Experimental Study on Fluid Transport Processes in the Cleat and

Nov 8, 2010 - Graduate University of Chinese Academy of Sciences, Beijing 100049, P. R. China. § Institute of Geology and Geochemistry of Petroleum a...
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Energy Fuels 2010, 24, 6653–6661 Published on Web 11/08/2010

: DOI:10.1021/ef100165w

Experimental Study on Fluid Transport Processes in the Cleat and Matrix Systems of Coal )

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Fengshuang Han,†,‡,§ Andreas Busch, Bernhard M. Krooss,§ Zhenyu Liu,^ Niels van Wageningen, and Jianli Yang*,† †

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State Key Laboratory of Coal Conversion, Institute of Coal Chemistry, Chinese Academy of Sciences, Taiyuan, Shanxi 030001, P.R. China, ‡Graduate University of Chinese Academy of Sciences, Beijing 100049, P. R. China, §Institute of Geology and Geochemistry of Petroleum and Coal, RWTH Aachen University, D-52056 Aachen, Germany, Shell International Exploration and Production B.V., 2288 GS Rijswijk-ZH, The Netherlands, and ^State Key Laboratory of Chemical Resource Engineering, Beijing University of Chemical Technology, Beijing 100029, P.R. China Received February 10, 2010. Revised Manuscript Received September 29, 2010

The fluid transport phenomena were studied on a cleat-plug (with cleats) and a matrix-plug (cleat-free) of a Chinese coal under controlled confining stresses (10-40 MPa). The single-phase fluid flow tests with argon (Ar) and water were performed under the steady-state. The gas breakthrough tests (twophase fluid flow tests) with helium (He), argon (Ar), methane (CH4), and carbon dioxide (CO2) were conducted on the water-wetted plugs under the nonsteady state by monitoring the gas pressure changes with time in two closed compartments separated by the plug. It was found that the permeability of both the matrix- and cleat-plugs for Ar and water are measurable under the test confining stresses and the steady-state. The cleats in the cleat-plug are not easily closed by the high confining stress, evidenced by the fact that the permeability of the cleat-plug under the 40 MPa confining stress is still higher than that of the matrix-plug under the 20 MPa confining stress. The permeability coefficient of a confined coal with respect to gas varies mainly with the mean gas pressure and the effective stress. A mathematical equation combining these two factors is proposed to model the observed permeability data with respect to Ar for the cleat-plug under the confining stresses of 10-40 MPa. The associated coefficients of determination (R2) with the regressions are in the range of 0.88-0.98. It is encouraging that the prediction made by this model may be extended to the other conditions. During the gas breakthrough tests, a residual pressure difference between the up- and downstream pressures is observed for the waterwetted cleat-plug, which is indicative of the capillary forces in the gas/water/coal system. However, the up- and downstream pressure profiles for the water-wetted matrix-plug vary continuously over time and no capillary breakthrough is observed. It represents a mixed gas transport process including diffusion and imbibition. The different flow patterns for gas passing through the water-wetted cleatand matrix-plugs are due to the differences in their capillary threshold pressures, which in turn depend on the throats radii of the largest interconnected flow paths of the plugs and the types of the fluid. The physical structure of the coal seams is generally characterized by a dual porosity configuration: a naturally occurring network of fractures called the cleat system, and a highly heterogeneous porous structure surrounded by the cleats called the matrix system.1,2 It is understood that during CBM production the transport process of CH4 in the cleats can be described as laminar flow and obeys Darcy’s law while the flow of CH4 in the matrix may be considered as diffusive flow.1,2 The fluid flow in the cleat system is relatively fast and well understood while the fluid flow in the matrix system is slow and lacks of detailed understanding.3,4 The characteristics of fluid transport in the matrix system are controlled by both the properties of the coal matrix (e.g., noncovalent bonds in the coal structure and porosity of the coal matrix) and the properties of the fluid (e.g., viscosity,

1. Introduction Carbon capture and storage (CCS) is attracting people’s attention as a measure for mitigating global climate change. Several types of geological formations, including depleted oil and gas reservoirs, deep saline formations, and unminable coal seams, are considered as potential options for underground CO2 storage. Among them, unminable coal seams represent a promising opportunity, because the injected CO2 may enhance coal bed methane recovery (CO2-ECBM), which could partly offset the costs of CCS. Technology development and application for the CO2ECBM process is still at a nascent stage. There is a lack of knowledge on the mechanism of the CO2-ECBM process due to the complexity of the coal seam structure and the mixed fluid transport processes. A detailed understanding of the transport mechanisms of fluids in the coal seams is important for revealing the mechanism of the CO2-ECBM process and evaluating the efficiencies for CO2 trapping and CH4 recovery.

