in methane at 12.8 MPa. The swelling strains were modeled by Pan and Connell swelling model with reasonable accuracy and can be explained with empirical Langmuir-like equations too. Coal is known to be a complicated organic carbon material in its packing form and material composition. The characteristics of different coals depend on their coalification processes (Somerton et al., 1975). Some coals are homogeneous porous materials, and others, even in the same coal seam, are heterogeneous materials. Therefore, the determination of gas permeability characteristics is complicated and difficult. Furthermore, gas permeability depends on the sampling location and the same permeability may not be representative for all coal seams, since cleats, or natural fractures in coal seams, are important contributors to gas permeability. The relationship between cleat density and coal rank was first investigated by Ammosov and Eremin (1963). Their results showed that the cleat density increases gradually from brown coal to medium volatile bituminous coal, and then decreases with further rise in coal rank. The gas permeability of a coal core usually is determined by using the Darcy equation, and assuming a laminar gas flow and a homogeneous porous medium. It also is assumed that the gas flows out uniformly through the surface of the core. However, many coal seams have a heterogeneous characteristic for gas permeability. In some cases, the gases only flow through cleats or natural fractures distributed in the coal seam. Thus, the gas permeability measured within coal cores changes greatly and logarithmically, because it has strong sensitivity to the fracture density in the core. In this paper, the use of the Darcy equation to determine gas permeability is referred to as the “conventional method”. Somerton et al. (1975) determined the empirical equation to express the relationship between mean stress and permeability, described as follows: k −3 −0:10 −4 1=3 1=3 = exp −3 × 10 ⋅ σ* ⋅ k0 + 2 × 10 ⋅ σ ⋅ k0 * k0
The simplified relationship between effective stress and permeability for coal cores was presented by Sasaki et al. (2004) as follows: k = exp ð−β ⋅ σe Þ k0
where, σe = effective stress = σ − P, MPa; β = stress attenuation coefficients, MPa− 1. Based on measurements by Somerton et al. (1975), it can be assumed that the second term of the exponential function in Eq. (1) is neglected, which means that β can be calculated by Eq. (3) by converting the units from psi to MPa: −0:10
β = 0:45 ⋅ k0
:
ð3Þ
The permeability (k) can differ among cores, even if the cores are taken from the same position in the coal seam (Fig. 1). This means that the cores are not composed of homogeneous coal matrices, and that they include fractures with different widths, lengths, and distribution densities. Thus, when a higher effective stress is loaded, the gas flow channels within micro-fractures become narrower and some of the micro-fracture may become closed completely. Thus, use of conventional gas permeability equipment may not show the real coal-matrix permeability, since almost all core samples have fractures on their surfaces. For cores containing fractures, the gas flows out through areas that include internal fractures, but not outside these areas. Therefore, if the total flow rate and total cross-section areas of the core sample are used to calculate the fracture permeability, the permeability results will be very low compared with its true value. This is because the flow is divided by total cross-sectional areas of core, even though almost all the area of the core does not contribute to the gas flow. The surface of coal included matrix and fracture areas (Fig. 2). There are two types of fractures — continuous and discontinuous. A discontinuous fracture refers to the lack of gas flow from fracture lines observed in a scanned image of the surface. Somerton et al. (1975) also mentioned the presence of fractures, but they did not carry out investigations on fracture permeability. This study aimed to measure active fractures by an original measurement procedure to determine gas flow from areas with fractures. Based on these data, fracture width, length, and density were estimated. It is expected that the fracture permeability range measured in core samples corresponds to those of their coal seams. Furthermore, these basic permeability data can be applied to numerical simulations on gas flow in coal seams within the double porosity model used in CBM or CO2-ECBM projects. Fracture widths of coal samples might be a valuable parameter to determine the injection or production wells locations.
ð1Þ
where, k = permeability under stress, mD, k0 = permeability under zero stress, mD, σ* = static stress on the core sample, in psi units. In this equation, gas pressure is close to atmospheric pressure, and pressure differences between the two end surfaces (ΔP) is much less than σ*. This means that σ* is almost equal to the effective stress, σe.
