Prediction of Coalbed Methane (CBM) Production Considering

Subscriber access provided by UB + Fachbibliothek Chemie | (FU-Bibliothekssystem)

Article

Prediction of coalbed methane (CBM) production considering bidisperse diffusion: model development, experimental test and numerical simulation Gongda Wang, Ting Ren, Qingxin Qi, Lang Zhang, and Qingquan Liu Energy Fuels, Just Accepted Manuscript • Publication Date (Web): 24 Apr 2017 Downloaded from http://pubs.acs.org on April 27, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Energy & Fuels is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Prediction of coalbed methane (CBM) production considering bidisperse diffusion: model development, experimental test and numerical simulation Gongda Wang a

a,b*

b

a

a

, Ting Ren , Qingxin Qi , Lang Zhang , Qingquan Liu

c

Mine Safety Technology Branch, China Coal Research Institute, 100013, Beijing, China

b

School of Civil, Mining and Environmental Engineering, University of Wollongong, Wollongong, New South Wales 2500, Australia c

Faculty of Safety Engineering, China University of Mining and Technology, Xuzhou 221000, China

Abstract: Gas flow in coal seam consists of laminar flow through coal cleat and diffusion through pores of coal matrix. Previous studies on the prediction of CBM production mostly focused on the impact of permeability change while the gas exchange between matrix and cleat was assumed to obey unipore diffusion assumption with a single diffusion coefficient. However, numerous scholars have found that a single diffusion coefficient cannot reproduce the sorption kinetic data precisely for a lot of coals, while bidisperse diffusion with fast and slow diffusion coefficients can represent the diffusion process well. Until now, attempts on studying the impact of bidisperse diffusion on CBM production are very limited and mathematical model describing the gas flow with bidisperse diffusion is unavailable. In this study, we propose a fully coupled coal seam gas flow model with consideration of bidisperse diffusion and the interaction between bidisperse diffusion, adsorption strain and geomechanical response of coal. A series of experiments were carried out to understand the characteristics of Sydney Basin required by the gas flow model. The sorption kinetic data was matched by unipore and bidisperse diffusion models, results show that bidisperse diffusion can describe the diffusion process much better than unipore diffusion. Based on the developed gas flow model, the difference of CBM production rates between applying the two diffusion assumptions was studied by using the determined bidisperse diffusion coefficients and the approximated unipore diffusion coefficient. Results show apparent deviations of the predicted production rates, the difference is reduced with decreasing cleat spacing while can still be observed with decreasing initial permeability. From the experimental and modelling results, we believe the assumption of bidisperse diffusion cannot be replaced by unipore diffusion if diffusion is a constraint of gas production. For history matching of field CBM production data, careful examination with consideration of bidisperse diffusion is also recommended to gain a better understanding of in-situ permeability change. Keywords: Bidisperse diffusion; CBM production; Gas flow model; permeability

1. Introduction Knowledge of the gas transport properties in coal is of great significance for the accurate prediction of CBM production and coal mine gas drainage. It is widely accepted that the gas transport in coal can be divided into two scales of flow, first is laminar flow driven by pressure gradient and flowing through the macroscopic coal cleat system, second is diffusion driven by concentration gradient and flowing through the microscopic pores of coal matrix. Darcy’s law is commonly used to describe the laminar flow in tight coal seams and calculate the permeability of samples in laboratory test, a lot of permeability models have been developed based on field or experimental observations [1-4]. The feasibility of using Fick’s law to describe the gas diffusion process in coal has been rarely challenged. However, there are different observations about whether one characteristic diffusion coefficient is sufficient to describe the entire diffusion process in highly heterogeneous micropore system of coal matrix. Through matching sorption kinetic data obtained from adsorption and desorption tests, some studies found a single coefficient was good enough to describe the diffusion process [5-7], while more required two coefficients at any given pressure to acquire good matching results. For example, as early as 1984, Smith and Williams[8] observed field desorption of methane from coal pieces shows pronounced curvature, and they thus claimed that the unipore model is inadequate for describing diffusional fluxes from coal over the entire time scale of desorption. Busch et al.[9,10] proposed a bidisperse modelling approaches to match the experimental results of gas

ACS Paragon Plus Environment

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 19

diffusion test on a high volatile bituminous coal, it was found that the two first-order diffusion mechanism can fit the results way better than the unipore model. Siemons et al. [11] determined the rate of carbon dioxide sorption in coal particles at various pressures and various grain size fractions, results show that the pressure history can be split into a fast and a slow process, and the slow process has characteristic times which is ten times longer than the fast process. As the unipore model yielded a poor match of the test date, Shi and Durucan [12] presented a bidisperse porediffusion model for competitive displacement of adsorbed methane by CO2 injection, and an excellent match was achieved. Pan et al.[13] studied the influence of moisture content on gas diffusivities, it was found that the gas diffusion mechanism follows a bidisperse approach rather than the unipore approach, both macro- diffusivity and micro-diffusivities are reduced by the increased sample moisture. Obviously applying unipore model and a single characteristic diffusion coefficient to represent the gas diffusivity in coal cannot be always satisfactory [14-16]. In a lot of cases, bidisperse model with two characteristic diffusion coefficients has been successfully used to reproduce the gas diffusion behaviour. However, it should be pointed out that the ultimate purpose of studying either gas diffusion or gas permeable phenomenon is to understand how it impacts the gas production rates. In this regard, although gas diffusion has been proved to have great impacts on gas production in some scenarios [17, 18], the attempts to incorporate the bidisperse diffusion behaviour into the entire gas flow process in coal seams are very limited. From this point of view, the present paper is mostly focusing on: i) How to link the bidisperse diffusion behaviour to the coupled coal seam gas flow model? ii) When predicting the gas production rate, how much difference between applying the approximated unipore diffusion coefficient and the more accurate bidisperse diffusion coefficients could be? To understand the above questions, the following works are conducted in this study: •