(1) Harpalani, S.; Chen, G. L. Geotech. Geol. Eng. 1997, 15, 303–325. (2) Shi, J. Q.; Durucan, S. Fuel 2003, 82, 1219–1229. (3) Van Wageningen, W.; Maas, J. Methane Symposium, Tuscaloosa, AL, May 21-25, 2007. (4) Van Bergen, F. Ph.D. Dissertation, Utrecht University, Utrecht, The Netherlands, 2009.

*To whom correspondence should be addressed. Telephone/Fax: þ86-351-4048571. E-mail: [email protected]. r 2010 American Chemical Society

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Table 1. Properties of the Test Coala maceral composition/%

proximate analysis/wt %

ultimate analysis/wt %, daf

VRr

vitrinite

inertinite

Mad

Ad

Vdaf

C

H

Ob

N

S

2.3

79.7

20.3

1.1

12.2

11.1

89.0

3.0

4.7

1.0

2.3

SiO2

Al2O3

TiO2

Fe2O3

K2O

CaO

MgO

Na2O

MnO2

60.13

32.17

3.84

0.66

0.48

0.36

0.30

0.071

0.0032

ash composition/wt %, d a

ad: air dried; d: dry; daf: dry-ash-free. b By difference.

polarity, and size of the fluid molecule). It is known that the permeability coefficients of the same coal sample vary with fluids. The decrease of the permeability coefficients in the order of He > N2 > CH4 > CO2 > H2O was found.5,6 This variation is mainly attributed to the viscosity of fluid, the wetting ability of coal to fluid, and the coal swelling induced by the fluid imbibitions (such as sorption). In a coal reservoir, the coal bed is under a confining stress. The coal bed swelling can significantly reduce its porosity, which in turn reduces its permeability to fluid. It has been known that the extent of the coal swelling induced by gas sorption increases in the order of N2 < CH4 < CO2,7-10 which agrees with the decrease of the permeability in the order of N2 > CH4 > CO2. Helium has negligible sorption on coal and causes undetectable coal swelling. It is consistent with the common understanding that helium passes through the coal matrix with the highest permeability.5,6 During the CBM or ECBM process, both the rock stress and formation water wetting are common coal reservoir conditions and usually appear simultaneously. It is important to understand the fluid transport in the matrix under the various conditions. It is well-known that the permeability of coal decreases with the increase of effective stress, which is the difference between total (lithostatic) stress and fluid pressure, due to the compressible nature of coal.1 However, the influence of effective stress on the transport of fluid in the coal matrix has not been clearly understood. It is noticed that gas migrates through the confined coal matrix with a significantly lower rate than that through the unconfined coal matrix.11 Most of the coal reservoir is wetted with formation water. Therefore water drainage for reservoir pressure depletion is necessary prior to CBM recovery or CO2 injection. However, the water in the micropores of the coal matrix is difficult to be removed. The residual water may act as a barrier hindering the transfer of gas in the matrix system.12 Only when the initial pressure difference between gas and water exceeds a minimum pressure difference, called the capillary threshold pressure or gas entry pressure,

the water in the flow path can be displaced by gas and a flow of gas through the coal matrix may be established. It is referred as visco-capillary controlled two-phase flow.13,14 In our previous paper, the transport behaviors of three kinds of fluids (Ar, CH4, and CO2) in a coal plug under the controlled stress and water-wetted conditions were reported. The coal plug used in that paper contained a cleat that was parallel to the flow direction and partly filled with mineral matters.15 The fluid flow phenomenon observed in that plug was a combination of laminar flow in the cleat and diffusive flow in the matrix. To decouple these two flows, a coal plug without visible cleats (matrix-plug) and a coal plug with visible cleats (cleat-plug) were selected in this study. The permeability coefficients of these two plugs with respect to Ar and water under different confining stress conditions (10-40 MPa) were determined and compared. The transport phonomena of He, Ar, CH4, or CO2 in the water-wetted plugs were also studied. 2. Experimental Section 2.1. Samples. Yangquan coal, originating from Qinshui Basin, one of the gas-rich coal basins in China, was selected in this study. The coal is not selected based on a specific location, because the aim of this study is to explore the general characteristics of fluid transport through the coal matrix. The properties of the coal used are listed in Table 1. Vitrinite reflectance (VRr) and carbon content are 2.3% and 89.0%, respectively, classifying this coal as anthracite. In order to study the transport processes of fluid in a coal sample with and without cleats independently, two coal plugs, described as follows were prepared from the same coal block by using a diamond drill bit: (I) Cleat-plug (28.5 mm in diameter and 21.2 mm in length): containing visible cleats (black lines in the digital photographs and the X-ray CT scan image of Figure 1a). (II) Matrix-plug (28.5 mm in diameter and 22.5 mm in length): without visible cleats as evident from its digital photographs and X-ray CT scan image shown in Figure 1b. Although the mineral matters in the coal plugs, the white parts in the X-ray CT scan images of Figure 1, can be distinguished from the organic part of the coal, they were dispersed randomly and are difficult to be quantified. Therefore, the mineral content of the test coal is reported as the ash content (obtained after coal combustion) as usual.16,17 The ash content of the test coal is 12.2%, and aluminosilicate minerals appear to be dominant (Table 1). 2.2. Fluid Flow Tests. The coal plug (air-dried) was placed in a triaxial flow cell with defined confining stress. The confining