ð2Þ
Fig. 1. Gas permeability versus effective stress.
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3
3. Measurement of gas permeability with the conventional method 3.1. Measurement apparatus A schematic diagram of the gas permeability measurement system is shown in Fig. 3. The system mainly consists of a Hassler core holder to set up tri-axial stresses conditions, with a high-pressure bomb for confining stress on the cylindrical surface, a hydraulic pump for axial stress on the end surfaces, gas cylinders with associated regulators and pressure gauges, relief valves, a differential pressure device, a gas flow meter and flow controller for flow rate measurements, and other necessary valves and tubes. To eliminate the influence of temperature variations on the permeability tests, the apparatus was placed in a temperature-controlled room. The Hassler sleeve permits applications of axial stress independently from the radial stress. CO2 gases were used to measure permeability of the core samples. Gas flow rate was controlled and measured by three kinds of flow meters, which were connected in series. The flow meters included a controller (Ueshima Brooks, Model 5893) with a maximum capacity of 20 cm3-std/min, a CO2 gas accumulated flow meter (KOFLOC, Model ACM-1A) with a maximum capacity of 500 cm3-std/min, and a soap-film flow meter for flow rates less than 5 cm3-std/min. Two pressure transducers (CHINO, Model PD-5119) and a differential pressure transducer (Rosemount, Model 11510P6S12M1B1) were set up in upstream and downstream positions near the end surfaces to measure the gauge pressures and differential pressure across the length of core sample.
Fig. 2. Definition of matrix and fractures.
2. Preparation of core samples Specimens were cored from a large block of coal (Table 1). The blocks were sampled from coal seams of Ha Lam, Maokhe coal mines in Quang Ninh coalfield (Vietnam), Shanxi coal field (China) and Bowen coal basin (Australia). After coring the coal blocks, the cores were covered with silicon rubber and wrapped with a thin rubber sleeve. After the 10 h required for hardening of the silicon rubber the core samples were cut into the required lengths with a diamond saw. To prevent breaking the coal samples under high hydrostatic stress conditions, the ends of the specimens were ground and made parallel to each other.
3.2. Permeability measurement procedure The sample was encapsulated between two stainless steel end caps equipped with perforations to evenly distribute gas flow and permeating pressure over the entire end surfaces. To ensure a leakfree seal, adjoining points between the end caps and the rubber jacket were clean, and a thin layer of grease was used on the seal. To investigate the effect of effective stress on gas permeability, the stress load on the coal core sample was increased from 1 to 6 MPa. A vacuum pump was used to remove air from the tubing lines for
Table 1 Specification of coal core samples. Core no.
Coal site
Weight (g)
Length (cm)
Diameter (cm)
Ash content (%)
Moisture content (%)
Volatile matter (%)
Fixed carbon
Coal rank
HL-11 MK-5 MK-4 MK-3 HL-4 MK-1 AUS-2 AUS-3 AUS-4 AUS-5 AUS-6 AUS-8 AUS-9 AUS-14 CH-4 CH-3 CH-5 CH-6 CH-7 CH-10 CH-11 CH-13
Vietnam Vietnam Vietnam Vietnam Vietnam Vietnam Australia Australia Australia Australia Australia Australia Australia Australia China China China China China China China China
60.29 86.43 79.71 114.17 103.07 121.61 99.10 98.89 98.68 100.27 99.36 99.22 103.75 71.66 74.09 84.49 71.80 80.30 84.40 86.40 87.30 75.00