Development of a fully coupled coal seam gas flow model with consideration of bidisperse (i.e. rapid and slow stages) diffusion behaviour and the interaction between bidisperse diffusion, gas adsorption strain and geomechanical response of coal.

•

A series of experiments including methane sorption kinetic/diffusion test on a bituminous coal from Sydney Basin, Australia and matching of sorption kinetic data using unipore diffusion and bidisperse diffusion model.

•

Numerical assessment of CBM production rates using the determined unipore/bidisperse diffusion coefficients and the reservoir characteristics.

2. Model development 2.1 Background of analytical diffusion models The widely used analytical unipore diffusion model assumes coal particles used in the experiment are homogeneous spheres with uniform radius , the fractional uptake of adsorbed gas mass can be written as[19]:

= 1 − ∑

exp (−n π t )

(1)

It should be noted that Eq.1 assumes the external/surface gas concentration is constant, which is not suitable for manometric sorption method, where the external gas concentration changes with time. The solution of fitting manometric sorption experimental data can also be found from Crank [19]. By


Page 3 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

assuming the initial gas concentration in coal is 0, the fractional uptake of adsorbed mass can be expressed as: = 1 − ∑ *

Here, +* are the non-zero roots of:

$ %

( ) !" (# &' () ))&'

tan+* =

(2)

-&' -.&'

The parameter / is calculated from the final fractional uptake of gas by coals: 01234 56

= .

(3)

(4)

The idea of bidisperse model divides the diffusion into a rapid macropore diffusion stage and a slow micropore diffusion stage [9, 13]. For experimental results obtained from volumetric and gravimetric adsorption methods: % % > >

% = 1 − 7 ∑ * * exp (−8 9 : < )

=1−

=

=

; ∑ exp (−8 9 : ? ) 7 * *

The overall uptake is sum of the two stages:

;

% > % >

@=B

= @ % + (1 − @) >

B%

%

% B>

>

(5) (6)

(7) (8)

2.2 Development of numerical unipore diffusion model for determining gas diffusivity As discussed above, analytical diffusion models are not suitable for fitting the results from manometric sorption method, which is widely used and also adopted in this study. To accurately determine the diffusion coefficients of both unipore diffusion and bidisperse diffusion, numerical diffusion models are developed to fit the variable external methane pressure and determine the gas diffusion coefficients. The gas concentration can be expressed by real gas law: *

C = ED = GHI D

F

(8)

By using Eq.8, the gas concentration can be transformed to gas pressure. Assuming the methane sorption obeys Langmuir model: JK =

E6F LM F

(9)

The gas mass in coal matrix can be described as:

NB = VP ρR ρST + UB VM/ZRT

(10)

Because gas diffusion is driven by the concentration gradient between exterior and interior of the coal sample, by applying the mass conservation law and Fick’s second law to the coal unit, we can obtain: \B] \^

+ ∇ ∙ (−ab M∇C) = 0

(11)

Substituting Eq.8 and 10 into Eq.11 and neglecting the change of coal porosity with respect to time, we can get:


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ρR ρST

\0d \^

+

e] \F GHI \^

Page 4 of 19

g + ∇ ∙ f− GHI ∇VB h = 0

;

(12)

Combining Eq.9 and 12, the unipore diffusion model can be expressed as: E6 LM ij i?k \F (LM F) \(

+

e] \F GHI \^

g + ∇ ∙ f− GHI ∇VB h = 0

;

VB = Vm l on ∂Ω ∇VB ∙ 8no = 0

(13)

For the unipore diffusion process, the Dirichlet and Neumann boundary conditions are defined as: (14)

The initial conditions of gas flow can be defined as:

pr (0) = ps in Ω

(15)

By giving the boundary and initial conditions, solving the partial differential equation 13 and matching the sorption uptake ratio measured from sorption kinetic experiment, the value of ab can be determined. 2.3 Development of numerical bidisperse model for determining gas diffusivity Fig.1 schematically illustrates the bidisperse diffusion of gas in sphere coal sample in sorption kinetic experiment, where two kinds of diffusions with different diffusion coefficients constitute the overall diffusion behaviour.