(5) Massarotto, P. Ph.D. Dissertation, The University of Queensland, Australia2002. (6) Sereshki, F. Ph.D. Dissertation, University of Wollongong, New South Wales, Australia, 2005. (7) Levine, J. R. In Coalbed Methane and Coal Geology, Vol. 109; Gayer, R., Harris, I., Eds.; Geological Society Special Publication: London, 1996; pp 197-212. (8) St. George, J. D.; Barakat, M. A. Int. J. Coal Geol. 2001, 69, 83–115. (9) Chikatamarla, L.; Cui, X.; Bustin, R. M. 2004 International Coalbed Methane Symposium Proceedings, Tuscaloosa, AL, May 3-7, 2004. (10) Robertson, E. P.; Christiansen, R. L. International Coalbed Methane Symposium, Tuscaloosa, AL, May 16-20, 2005. (11) Pone, J. D. N.; Halleck, P. M.; Mathews, J. P. Energy Fuels 2009, 23, 4688–4695. (12) Wolf, K. H. A. A.; Barzandji, O. H.; Bruining, H.; Ephraim, R. In PETROTECH, New Delhi, India, January 9-12, 2003.

(13) Marschall, P.; Horseman, S.; Gimmi, T. Oil Gas Sci. Technol. Rev. IFP 2005, 60, 121–139. (14) Egermann, P.; Lombard, J. M.; Bretonnier, P. International Symposium of the Society of Core Analysis, Trondheim, Norway, September 12-16, 2006. (15) Han, F.; Busch, A.; van Wageningen, N.; Yang, J.; Liu, Z.; Krooss, B. M. Int. J. Coal Geol. 2010, 81, 128–138. (16) L opez, I. C.; Ward, C. R. Int. J. Coal Geol. 2008, 73, 3–18. (17) Gluskoter, H. J. Trace Elem. Fuel 1975, 1–22.

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and the permeability coefficient (k) divided by the dynamic viscosity of fluid (η) as the constant of proportionality.   k dP q ¼ ð1Þ η dx For an essentially imcompressible fluid (such as water), according to eq 1 the permeability coefficient (kwater) is expressed as eq 2. k water ¼ -

qηL ðP2 - P1 Þ

ð2Þ

where L denotes the length of the sample plug; P1 and P2 denote the up- and downstream pressures of the fluid. For a compressible fluid (such as gas), however, the gas volume flux (qm) at the mean gas pressure (Pm = (P1 þ P2)/2) of the up- and downstream compartments is used to calculate the permeability coefficient (kgas). According to eq 1, kgas is expressed as eq 3. k gas ¼ -

qm ηL qP2 ηL 2qP2 ηL ¼ ¼ ð3Þ ðP2 - P1 Þ Pm ðP2 - P1 Þ ðP2 2 - P1 2 Þ

The permeability coefficient of the plug with respect to Ar (kAr) was determined by single-phase Ar permeability measurements with different upstream pressures ranging from 0.2 to 8 MPa at a constant confining stress of 40, 30, 20, 15, or 10 MPa that proceeded in sequence. The associated uncertainty in the assessment of the kAr values depends on the accuracy of the measurements for the variables shown in eq 3. The gas flow rate measurement by the microburet is the main source of error. The uncertainty of time reading is on the order of Δt = (1 s and may result in a maximum relative error of 2% for kAr. Considering all parameters used in the computation, the maximum relative error for kAr can be estimated to be 4%. The permeability of the plug with respect to water (kwater) was determined after the end of the single-phase Ar permeability measurements. In order to remove the residual gas from the coal plug, the up- and downstream compartments of the flow cell were exposed to atmospheric pressure for several days. Then the single-phase fluid flow test with water was started by applying a water pressure of 5-6 MPa at the upstream side. The maximum error for the kwater value assessment depends on the accuracy of the measurements for the variables used in eq 2. The water flow rate measurement by the microburet is the main source of error. A maximum reading error for water volume is on the order of ΔV = (0.002 mL. This is corresponding to a maximum relative error of 6% for kwater. Considering all parameters used in the computation, the maximum relative error for kwater can be estimated to be 8%. The lower detection limit of the water permeability measurement can be determined by the precision of the volume readings on the microburet. The microburet used in this study is capable of resolving volumes of 0.002 mL. Assuming a volume increase of 0.002 mL in 24 h, the lower detection limit of the water permeability coefficients for the plug with the dimensions used in this study is around 0.1 nD (10-22 m2). 2.2.2. Gas Breakthrough Test (Two-Phase Fluid Flow Test). The plug used for the single-phase water flow test was used subsequently as the water-wetted coal plug. It is assumed that the maximum water imbibition is obtained after the single-phase water flow test, although some of the pores may be inaccessible to water. The gas breakthrough test (two-phase fluid flow test) was performed under nonsteady state conditions (fluid flow driven by variable pressure gradients through the coal plug) by using the system shown in Figure 2. The gas breakthrough test was started by pressurizing the upstream compartment with the measuring gas (He, Ar, CH4, or CO2) to the desired initial pressure, while the downstream side was initially set to