4.30 5.23 4.82 6.90 3.80 7.35 7.50 7.00 7.00 7.00 7.00 7.00 7.00 5.23 4.30 5.00 4.30 4.40 4.95 5.00 4.80 4.40
3.50 3.80 3.81 3.80 3.50 3.80 3.80 3.80 3.81 3.80 3.80 3.80 3.80 3.80 3.80 3.81 3.80 3.80 3.81 3.80 3.88 3.84
2.5 29.7 30.5 30.8 2.6 28.3 4.2 4.1 4.6 4.3 4.4 4.0 4.5 4.3 15.2 16.2 13.5 15.1 14.8 14.6 15.3 15.5
3.0 4.5 4.6 5.0 4.8 4.1 9.9 8.3 8.9 8.6 9.4 8.2 7.9 8.7 2.3 3.1 2.7 3.0 2.6 2.9 2.7 3.2
6.9 6.5 5.9 5.8 6.2 5.9 36 36 33 25 35 36 35 34 7.2 5.3 6.9 5.9 6.8 5.7 6.4 5.8
87.6 59.3 59.0 58.4 86.4 61.7 50.2 52.0 54.0 61.7 51.3 51.7 52.3 53.3 75.3 75.4 76.9 76.0 75.8 76.8 75.6 75.5
Anthracite Anthracite Anthracite Anthracite Anthracite Anthracite Bituminous Bituminous Bituminous Bituminous Bituminous Bituminous Bituminous Bituminous Anthracite Anthracite Anthracite Anthracite Anthracite Anthracite Anthracite Anthracite
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Fig. 3. Schematic diagram of gas permeability measurement system.
permeation testing. Pore pressures were applied using CO2 gas, and the desired average and differential gas pressures were controlled by adjusting the regulator and the relief valve. The average gas pressure (pore pressure) changed from 0.1 to 0.7 MPa depending on the effective stress that was applied to the upstream tubing line by the regulator. The flow rate of CO2 gas released from the downstream line was measured with the flow meters. Gas permeability can be defined by Darcy's equation as follows: k=
2Q 0 μLP0 A P12 −P22
ð4Þ
where, k = gas permeability, (m2); Q0 = volumetric rate of flow at reference pressure, (m3/s); μ = gas viscosity, (Pa s); L = length of core sample, (m); P0 = reference pressure, (Pa); A = cross-section area of core sample, (m2); P1 = upstream gas pressure, (Pa); P2 = downstream gas pressure, (Pa). In this paper permeability, k, is defined in SI unit of m2, however unit of [mD] has been commonly used and easy to understand. The conversion factor from m2 to mD is expressed by 1 mD= 10− 15 m2. 4. Measurement of fracture aperture 4.1. Measurement apparatus Gas flow measurements were modified from the conventional method using the relative permeability testing apparatus (Core
Laboratory, USA). It mainly includes a core holder of 38 mm internal diameter, with an adjustable length core holder to measure core samples of various lengths. A synthetic rubber sleeve was used to hold the core sample. The higher pressure end was sealed by a cap, and the other end was open to the atmosphere (Fig. 4). The effective stress was created by a high-pressure bomb of N2, and the gas flow was supplied by a CO2 bomb with accurate pressure transducers. The effective pressure and pore pressure were adjusted independently. A tube of 3.0 mm in diameter and the soap-film gas flow meter were used to check the presence of gas flowing out from the fractures connected to the end surface of the core sample (Fig. 5). 4.2. Measurement procedures The procedure to estimate gas flow rate through fractures included the following steps: Step 1. Specification of fracture positions using a visualization method. In this step, the end surface of the core was opened to the atmosphere. Then, liquid soap was coated on the end surface. Soap bubbles were observed and the position of fractures noted (Fig. 6). Step 2. Measurement of gas flow rate through fractures. A pipe with 5.5 mm in diameter was used to separate gas flow from the surface area, including fractures (Fig. 7), and flow rates were measured with the soap-film flow meter.
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5
Fig. 4. Schematic diagram of experimental apparatus.