Fig.1 Schematic illustration of bidisperse diffusion in sorption kinetic experiment

The mass of gas in a unit of coal matrix involved in rapid diffusion N< and slow diffusion Nm can be written as the following expressions: NB< = @ t

06 F]% ρR ρST u F]%

NBm = (1 − @) t

+ @UB VB< M/ZRT

06 F]> ρR ρST u F]>

(16)

+ (1 − @)UB VBm M/ZRT

(17)

By applying the mass conversation law to Eq. 16 and 17, we can obtain: vE6 LM ij i?k \F]% (LM F]% )

\(

+

ve] \F]% GHI \^

( #v)E6 LM ij i?k \F]> (LM F]> )

\(

+

% + ∇ ∙ f− GHI ∇VB< h = 0

( #v)e] \F]> GHI \^

;

+ ∇ ∙ f−

;> ∇VBm h GHI

VB< = VBm = Vm w ∇VB< ∙ 8no = 0 on ∂Ω ∇VBm ∙ 8no = 0

(18) =0

(19)

For the bidisperse diffusion process, the Dirichlet and Neumann boundary conditions are defined as:

The initial conditions of gas flow can be defined as:


(20)

Page 5 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

VB< (0) = VBm (0) = Vs in Ω

(21)

By giving the boundary and initial conditions, solving the partial differential equations 18 and 19 and matching the sorption uptake ratio measured from sorption kinetic experiment, the values of a< , am and @ can be determined. 2.4 Development of gas flow model with bidisperse diffusion

As discussed in Section 1, gas flow in coal seams includes the Darcy’s flow in coal cleat and the gas diffusion between coal cleat and coal matrix. Eq.16 and 17 can still be used to represent the mass of gas in the matrix of a unit of coal involved in rapid diffusion and slow diffusion. However, different from the crushed coal particles used in the sorption kinetic test (the coal matrix size can be deemed to be equal to the sample size), the matrix shape factor y (1/m2) decides the size of the coal matrix and thus impacts the diffusion effect as well. Fig. 2 is a schematically illustration of the bidisperse diffusion in gas flow in coal seams. Coal seam can be treated as cubic coal matrixes with interconnected coal cleat, and the cubic coal matrix contains macropores with rapid diffusion coefficient and micropores with slow diffusion coefficient. Fig.2 includes a scanning electron microscope (SEM) photo of Sydney Basin coal sample, which will also be used for other experiments. Distinct difference of pore sizes can be seen from the photo, implying the diversity of matrix pores which lead to difference speeds of diffusion.

Fig. 2 Schematic illustration of bidisperse diffusion in gas flow in coal seams, SEM photo is taken from Sydney basin sample

For cubic coal matrix blocks, the value of y can be obtained from [20]: y=

-7

K

For unipore gas diffusion, the gas exchange rate z can be expressed as [21]: z = −ab y {| (VB − V} )

(22)

(23)

Similarly, the total gas exchange rate of bidisperse gas diffusion can be expressed as the sum of rapid diffusion z} and slow diffusion zm : z = z} + zm

z} = −@a< y {| (VB< − V} )

zm = −(1 − @)am y {| (VBm − V} )

(24) (25) (26)

Combining Eq.16-17 and 25-26 and applying the mass conversation law, we can get the governing equations of gas flow in coal matrix with bidisperse diffusion:


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

E6 LM ij i?k \F]% (LM F]% ) \( E6 LM ij i?k \F]> (LM F]> ) \(

+

+

e] \F]% GHI \^

e] \F]> GHI \^

Page 6 of 19

= −a< y {| (VB< − V} )

(27)

= −am y {| (VBm − V} )

(28)

For the Darcy’s flow in coal cleat, permeability is the key factor controlling the coal bed methane production rate. The commonly used permeability models have been developed depending on two different views, i.e., the cleat porosity-permeability point of view and the stress-permeability point of view, both use strain as an intermediate variable [3]. Here we adopt the Shi and Durucan permeability model which was developed from stress-permeability point of view [22]. Biot coefficient decdies the relationship between effective stress and pore pressure. Some specific studies have been conducted to determine the value of biot coefficient of some coals[23-24]. Due to lack of data, here we assume Biot coefficient α = 1: 6

= #-D ∆

where } is the cleat compressibility (1/Pa), y is the effective horizontal stress (Pa) given as: > ∆y = − # V} − V}s + -( #) (F

F]

] LM

−F

F]6

]6 LM

)

(29)

(30)

where the subscript 0 denotes the initial state. The first and second terms on the right side of Eq.30 are the effect of effective stress and the effect of sorption induced coal deformation, respectively. For gas flow with bidisperse diffusion, the sorption induced coal deformation is the sum of rapid diffusion-sorption induced coal deformation and slow diffusion-sorption induced coal deformation. Eq.30 can be modified as: > ∆y = − # V} − V}s + -( #) fF

v

F]%

]% LM

−F

F]%6

]%6 LM

h+

( #v)> F f ]> -( #) F]> LM

−F

F]>6

]>6 LM

h

(31)

Combining Eqs.29 and 31 yields the permeability change with respect to the initial state under bidisperse diffusion conditions: k = ks

#-D #

> ()> ]% # ]%6 ]> # ]>6 F #FD6 () D ]% M ]%6 M () ]> M ]>6 M

(32)

The mass of gas in the cleat of a unit of coal can be written as: N} =

eD FD {|

(33)

By applying Darcy’s law, the mass conversion equation of gas in coal cleat can thus be deduced as: eD (