Figure 1. Images of the cleat- (a) and matrix- (b) plugs used in the fluid flow tests.

Figure 2. System for the fluid flow tests.

stress was applied from the side and axial directions. Stainless steel porous disks were placed at the top and bottom of the plug and used as supporters and flow diverters. The stainless steel pistons were equipped with boreholes for the fluid inlet and outlet. Three pressure transducers (maximum pressure 16 MPa with a precision of 0.25% of the full scale value) were used for measuring the pressure changes at different locations. A system for the fluid flow tests is shown in Figure 2. Detailed descriptions of the triaxial flow cell were given by Hildenbrand et al.18,19 and Han et al.15 All the fluid flow tests reported here were performed at 45 C. 2.2.1. Single-Phase Fluid Flow Test. The single-phase fluid flow test was performed under steady-state conditions by using the system shown in Figure 2. The pressure at the upstream was kept constant by a pump (for water) or a pressure gauge (for gas) while the downstream pressure was set to atmospheric. The volumetric flow rate of the fluid was monitored at the downstream side by a microburet. The volumetric flux is defined as the volumetric flow rate divided by the cross-sectional area of the plug. According to Darcy’s law (eq 1) for laminar flow through a porous medium, the volumetric flux (q) is expressed as a function of the pressure gradient (dP/dx) (18) Hildenbrand, A.; Schl€ omer, A.; Krooss, B. M. Geofluids 2002, 2, 3–23. (19) Hildenbrand, A.; Schl€ omer, A.; Krooss, B. M.; Littke, R. Geofluids 2004, 4, 61–80.

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Figure 3. Sequences of the fluid flow tests on the cleat- and matrix-plugs.

2.3. Gas Analysis by GC. The compositions of the original gas desorbed from the coal plug were determined by gas chromatography (GC). A thermal conductivity detector (TCD) was used to detect Ar, air, CH4, and CO2. 2.4. Porosity Measurement by Helium Expansion. The porosity of the coal plug was determined by helium expansion in the same system used for the fluid flow tests shown in Figure 2. The helium expansion test involved successive filling of the known volume of the void between valves 3 and 4 (Vrc, as the reference cell) with the low pressure helium (below 0.8 MPa) and expanding it into the void between valves 1 and 2 including the triaxial flow cell (Vsc, as the sample cell). The value of Vrc was predetermined. The pressures of both reference and sample cells were recorded by the pressure transducers before and after He expansion. The value of Vsc is calculated according to eq 5 based upon the ideal gas law.

atmospheric pressure. Both compartments were then sealed by switching off valves 1 and 2 and pressure monitoring was started. The downstream pressure increased when the gas pushed away or passed through the water in the passage. The effective permeability coefficients (keff) at the different time under a specified confining stress were calculated according to eq 4, which was derived from eq 3.18,19 keff ¼ -

2V2 ηL dP2 AðP2 2 - P1 2 Þ dt

ð4Þ

where A denotes the cross section area of the plug; t denotes time; V2 denotes the volume of the downstream compartment; dP2/dt is the rate of the pressure increase at the downstream compartment. It should be noted that the values of the keff for Ar are controlled by both the transport and imbibition processes in the coal plug. The error involved in keff assessment depends on the accuracy of the variables used in eq 4. The absolute pressure measurement at the low-pressure side is crucially important because it is used for the calculation of the mass flux of gas. A maximum reading error for pressure is on the order of ΔP2 = (0.04 MPa. It will result in a maximum relative error of the effective permeability of 5%. According to the data used in the computations, the maximum relative error for keff can be estimated to be 8%. The sequences of the fluid flow tests for the two plugs are shown in Figure 3 and the test conditions are described as follows: (I) For the cleat-plug, the single-phase Ar flow tests were performed under the mean gas pressures of 0.2-4 MPa and the confining stresses of 10-40 MPa. The single-phase water flow test and the Ar or He breakthrough test were performed under a confining stress of 20 MPa. (II) For the matrix-plug, the single-phase Ar flow tests were performed under the mean gas pressures of 0.2-4 MPa and a confining stress of 20 MPa. The single-phase water flow test and the Ar, He, CH4, or CO2 breakthrough test were performed under a confining stress of 20 MPa.