Step 3. Calculation of fracture widths. Fluid flow rates (under laminar flow condition) through narrow channels can be calculated with the following equation:
q=
W 3 ΔPl 12μL
ð5Þ
where, W = fracture width, (m); q = gas flow separated by the pipe at a part of fracture line, (m3/s); ΔP = pressure difference over the core length, (Pa); l = length of the fracture separated by the pipe (roughly equal to the pipe diameter), (m). Thus, fracture width was obtained from following Eq. (6) W=
Fig. 5. Parameters of core and fracture.
rffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 12qμL ΔPl
Fig. 6. Visualization of gas flow with soap liquid.
ð6Þ
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Fig. 8. Gas permeability versus effective stress of Vietnamese coal.
Fig. 7. Positioning of active fractures.
Step 4. Estimation of gas permeability on the fracture area. Darcy's law for incompressible fluid flow was calculated as: q=
kAΔP μL
ð7Þ
From Eqs. (5) and (7), the permeability within fracture areas, Ks, was evaluated with the following equation: Ks =
W3 l 12As
ð8Þ
where, As is the cross section of the flow tube, including fractures, (m2). It was assumed that the diameter of the tube (d) was roughly equal to the length of one fracture on the surface (Fig. 5). As =
π 2 l 4
ð9Þ
By substituting Eq. (9) into Eq. (8), Ks is obtained as follows: Ks =
1 W3 : 3π l
ð10Þ
wide range (0.6 to 1.2), compared with the Chinese and Australian coals. The value of β ranged from 0.8 to 1.2 for low permeability cores of k0 b 1 mD. However, the values decreased to a range of 0.6 to 0.8 for high permeability cores of k0 N 1 mD. It is assumed that the high permeability coal samples included both matrix pores and fractures, but flow rates depend on mainly fractures. Gas flow through the fractures constituted a large share of the total gas flow. For Australian coal (bituminous coal), β was not sensitive to the effective stress. This can be explained by the fact that the structure of bituminous coal has less micro-fractures than anthracite coal. Gas flow through micro-fractures depends on the effective stress, but β is not as sensitive to effective stress. Eq. (2) shows the relationship between gas permeability (k) and effective stress (σe). The behavior of stress-permeability can be modeled if k0 and β are determined. This means that there is an effect by fracture structure on permeability. The k0 range of Vietnamese coal cores was very wide (from 0.14 to 10 mD). Within this range, there are two permeability categories that are low and high permeabilities. Low permeability is considered to be less than 1 mD and high permeability is more than 1 mD. The average value of β for low permeability coals shows higher values than those of high permeability coals. This means that low permeability coals are highly dependent on effective stress. In low permeability coals, gas flow was mainly affected by pore arrangement and pore size. Samples with small pore sizes seemed to be gas-tight and well-packed.
5. Results and discussion 5.1. Conventional gas permeability and stress attenuation coefficient Results of CO2 permeability (k) versus effective stress (σe) for Vietnamese, Australian and Chinese coal cores are shown in Figs. 8–10. The graphs show that permeability of the cores was different from core to core even though they had been taken from the same coal block. Low permeability coals have low distribution densities of pores and microfractures, and they are very sensitive to σe. In the high effective stress range, the permeability decreased exponentially with σe, because the micro-pores and fractures were closed with increasing σe. The average permeability of coal core samples at σe = 0 is denoted as k0, and shows relative incidence of existing pores and fractures in the core samples. The stress attenuation coefficient (β) is the power constant of exponentially decreasing permeability against σe, which is not constant for the same kind of coal seams. Fig. 11 shows the relationship between k0 and β. For Vietnamese coal cores, β had a
Fig. 9. Gas permeability versus effective stress of Australian coal.
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Using measurements of gas flow at the outlet fracture area, the fracture width can be evaluated (see Fig. 14). The stress reduction exponent for the fracture width (ζ), and average fracture width, W (μm), are roughly expressed by an equation as follows: −1
W≈γ0 exp ð−ζσe Þ; γ0 = 7:7 e 20 μm and ζ = 0:11 e 0:14 MPa
Fig. 10. Gas permeability versus effective stress of Chinese coal.