V} {|

FD (

+ U} {|

+ ∇ ∙ f−

FD ∇V} h {|

=z

(34)

where μ is the gas viscosity. From cubic law, the relationship between cleat porosity ϕ (1) and cleat permeability can be expressed as: U} = U}s

6

(35)

Combining Eqs. 24-26, 32 and 34-35, the governing equation of gas flow in coal cleat with bidisperse diffusion can be deduced as: > M D D6 £(U} − D D6 ) D + (]% ¦ # 6 ( -( #)(LM F]% )

6 ¢ ¥ = @a< yVB< − V} + (1 − @)am y(VBm − V} ) (36) ¢ + ( #v)>LM FDeD6 F]> + ∇ ∙ f− FD ∇V h ¥ ( } -( #)(LM F]>)

¡ ¤ 6

F e

F

v L F e

F


Page 7 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Eqs.27, 28 and 32, 36 constitute the mathematical model describing the coal seam gas flow process with bidisperse diffusion behaviour. Comparing to the mathematical model of gas flow with unipore diffusion [18], the proposed model contains two separate coal matrix pressures due to the different diffusion speeds, the gas exchange between coal matrix and coal cleat is decided by two diffusion processes simultaneously. The change of cleat permeability and cleat porosity are also influenced by the coupling effect of overall sorption swelling effect and the mechanical response to the effective stress. The Dirichlet and Neumann boundary conditions of gas flow in coal seam are defined as: VB< = VBm = V} = Vm ∇VB< ∙ 8no = 0 on ∂Ω ∇VBm ∙ 8no = 0 ¨ ∇V} ∙ 8no = 0 §

(37)

VB< (0) = VBm (0) = V} (0) = Vs in Ω

(38)

©

The initial conditions of gas flow are defined as:

3. Experiments 3.1 Adsorption and diffusion properties Methane adsorption isotherm is required by the determination of diffusion coefficients and the numerical simulation of CBM production. Sorption isotherm test was conducted at University of Wollongong by using manometric adsorption method [10]. Fresh coal sample was collected from Bulli seam, Sydney Basin and crushed to 2.38-3.36mm particles. The crushed sample was vacuumed at 60ª for 24hours to remove moisture. The maximum methane pressure used in the test was around 4.5MPa, which is higher than the in-situ gas pressure (4MPa) and thus can be deemed as sufficient. Excess adsorption volumes of methane with respect to gas pressure were measured at 30ª and Langmuir model (Eq.9) was used to fit the data, the result is shown in Fig.3. A very good fitting result (R2=0.999) is achieved as shown in the figure, and the determined Langmuir volume Vs and Langmuir pressure P¬ are 18.8e-3 m3/kg and 1.51MPa, respectively.

Fig.3 Methane adsorption isotherm and Langmuir fitting

Numerous studies have observed the influence of gas pressure on the determined diffusion coefficients, however, disagreement on whether diffusion coefficients increase or decrease with rising pressure was argued [5,6,9,11,12,25]. Because in this paper the trend between gas pressure and diffusion coefficients is not our focus, the coal sample was re-vacuumed and a one-step diffusion test was conducted, i.e., gas pressure inside the sample cell was increased from 0 to nearly 3MPa to observe the diffusion process in a relatively wide pressure range. The pressure change inside the


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

sample/reference cell was recorded and fitted by a third order of exponential decay function to describe the value of Vm in Eqs.14 and 20, as shown in Fig.4.

Fig.4 Mathematical description of the change of external pressure Vm

By using the unipore diffusion model developed in section 2.2, the value of ab is adjusted to match the measured sorption uptake ratio as shown in Fig.5. As plotted, the value of 6.0e-12 m /s overestimates the diffusion rate in most of the time and in comparison the value of 1.0e-12 m /s underestimates the diffusion rate along the whole process. Modelling using 3.0e-12 m /s seems to fit better but apparent deviations can still be seen. In order to obtain a perfect fitting line, the diffusion coefficient should be greater at the initial stage but smaller at the later stage. This conflict indicates the unipore diffusion model can only yield a first-order approximation of the experimental results and the deviation is obvious and ‘irremovable’.

Fig.5 Comparison between measured sorption uptake ratio and the modelling results using different unipore diffusion coefficients

In contrast, history match using bidisperse model can yield a more representative curve as shown in Fig.6. By using the bidisperse diffusion developed in Section 2.3 and adjusting the values of a< , am and β, the measured gas sorption uptake ratio is matched. Although there is slight difference in the early stage of diffusion, the overall fitting result is much better than that of unipore diffusion shown in Fig.5. The values of a< , am and β are determined as 7.2e-12 m /s, 3.8e-13 m /s and 0.69, respectively. It can be seen that the fast diffusion coefficient is about 10 times of the slow diffusion coefficient, indicating two distinctly different speeds of diffusion. The calculated ratio between fast


Page 8 of 19

Page 9 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

and slow diffusion coefficients is in agreement with the previous observations (10-100 times) [13, 26-27], suggesting our finding is not occasional.