Vsc ¼

Prc, 0 - Pf Vrc Pf - Psc, 0

ð5Þ

where Prc,0 and Psc,0 denote the pressures of the reference and sample cells before the helium expansion; Pf denotes the pressure of the sytem after the helium expansion. The porosity of the sample plug (ε) is calculated according to eq 6. ε ¼

Vsc;plug - Vsc;sealed-plug Vbulk

ð6Þ

where Vsc,plug and Vsc,sealed-plug denote the void volumes of the sample cell with the plug and with the sealed-plug; Vbulk denotes the bulk volume of the plug.

3. Results and Discussion 3.1. Single-Phase Fluid Flow Test with Ar. The single-phase Ar flow test was performed in the triaxial flow cell system 6656

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Figure 4. Relationships between the permeability coefficients (kAr) of the cleat- (a) and matrix- (b) plugs and the mean gas pressures at the specified confining stresses (kAr was determined under the steady-state conditions).

same driving force.1,22 This is caused by the difference in the drag force of the fluid conduit. A velocity gradient is built up along the radial direction of the conduit when the fluid passes through the conduit. The flow velocity decreases from the center to the wall of the conduit, and a so-called boundary layer is built up near the wall. The decrease in the flow velocity results in a decrease in the fluid flux that in turn decreases the permeability of the medium. The extent of this effect depends on the nature of the fluid and the pressure gradient between the up- and downstream compartments (characterized by the mean gas pressure Pm). Higher fluid viscosity and higher Pm result in a higher velocity gradient and lower permeability of the medium. As the Pm increases, the permeability decreases.1,22 The increase of the Pm shows a negative effect on the permeability. A relationship, which correlates the gas permeability and the mean gas pressure, was established by Klinkenberg and is expressed as eq 7.22   b ð7Þ k gas ¼ kl 1 þ Pm

shown in Figure 2. Figure 4 illustrates the relationships between the permeability coefficients of the cleat- and matrix-plugs for Ar (kAr) and the mean Ar pressure of upand downstream compartments (Pm = 0.2-4 MPa) under the different confining stresses (10-40 MPa). At a fixed Pm, the kAr of the cleat-plug decreases with the increase of the confining stress. However, the kAr of the cleat-plug even at the confining stress of 40 MPa is still higher than that of the matrix-plug at the confining stress of 20 MPa. This indicates that the cleats in the cleat-plug cannot be totally closed with a confining stress up to 40 MPa. For the cleat-plug under the confining stresses of 10, 15, and 20 MPa, the kAr decreases with the increase of Pm, reaches minimum values of 627, 303, and 184 nD at around 2 MPa, then increases as the Pm increases. Under the confining stresses of 30 and 40 MPa, although the notable decrease of the kAr with the increase of Pm can be observed when the Pm < 2 MPa, the kAr remains unchanged afterward. For the matrix-plug under a confining stress of 20 MPa, the kAr decreases significantly with the increase of Pm first, then remains unchanged (about 2.4 nD) after Pm reaches 3 MPa. The kAr of the matrixplug is 2 orders of magnitude lower than that of the cleat-plug (184 nD) under the same confining stress. The decrease of kAr with the increase of Pm is mainly due to the increase in the extent of both the coal swelling and the drag force at the boundary layer between the fluid and the wall of the fluid flow passage. It has been noticed that Ar can be adsorbed on coal, although the adsorbed amount is lower than that of CH4 and CO2.20 Under a confining stress condition, the coal swelling induced by Ar sorption may reduce the porosity and the permeability of the coal plug. An increase in the extent of the coal swelling induced by other gases including N2 with the increase of gas pressure was observed, although the extent of the coal swelling induced by Ar has not been reported.21 Under a confining stress, the coal swelling results in a negative effect on the permeability. It could be one of the reasons that the permeability of the coal plug decreases with the increase of Pm at the lower Pm regime. It is known that the permeability for gas through a compacted porous medium is higher than that for liquid under the

where b is a constant, kgas and kl are the gas permeability coefficients at the Pm and at very high pressure. Furthermore, the effective stress (σ) is defined as the difference between the confining stress (Pt) and the mean gas pressure (Pm): σ ¼ Pt - Pm

ð8Þ

Under a constant Pt, an increase in the Pm can result in a decrease in the σ. As the σ decreases, an increase in the porosity of the cleat-plug is observed (see Figure 5). The decrease of the σ should result in a positive effect on the permeability. The kAr increases with the increase of Pm at the higher Pm regime. The kAr remains unchanged with the Pm somewhere between the lower and the higher Pm regime when the negative and positive effects are balanced. The increase of the permeability coefficient of coal (k) with the decrease of the σ can be quantitatively expressed by an exponential relationship:23,24 k ¼ k0 expð - BσÞ

ð9Þ

(23) Harpalani, S.; McPherson, M. J. Q. Rev. Methane .Coal Seams Technol. 1985, 3, 23–28. (24) Somerton, W. H. Int. J. Rock Mech. Min. Sci. Geol. Abstr. 1975, 12, 129–145.