A large reduction in low permeability coals may be attributed to the small size of pores. Somerton et al. (1975) showed that permeability is a function of four power of the pore radius. The low permeability coals normally include pores and a few micro-fractures. Thus, when the effective stress increases, the flow channels within micro-fractures become narrower, and some may close completely. Consequently, the permeability decreases dramatically at high effective stress levels, and gas permeability may even become zero when the effective stress is more than 5 MPa (MK-1 sample).
5.2. Fracture width and permeability Fig. 12 showed the gas flow distribution on the surface of core samples by using a new measurement method. Based on this method, active and inactive fractures can be clarified. The cross-section photo of core showed that many areas seem to be fractures, but in fact there is no any gas flow out. Permeability measurements on the fracture areas within Australian cores (see Fig. 13) are referred to as the average fracture permeability. The cores showed a wide range of fracture permeabilities from 14 to 230 mD. (1 mD = 10− 15 m2). When conventional permeability measurement methods were applied, the average core permeability was evaluated as less than 10 mD. Thus, the permeability range differed between the conventional evaluation and the one derived from the new method. The stress attenuation coefficient (β) of fracture cores are from 0.27 to 0.38, and this range is not as great as the one obtained with the average permeability (conventional method). This means that fracture permeability was reduced gradually with increasing effective stress.
ð11Þ
where, γo(μm) is average fracture at zero stress (σe = 0). This result is in agreement with research by Paul et al. (1993), who determined the fracture width (5.0 to 20 μm) for Bowen coal using scanning electron microscopy (SEM). This comparison demonstrates that even using simple measuring equipment, fracture width can be obtained with confidence. This method was confirmed to be an easy and simple way to identify the active fractures. In this study, the downstream end surface of the core was opened to the atmosphere. To safely measure at high pressure, a core stopper was attached. The core stopper was an empty cylinder with a smaller diameter than the core diameter. For the safety reason, this measurement was carried out with pressure range from 0 to 2 MPa. In this pressure range, stress reduction exponent (ζ) was not so high (ζ = 0.11–0.14). This result showed that fracture wide is not depended much on effective stress at low pressure range (less than 2 MPa). Measurement of fracture permeability by using high-pressure range will be a challenge for the future work. The contact between tube or straw and core surface is very important. To prevent leakage from the contacting surface area, a silicon rubber was used at the head of tube or straw. Fig. 15 shows the stress attenuation coefficient for several types of coal. The stress attenuation coefficient for the averaged permeabilities increased with decreasing permeability. Conversely, the stress attenuation coefficient of fracture permeabilities changed only slightly with changing permeability. Those result points out the fact that fracture permeability is not affected strongly by effective stress. 5.3. Overall permeability As described above, coal is not homogeneous. Many coal samples usually have more cleats or fractures. For cores with fractures, a revised measurement system and methodology was employed to evaluate the overall permeability. This methodology considered both fracturing and matrix areas on the surface of core samples. Overall permeability (k) was assumed to consist of two types of permeability, as illustrated with the following equation: n
k = a ∑ Kfi + ð1−aÞKm
ð12Þ
i=1
where: Km = matrix permeability, (m2); Kfi = permeability within the fracture area number i (i = 1 to n), (m2); n = number of fracture or number of investigating point using a tube; a = area contribution coefficient. The area contribution coefficient (a) was calculated considering the ratio of core area, A, and fracture area Af as follows: n
∑ Afi
a=
i=1
A
=
nd2 D2
ð13Þ
where: Afi is each area separated by a pipe, (m2), d = diameter of pipe which is roughly equal to length of fracture l, (m); D = diameter of core sample, (m). Eq. (13) was then substituted into Eq. (12), and the k was obtained as follows: k= Fig. 11. Permeability and average stress attenuation coefficients of various coals.
n 1 3 ∑ li Wi + 2 3πD i = 1
1−
nd2 D2
!