Fig. 6 Comparison between measured sorption uptake ratio and the modelling result using bidisperse model

3.2 Coal properties and in-situ parameters Apart from the gas adsorption and diffusion properties, the other coal properties and in-situ parameters required by the numerical simulation of CBM production rate were either measured or sourced from literature as shown in Table 1. All the parameters were gained from Bulli seam coal of Sydney Basin. The density of coal ρR was determined from mercury intrusion test and the porosity of matrix UB was determined from 77K liquid adsorption test. The free sorption swelling strain °± was measured by using strain gauge method. The cleat compressibility } was calculated from triaxial stress-permeability test from ² = ²s exp³−3} (VF − VFs )µunder constant confining stress [28]. The measurements of modelling parameters can provide a solid base for numerical simulation. Table 1 Characterization of Bulli seam, Sydney Basin and the corresponding sources Parameters and unit

Value

Source

Seam thickness, m

3

Site data

Young’s modulus of coal ¶ , MPa

4.0

Site data

2300

ACARP report

[29]

Density of coal ¸ , kg/m

0.32

ACARP report

[29]

1350

Lab measurement

18.8e-3

Lab measurement

1.51

Lab measurement

0.29

Lab measurement

3.0e-12

Lab measurement

7.2e-12

Lab measurement

3.8e-13

Lab measurement

0.69

Lab measurement

4.9

Lab measurement

Initial gas pressure Vs , MPa

Passion’s ratio of coal ·, dimensionless 3

Langmuir Volume J± , m /kg 3

Langmuir Pressure ¹± , MPa Strain coefficients °± , %

Unipore diffusion coefficient ab , m /s 2

Rapid diffusion coefficient of bidisperse model a< , m /s 2

Slow diffusion coefficient of bidisperse model am , m2/s

ratio of macropore adsorption to the total adsorption β, dimensionless Porosity of coal matrix UB , %


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

cleat compressibility } , 1/MPa

Page 10 of 19

0.269

Lab measurement

4. Numerical simulation of CBM production rate with different diffusion assumptions 4.1 Model description and input parameters Since the governing equations of gas flow are partial differential equations which cannot be solved manually, numerical simulation is utilized to understand how the assumption of bidisperse diffusion will impact the prediction of CBM production rate of Sydney Basin. The software used in this study is COMSOL Multiphysics (version 5.2), geometry of a CBM recovery activity is built as shown in Fig.7. The CBM recovery is carried out in a 300m*300m area and a vertical well with 1m of diameter sits in the middle of the area. Zero flux and roller condition are applied to all sides of the area and constant pressure (0.1MPa) is applied to the wall of production well. The seam is assumed to be dry and the length of the total modelling time is 5 years and the time step is 1 hour.

Fig.7 Geometry and boundary conditions for the numerical simulation of CBM production

Table 1 provides most of the parameter required by the numerical simulation. It should be note that apart from those parameters, in-situ permeability and cleat spacing are two important but difficultto-measure variables. Even for the same coal seam, their values could be largely regional dependent due to the heterogeneous and anisotropic characteristic of coal reservoir. In this study, different values of permeability and cleat spacing are selected to understand the difference of CBM productions with unipore/bidisperse diffusion assumptions in different reservoir scenarios. Using injection/falloff and step-rate testing methods, the in-situ permeability of Bulli seam was measured [30] and the results demonstrate a variety of in-situ permeability ranging from 0.005mD to 5.8mD. Due to lack of field data, the cleat spacing used in numerical simulation is selected by reference to literature. Laubach and Tremain[31] investigated the cleat spacing of medium-brightness coals in northern San Juan Basin and results show the value varies from 10mm to 200mm. Dawson and Esterle[32] studied the cleat spacing of four ranks of coals from Bowen Basin in Queensland, which is adjacent to the Sydney Basin in our study. It was found that the master cleat spacing is in range of 5mm to 150mm. Paul and Chatterjee [33] studied the cleat spacing from two underground mines in Jharia coalfield in India and an average of 200m cleat spacing was observed. Mazumder et


Page 11 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

al.[34] used X-ray computed tomography to scan two different coal blocks from a French coal mine and a Polish mine, the cleat spacing is calculated as a range from 30mm to 300mm. In summary, previous knowledge from all over the world shows the cleat spacing of coal varies from 5mm to 300mm. In this study, 10mm, 50mm and 200mm of cleat spacing, and 0.05mD, 0.5mD and 5.8mD of initial permeability are selected for comparison study. As shown in Fig.8, the CBM production rate, the accumulated production and the production from fast/slow diffusions (for bidisperse diffusion) will be assessed by carrying out numerical simulation with different diffusion assumptions. 5 cases with different cleat spacing and permeability are selected and for cross-comparison, they can be classified into 2 groups: group 1 with same permeability and different cleat spacing, group 2 with different permeability and same cleat spacing.