(20) Bae, J. S.; Bhatia, S. K. Energy Fuels 2006, 20, 2599–2607. (21) Reucroft, P. J.; Sethuraman, A. R. Energy Fuels 1987, 1, 72–75. (22) Klinkenberg, L. J. American Petroleum Institute, Drilling and Productions Practices 1941, 200–213.

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Figure 5. Porosity of the cleat-plug versus effective stress (measured by helium expansion).

Figure 7. ka, a, and c values of the eq 10 fit to the permeability coefficients in Figure 4a.

Figure 6. Permeability coefficients of the cleat-plug for Ar at different mean gas pressures and confining stresses fit to eq 10 (lines represent predictions, points represent the observed data).

where kAr,obs,i and kAr,pre,i denote the ith observed and predicted permeability coefficients, and n denotes the total number of the data points. Figure 6 illustrates the modeling results along with the associated coefficients of determination (R2). The reasonably high R2 values indicate good fitting of the proposed model to the observed data. The obtained ka, a, and c values at different confining stresses (10-40 MPa) are plotted in Figure 7. Figure 8 reveals the relationships among the permeability coefficient kAr, the effective stress σ, and the mean gas pressure Pm. The predicted values at Pm = Pt or σ = 0 are also included. It is important to notice that Figures 6-8 may be used to estimate the parameters at other conditions. As an example, for the reservoir situation of Pt = 3 MPa and Pm = 2 MPa (σ = 1 MPa), the following estimated values can be obtained: ka = 0.07 mD (7  104 nD), a = 1.25 MPa-1, c = 7.65 MPa, and kAr = 0.1 mD (1  105 nD). It is encouraging that the estimated permeability coefficient is similar to the value of the permeability coefficient of the related coal reservoir.25 It is commonly understood that the permeability coefficient for Qinshui Basin is in the range of 0.01-5.71 mD (0.015.71  106 nD).25

where k0 denotes the permeability coefficient when the σ approaches to zero; B is a constant, which is related to the coal compressibility. Hereinbefore, the factors that affect the values of kAr have been discussed from different aspects. Unfortunately, eq 7 only can be used to describe the negative effect of the Pm while eq 9 only can be used to describe the positive effect of the Pm. As discussed above, the negative effect prevails at the lower Pm regime and the positive effect is the other way around. The two effects are balanced at the moderate Pm regime. Therefore a combined mathematical equation is proposed as eq 10 to fit the observed values of the kAr for the cleat-plug shown in Figure 4a.   c ð10Þ k Ar ¼ k a expð - aðPt - Pm ÞÞ 1 þ Pm where ka, a, and c are constants at a specified confining stress Pt. When the Pm approaches to Pt, i.e., the σ approaches to zero, the kAr approaches to ka(1 þ c/Pm). When the σ and c/Pm approach to zero, the kAr approaches to ka. The program of lsqnonlin in Matlab, was used for the nonlinear regression by adjusting ka, a, and c simultaneously to minimize the residual sum-of-squares (RSS), which is defined as n X ðkAr;obs, i - kAr;pre, i Þ2 ð11Þ RSS ¼

(25) Fu, X. H.; Qin, Y.; Li, G. Z.; Li, T. Z.; Hu, C. J. Geomech. 2001, 7, 45–52.