2Q 0 μLP0 A P12 −P22
ð14Þ
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Fig. 12. Gas flow from the surface of core samples.
where: k = total gas permeability of core, (m2); Wi = width of fracture number i, (m); li = length of fracture number i on the surface (roughly equal to the pipe diameter, d), (m); Q0 = the volumetric flow rate at reference pressure, (m3/s); μ = fluid viscosity, (Pa s); L = the length of core sample, (m); P0 = the reference pressure, (Pa); P1 = upstream gas pressure, (Pa); P2 = downstream gas pressure, (Pa). Based on Eq. (14), maximum and minimum permeabilities of coal core samples can be estimated from the fracture and matrix permeabilities, respectively. This means that if both of the permeabilities can be measured with one coal core sample, almost the entire range of permeabilities in the core samples can be estimated. The coefficient (a) depends on the fracture structure of the core. Even if a is a small value, the overall permeability results in a large value, since permeability at the fracture area is one order of magnitude higher than the matrix permeability. Fig. 13. Average fracture permeability versus effective stress of Australian coal.
Fig. 14. Average fracture width versus effective stress of Australian coal.
Fig. 15. Stress attenuation coefficient for several coals.
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9
Fig. 16. Contribution of fracture length, width to permeability.
In the fracture system, both the fracture length and width contributes to the permeability of core samples. But according to the results of these experiments, the fracture length does not contribute to the gas permeability. In Fig. 16, the total fracture lengths over the diameter of core samples (the secondary vertical axis) expressed the contribution of fracture length compared with diameter of the core. The permeability is small when this ratio is N1 and the permeability is high in case of that ratio less than 1. This result shows that, in some cases, the permeability of fracture areas does not depend on the fracture length. In contrast, fracture width has much to contribute to gas permeability. The permeability is increased with increase with the total of W3 over the diameter of core samples. The Fig. 8 indicates that fracture width is the main factor in the first component of Eq. (14). The value of total fracture length was evaluated as (0.6 to 1.4)D. In average, this ratio is equal to 1. In that case, the second component (matrix component) of Eq. (14) will become zero. This result pointed out that overall permeability of fracture cores were dominated by the fracture width more than fracture length, Σl. Because the second term of Eq. (14) is much smaller than the first term, the Eq. (14) can be rewritten as follows:
k=
n n 1 d 3 3 ∑ Wi li ≈ ∑ Wi 2 2 3πD i = 1 3πD i = 1
ð15Þ
6. Conclusions Permeability of core samples of coal from Vietnam, Australia and China were investigated using a conventional and a revised method to evaluate fracture width. The results of the present study are summarized below: (1) The relationship of permeability against effective stress, σe, was roughly expressed by Eq. (2), and stress attenuation coefficient, β, has been presented against permeability at zero effective stress for each coal sample in Fig. 15 with comparisons to previous measurements by Somerton et al. (1975) and Sasaki et al. (2004). It was shown clearly; especially for Vietnamese coal core samples, that the stress attenuation coefficient for low permeability cores has larger values than those of high permeability cores. (2) The typical permeability measurement method of fracture width in coal core samples was improved with a new method. This work demonstrated that fracture permeability can be estimated from measurements of gas flow rates within small areas using a pipe attached to the end surface of the core. The
fracture widths of Australian core samples were determined to be from 7.7 to 20 μm with this method. (3) Gas permeabilities that considered a contribution by fractures and matrix were calculated with Eq. (14). For the coal samples, Eq. (14) can be shortening using with fracture width of each fracture, Wi, which is the dominant parameter to estimate coal core permeability as Eq. (15). Thus, the fracture length of core samples does not contribute to the permeability but fracture aperture width contributes strongly to the permeability. Especially, fracture permeability of Australian coals had a wide range from 14 to 230 mD. These results may provide fracture and matrix permeabilities to simulate the gas flow with a dual permeability model for CBM and ECBM projects.
Acknowledgments This study was carried out as a part of a project entitled “Technology Development for Carbon Dioxide Sequestration in Coal Seams” and G-COE “Novel Carbon Science”, Kyushu University.
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