Fig.8 Illustration of the groups selected for cross-comparison

4.2 Modelling results Fig.9 shows the modelling results of CBM production rates of group 1. It can be seen that different CBM production rates between applying unipore and bidisperse diffusions is distinct for case 1, of which the cleat spacing is 200mm. The production rate with bidisperse diffusion increases to about 4500m3/day quickly and then drops sharply. In the first 10 months, the gas production rate with unipore diffusion is obviously smaller than that of bidisperse diffusion and the peak of production rate is only about 3000m3/day. With the production continuing, the production rate with unipore diffusion decreases slower and exceeds the production rate with bidisperse diffusion at about 14 months, after that the difference of production rates is enlarged and production rate of unipore diffusion is about 2 times of that of bidisperse diffusion from 25 to 50 months. The result of case 1 demonstrates that even with the same initial permeability, the predicted production rates by using unipore and bidisperse diffusion assumption can differ prominently. Cross-comparison of the three cases shows the difference between two assumptions is reduced with decreasing cleat spacing. For case 2 with 50mm cleat spacing, the trend (production rate of bidisperse diffusion is greater in the early stage while smaller in the late stage) is similar to case 1, but the difference is much smaller. After 40 months’ production, the production rates of two diffusion assumptions become similar and negligible due to the depletion of methane in the area. When the cleat spacing is down to 10mm, the production rates of two diffusion assumptions are almost the same along the whole production history. Another distinguished feature of case 3 is the greatest production rate which is up to 22000m3/t, while it is only about 4500m3/t for case 1 and 14000m3/t for case 2. It is in agreement with the previous findings about the impacts of gas diffusion on gas production [17, 18].


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

a)

b)

c) Fig.9 Modelling of CBM production rates of group 1

Fig.10 illustrates the accumulated gas productions of group 1. It can be seen that the difference between using two diffusion assumptions in case 1 is similar to the production rate of case 1, i.e., the accumulated production of bidisperse diffusion is greater in the early stage while smaller in the late stage. Cross-comparison of the three cases shows that the accumulated production of case 1 is smaller than the other 2 cases (about 4.5e6 m3 at 60 months), and in case 1 the accumulated production of bidisperse diffusion after 5 years is only 75% of the accumulated production of unipore diffusion and the difference can be as much as one million m3. It again proves how the diffusion and also the bidisperse/unipore diffusion assumption influence the predicted CBM production. In case 2, the accumulated production of bidisperse diffusion is great than that of unipore diffusion along the whole production history, which is different from the trend of production rate in Fig.9. It shows that besides diffusion coefficients, the difference between using two assumptions also relies on some other factors, such as production time, cleat spacing and the evaluated index. Similar to the gas production rates of case 3, the accumulated productions of two diffusion assumptions are almost the same, implying permeability may become the restriction of gas production in this case.

a)

b)


Page 12 of 19

Page 13 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

c) Fig.10 Modelling of accumulated CBM production of group 1

To understand how the fast and slow diffusions contribute to the total gas production rate of bidisperse diffusion, the comparison of gas production rates are shown in Fig. 11. It should be noted that the ratio of macropore adsorption to the total adsorption β is 0.69, thus the production from fast diffusion will be about 3 times of the production from slow diffusion by giving the same normalized contribution, such as in case 3, the initial gas production rates from fast diffusion is about 16000 m3/day while 5000 m3/day from slow diffusion, this 3 times of ratio continues until the gas in the recovered area is depleted in the late stage. In comparison, the initial gas productions rates from fast diffusion are way greater than that of slow diffusion for case 1 and case 2. With increasing production time, the difference is reduced for case 2 while still great for case 1. The results indicate the contribution of slow diffusion is tiny in the early stage when the cleat spacing is relative large, however the constantly increased production rate from slow diffusion in case 1 may explain the increased gas production rates encountered in the San Juan basin after several years of production [17], which was making confusion from permeability point of view.

a)

b)

c) Fig.11 Comparison of gas production rates from fast and slow diffusions of group 1


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fig.12 shows the modelling of CBM production rates of group 2, of which the permeability differs while cleat spacing is the same (200mm). The reason of choosing a large cleat spacing is to examine whether the apparent difference of gas production between using unipore and bidisperse diffusions will be changed under different permeability scenarios. As can be seen from Fig.12, the most apparent feature of cross-comparing the three cases is the remarkable difference of overall gas production rate (from thousands m3/day down to 200 m3/day), indicating permeability is still the primary constraint of CBM production. Due to the depletion of gas in the production area, the gas production rate reduces quickly for case 1, while the reduction rate is much slower for case 4 and nearly nil for case 5. Different from Group 1, the difference of gas production rates between unipore and bidisperse diffusions does not disappear with decreasing permeability. It can be seen that all the three cases have a similar trend, i.e., the production rate of bidisperse diffusion is greater from beginning to 10-20 months, while be exceeded by the production rate of unipore diffusion after 1020 months. The accumulated production of Group 2 is shown in Fig.13. It can be seen that the reduction of permeability diminish the differences of accumulated production between unipore diffusion and bidisperse diffusion. However, the difference seems to be more and more apparent at the late production stage, implying a larger difference will be encountered after 5 years’ production.

a)

b)

c) Fig. 12 Modelling of CBM production rates of group 2


Page 14 of 19

Page 15 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

a)

b)

c) Fig.13 Modelling of accumulated CBM production of group 2

The comparison of gas production rates from fast and slow diffusions of group 2 is shown in Fig.14. It can be seen that the initial gas production rate from fast diffusion is much greater than that of slow diffusion for all three cases. For case 1, the red and the blue lines become very close after 45 months’ production, while the differences are still obvious for case 4 and case 5. In all three cases, the production rates from slow diffusion show a slow but constant increase along 60 months’ production history, in comparison the production rates from fast diffusion decay sharply for case 1 and case 4. It illustrates that for all kinds of permeability scenarios, slow diffusion may contribute to maintaining the gas production rate for a long term of gas recovery.