i¼1

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3.3.1. He and Ar Breakthrough Tests on the Cleat-Plug. The pressure changes of the up- and downstream compartments (P1 and P2) during the He and Ar breakthrough tests on the cleat-plug are shown in Figure 9. For the He case, a slow increase of the P2 (from 0.10 to 0.12 MPa) accompanied with a significant drop of the P1 (from 5.77 to 4.65 MPa) is observed in the first 10 h (stage I), followed by a rapid increase of the P2 (from 0.12 to 1.79 MPa) with a simultaneously steep drop of the P1 (from 4.65 to 2.29 MPa) in the next 90 h (stage II), and then the P1 and P2 approach to an equalibrium stage when the pressure difference (Pdifference) between the P1 and P2 approaches to 0.50 MPa (stage III). The pressure profiles for the Ar breakthrough test also exhibit the three-stage characteristic. The three-stage characteristic reflects a typical visco-capillary controlled two-phase flow and is similar to the results of the gas breakthrough tests for the pelitic rocks.18,19 The observed gas breakthrough after a time lag indicates that both He and Ar can displace (drain) water from part of the flow paths and flow through them as viscous flow. The variation in the water content of the cleat-plug can be reflected in the change of the effective permeability for He or Ar with time. The effective permeability coefficients (keff) for both He and Ar increase after the breakthrough, reach the maximum values (8.9 nD for He and 7.7 nD for Ar), then decrease with time until they approach to zero as the Pdifference approaches to the value of 0.5 MPa. The corresponding transport for water in the cleat-plug involves: the water content decreases to a minimum value (water drainage) and then increases (water imbibition) to an equilibrium state. Detailed descriptions of the water drainage and imbibition processes were given by Hildenbrand et al.18,19 It can be noticed that the Pdifference still decreases slowly with time after the keff reaches zero. This may be attributed to the presence of the diffusive flow of gas across the plug. A parameter called the capillary threshold pressure (Pc), which is the difference of the intercepts (at the time zero) of the tangents of the up- and downstream pressure curves (at the beginning of stage III), is used to characterize the phenomenon of gas draining water from the sample.15 The capillary threshold pressure (Pc) of the cleat-plug is 0.7 MPa for both the He and Ar cases (see Figure 9). 3.3.2. He, Ar, CH4, and CO2 Breakthrough Tests on the Matrix-Plug. The pressure changes of the P1 and P2 during the He, Ar, CH4 and CO2 breakthrough tests on the matrix-plug are illustrated in Figure 10. Only continuous and smooth changes of the P1 and P2 over time can be observed. It is different from that on the cleat-plug, in which the three-stage characteristic of the P1 and P2 changes over time is observed. This indicates that viscous flow of gas may be prevented by the water in the matrix-plug and the initial gas pressure differences (7.4, 7.3, 6.0, and 4.5 MPa for He, Ar, CH4, and CO2, respectively) applied in the gas breakthrough tests are perhaps lower than the capillary threshold pressure (Pc) of the waterwetted matrix-plug system. In other words, the Pc of the waterwetted matrix-plug system is probably greater than 7.4 MPa for He, 7.3 MPa for Ar, 6.0 MPa for CH4, or 4.5 MPa for CO2. Diffusive flow of He, Ar, CH4, or CO2 may prevail in the matrix-plug. With comparison of the pressure profiles for different gases, especially the P2 profiles, it can be found that (I) for the nonsorbing gas He, the P1 drops smoothly from 7.4 to 5.0 MPa while the P2 increases from 0.1 to 1.5 MPa; (II) for the weak sorbing gas Ar, only a slight increase in the P2 from 0.1 to 0.4 MPa occurs although the P1 drops from 7.3 to 6.1 MPa

Figure 8. Relationships among the permeability coefficient kAr, the effective stress σ, and the mean gas pressure Pm. Table 2. Water Permeability Coefficients of the Cleat- and MatrixPlugs (Determined under the Steady-State Conditions at a Confining Stress of 20 MPa) kwater [nD] coal plug

1st

2nd

3rd

4th

average

cleat-plug matrix-plug

57 0.3

46 2.7

29 1.4

26 2.1

39 1.6

3.2. Single-Phase Fluid Flow Test with Water. The singlephase water flow test was also performed in the triaxial flow cell shown in Figure 2. The water permeability coefficients of the plugs (kwater) were determined under the steady-state conditions. The pressure difference (between up- and downstream compartments) of 5-6 MPa and confining stress of 20 MPa were selected. The values of the kwater were measured four times according to the sequence shown in Figure 3, and the results are summarized in Table 2. The sequence selected was mainly for wetting the plug and obtaining the kwater value at the same time. Unfortunately, the reproducibility of the kwater is relatively poor. The values of the kwater range from 26 to 57 nD for the cleat-plug and from 0.3 to 2.7 nD for the matrix-plug. Nevertheless, the average value of the kwater for the cleat-plug (39 nD) is 24 times that for the matrix-plug (1.6 nD). The poor reproducibility of the kwater measurements is partly attributed to the presence of the residual gas that may be sorbed in the porous structure or trapped in the dead-end of pores. The residual gas was released slowly during the experiment and hindered the water flow. This is suggested by the gas bubbles in the microburet and enriched CO2 (∼2%) and CH4 (∼21%) components in the gas stream during the first water permeability measurement. The plug was previously treated with neither CH4 nor CO2, so that CO2 and CH4 in the residual gas must represent the original gas sorbed on this sample. The coal swelling induced by water sorption may affect the permeability as well. However, it needs more detailed experiments to be verified. Furthermore, for the matrix-plug, the values of the kwater (0.3-2.7 nD) are very low and close to the lower resolution limit of the experimental system and therefore larger measurement errors may be associated with these values. 3.3. Gas Breakthrough Test (Two-Phase Fluid Flow Test). As mentioned in the Experimental Section, the gas breakthrough tests were carried out for water-wetted plugs in a sealed triaxial flow cell under a confining stress of 20 MPa. 6659

Energy Fuels 2010, 24, 6653–6661

: DOI:10.1021/ef100165w

Han et al.

Figure 9. Observed results during the He and Ar breakthrough tests on the water-wetted cleat-plug under a confining stress of 20 MPa.

and water/CO2, respectively,26-28 Pc = 0.7 MPa for the water-wetted cleat-plug and He and Ar cases, and Pc > 7.4, > 7.3, > 6.0, > 4.5 MPa for the water-wetted matrix-plug and He, Ar, CH4, and CO2 cases into eq 12, respectively, the estimated values of Rthroat for different contact angles (θ) can be obtained and are listed in Table 3. For a completely waterwetted system with θ = 0, the estimated values of Rthroat are around 196 and 185 nm for the cleat-plug with respect to He and Ar, and are < 19, < 18, < 22, and < 27 nm for the matrix-plug with respect to He, Ar, CH4, and CO2. As θ increases from 0 to 80, the Rthroat values decrease for both the cleat- and matrix-plugs. It is clear that the Rthroat values for the cleat-plug are at least 10 times that for the matrix-plug at a specified contact angle. This may be a reason for the differences in the flow patterns when the gas passes through different plugs. It should be noted that the Rthroat value of the cleat-plug with respect to Ar is lower than that to He due to the coal swelling induced by Ar sorption. Because the exact values of the Rthroat for the matrix-plug are unknown, it is difficult to compare the values of Rthroat for the matrix-plug with respect to different gases.

obviously; (III) for the strong sorbing gas CH4 and CO2, the P2 is nearly unchanged during the whole test period while the P1 decreases from 6.0 to 5.1 MPa for CH4 and from 4.5 to 3.1 MPa for CO2. The characteristics of the changes in the P1 and P2 profiles over time for the matrix-plug are attributed to the involvement of several processes: gas diffusion through the matrix, gas imbibition in the matrix, and gas dissolution in the water. The differences in the P1 and P2 profiles for different gases (He, Ar, CH4, and CO2) reflect the differences in their diffusion and imbibition mechanisms during the gas passing through the matrix-plug and their different solubility in water. In order to understand the fluid transport in coal quantitatively, numerical approaches will be introduced in our follow-up paper. Furthermore, from the theoretical view, the differences in the flow patterns for gas passing through the water-wetted coal plugs (cleat- and matrix-plugs) can be attributed to the differences in the capillary threshold pressure (Pc), which in turn depends on the throat radius of the largest interconnected flow path (Rthroat), the contact angle (θ), and the interfacial tension between the fluid phases (γ), as shown in the Washburn equation, a special form of the Young-Laplace equation:14 Pc ¼

2γ cosðθÞ Rthroat

(26) Ren, Q. Y.; Chen, G. J.; Yan, W.; Guo, T. M. J. Chem. Eng. Data 2000, 45, 610–612. (27) Yan, W.; Zhao, G. Y; Chen, G. J.; Guo, T. M. J. Chem. Eng. Data 2001, 46, 1544–1548. (28) Masterton, W. L.; Bianchi, J.; Slowinski, E. J., Jr. J. Phys. Chem. 1963, 67, 615–618.

ð12Þ

Substituting the known values of γ = 69, 67, 66, and 60 mN m-1 for the systems of water/He, water/Ar, water/CH4, 6660

Energy Fuels 2010, 24, 6653–6661

: DOI:10.1021/ef100165w

Han et al.

Figure 10. Observed pressure changes during the He, Ar, CH4, and CO2 breakthrough tests on the water-wetted matrix-plug at a confining stress of 20 MPa.

determination (R2) corresponding with the regressions are in the range of 0.88-0.98. It is encouraging that the prediction made by this model may be extended to the other conditions as well as for the field situations. (3) The fluid transport characteristics in the plugs depend on the types of fluid. The permeability coefficient of the corresponding plug for water is lower than that for argon; the effective permeability coefficient of the water-wetted cleat-plug for He is higher than that for Ar; different pressure curves for the water-wetted matrix-plug are observed when different fluids (He, Ar, CH4, and CO2) are tested during the gas breakthrough tests. (4) Viscous flow of gas in the waterwetted cleat-plug is observed but not for the water-wetted matrix-plug. It is possibly due to the differences in the capillary threshold pressure (Pc) of the two plugs. Pc of the cleat-plug is much lower than that of the matrix-plug. The values of Pc mainly depend on the throat radii of the largest interconnected flow paths of the plugs and the types of the fluid.

Table 3. Estimated Throat Radii of the Largest Interconnected Flow Path of the Cleat- and Matrix-Plugs at Different Contact Angles coal plug

cleat-plug

matrix-plug

gas

He

Ar

He

Ar

CH4

CO2

Pc [MPa] γ [mN/m] Rthroat [nm] (θ = 0) Rthroat [nm] (θ = 20) Rthroat [nm] (θ = 50) Rthroat [nm] (θ = 80)

0.7 69 196 185 126 34

0.7 67 191 179 122 33

>7.4 69