a)

b)


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

c) Fig.14 Comparison of gas production rates from fast and slow diffusions of group 2

4.3 Discussion Previous studies have provided in-depth knowledge of the relationship between sorption, diffusion and the laminar flow in coal seams, especially the influence of sorption swelling on permeability change and diffusion process[35-38]. However, the difference of adopting unipore/bidisperse diffusion assumption to predict gas production rate has not attracted enough attentions. From the above modelling results and analysis, we believe there are two important knowledges should be learned from this study: •

The impact of diffusion on CBM production depends on diffusion coefficient which decides the diffusion speed, and also the cleat spacing which decides the length of diffusion path. If the impact of diffusion on CBM production is apparent (case 1, 2, 4 and 5), the assumption and application of bidisperse diffusion cannot be replaced by unipore diffusion. The experimental study shows how large deviation of applying the unipore diffusion model to model real/experimental diffusion process is, and this has been observed by numerous previous studies as well. Therefore, using an approximated single diffusion coefficient to predict the CBM production rate may induce large inaccuracy, as can be seen from the results of numerical simulation.

•

Field CBM production data has been widely used to back-calculate the change of in-situ permeability. The calculated permeability data were used for history matching when permeability models are developed and the authors want to examine the correctness of the developed models. This is the common approach of studying the characteristic of laminar flow in coal seam. However, if the bidisperse diffusion was overlooked, the change of in-situ permeability may be misunderstood. In this regard, careful examination of the field data considering bidisperse diffusion is recommended.

5. Conclusion In this study, the mathematical model of gas flow with bidisperse diffusion was developed and laboratory tests were conducted to measure the parameters required by the model. Matching of the methane sorption kinetic data demonstrates bidisperse diffusion model can describe the diffusion process more precisely than the unipore diffusion model. Using the developed model and the measured parameters, the difference of gas production rate, accumulated production between applying unipore and bidisperse diffusions were compared. Results show the production rate with bidisperse diffusion is greater than that of unipore diffusion in the initial stage while smaller in the late stage for a 60 months’ production time. The differences are more apparent for coal seams with larger cleat spacing, in which the diffusion is a prominent constraint of CBM production. With


Page 16 of 19

Page 17 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

decreasing permeability, the differences can still be found although the overall production rate is decreased sharply. Analysis on the production rates from fast and slow diffusions in bidisperse diffusion show a large difference between the two diffusions in the initial stage, most of the production rates are from fast diffusion. With the production continuing, the productions from fast diffusion drop quickly while the productions from slow diffusion keep increasing for a lot cases. Our study demonstrates that bidisperse diffusion match the experimental data better for Sydney Basin coal, the bidisperse diffusion cannot be overlooked and replaced by unipore diffusion when cleat spacing is relatively large. We also suggest that reviewing of the field data should take bidisperse diffusion into consideration to obtain a reliable in-situ permeability change data. Nomenclature

º( amount of adsorbed gas at time t (g) º final adsorbed amount after equilibrium (g) a diffusion coefficient (m /s) : sorption time (s). / ratio of the void volume V¼½¾¿ volume of the solid spheres (1) Cs the initial gas concentration of void space (mol/m- ). subscripts rapid diffusion subscripts Á slow diffusion Cs the initial gas concentration of void space (mol/m- ). @ the ratio of macropore adsorption to the total adsorption (1). C the free gas concentration (mol/m- ) n free gas molar volume (mol) V free gas volume (N- ) V free gas pressure (Pa) Z free gas compressibility factor (1) R gas constant (J/K ∙ mol) T system temperature (K). JK adsorbed gas volume (m- /kg) Vs Langmuir gas volume (m- /kg) P¬ Langmuir gas pressure (Pa) NB total gas mass in a unit of coal (g) ρR density of coal (kg/m- ) ρST density of gas at the standard condition (kg/m- ) M gas molar mass (kg/mol) UB porosity of coal matrix (1) ab diffusion coefficient of Unipore model (m /s) Vm known constant pressure on the boundaries (Pa) 8no outward normal unit vector on the boundary VB< gas pressure in rapid diffusion pores (Pa) VBm gas pressure in slow diffusion pores (Pa) a< diffusion coefficient of rapid diffusion (m /s) am diffusion coefficient of slow diffusion (m /s) Å cleat spacing (m) V} gas pressure in coal cleat (Pa) v the Poisson's ratio of coal (1) ¶ Young’s modulus of coal (MPa) °m maximum sorption strain (1) VF pore pressure (MPa) ACS Paragon Plus Environment

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Acknowledgements This work was supported by the National Natural Science Foundation of China 51604153, Beijing Natural Science Foundation 2164057, China Postdoctoral Science Foundation (No. 2016M600982), National Science and Technology Major Project (2016ZX05045-004-006) and The Australian Coal Industry’s Research Program (ACARP C24019). References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

19. 20. 21.

Li, J., Liu, D., Lu, S., Yao, Y., Xue, H., 2015. Evaluation and modeling of the CO2 permeability variation by coupling effective pore size evolution in anthracite coal. Energy & Fuels 29, 717-723. Li, J., Liu, D., Yao, Y., Cai, Y., Xu, L., Huang, S., 2014. Control of CO2 permeability change in different rank coals during pressure depletion: an experimental study. Energy & Fuels 28, 987-996. Pan, Z., Connell, L., 2012. Modelling permeability for coal reservoirs: A review of analytical models and testing data. International Journal of Coal Geology 92, 1–44. Wang, G., Ren, T., Wang, K., Zhou, A., 2014. Improved apparent permeability models of gas flow in coal with Klinkenberg effect. Fuel 128, 53-61. Charrière, D., Pokryszka, Z., Behra, P., 2010. Effect of pressure and temperature on diffusion of CO2 and CH4 into coal from the Lorraine basin (France). International Journal of Coal Geology 81, 373–380. Pone, J.D.N., Halleck, P.M., Mathews, J.P., 2009. Sorption capacity and sorption kinetic measurements of CO2 and CH4 in confined and unconfined bituminous coal. Energy & Fuels 23, 4688–4695. Švábová, M.,Weishauptová, Z., Přibyl, O., 2012. The effect of moisture on the sorption process of CO2 on coal. Fuel 92, 187–196. Smith, M., and Williams, L., 1984. Diffusion models for gas production from coals: Application to methane content determination. Fuel, 63(2):251-255. Busch, A., Gensterblum, Y., Krooss, B., Littke, R., 2004. Methane and carbon dioxide adsorption–diffusion experiments on coal: upscaling and modeling. International Journal of Coal Geology 60, 151-168. Busch, A., Gensterblum, Y., 2011. CBM and CO2-ECBM related sorption processes in coal: A review. International Journal of Coal Geology 87, 49–71. Siemons, N., Wolf, K.H.A.A., Bruining, J., 2007. Interpretation of carbon dioxide diffusion behavior in coals. International Journal of Coal Geology 72, 315–324. Shi, J., Durucan, S., 2003. A bidisperse pore diffusion model for methane displacement desorption in coal by CO2 injection. Fuel 82, 1219-1229. Pan, Z., Connell, L., Camilleri, M., Connelly, L., 2010. Effects of matrix moisture on gas diffusion and flow in coal. Fuel 89, 3207–3217. Zhang, J., 2016. Experimental study and modeling for CO2 diffusion in coals with different particle sizes: based on gas absorption (imbibition) and pore structure. Energy & Fuels 30, 531-543. Staib, G., Sakurovs, R., Gray, E. M. A., 2015. Dispersive diffusion of gases in coals. Part I: Model development. Fuel 143, 612-619. Staib, G., Sakurovs, R., Gray, E. M. A., 2013. A pressure and concentration dependence of CO2 diffusion in two Australian bituminous coals. International Journal of Coal Geology 116–117, 106–116. Pillalamarry, M., Harpalani, S., Liu, S., 2011. Gas diffusion behavior of coal and its impact on production from coalbed methane reservoirs. International Journal of Coal Geology 86, 342-348. Liu, Q., Cheng, Y., Zhou, H., Guo, P., An, F., Chen, H., 2015. A mathematical model of coupled gas flow and coal deformation with gas diffusion and klinkenberg effects. Rock Mechanics and Rock Engineering 48, 1163-1180. Crank, J., 1975. The mathematics of diffusion. Clarendon Press. Lim, K. T., Aziz, K., 1995. Matrix–fracture transfer shape factors for dual-porosity simulators. Journal of Petroleum Science and Engineering 13(3), 169–178. Mora, C. A., Wattenbarger, R. A., 2009. Analysis and verification of dual porosity and CBM shape factors. Journal of Canadian Petroleum Technology 48(2), 17–21.


Page 18 of 19

Page 19 of 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

22. Shi, J., Pan, Z., Durucan, S., 2014. Analytical models for coal permeability changes during coalbed methane recovery: Model comparison and performance evaluation. International Journal of Coal Geology 136, 1724. 23. Connell, L., Mazumder, S., Sander, R., 2016. Laboratory characterisation of coal matrix shrinkage, cleat compressibility and the geomechanical properties determining reservoir permeability. Fuel, 165,499-512. 24. Wang, S., Elsworth, D., Liu, J., 2013. Mechanical Behavior of Methane Infiltrated Coal: the Roles of Gas Desorption, Stress Level and Loading Rate. Rock Mech Rock Eng 46, 945-958. 25. Jian, X., Guan, P., Zhang, W., 2012. Carbon dioxide sorption and diffusion in coals: experimental investigation and modeling. Science China Earth Sciences 55, 633-643. 26. Clarkson, C. R., Bustin, R. M., 1999. The effect of pore structure and gas pressure upon the transport properties of coal: a laboratory and modeling study.2. Adsorption rate modeling. Fuel 78, 1345-1362. 27. Cui, X., Bustin, R. M., Dipple, G., 2004. Selective transport of CO2, CH4, and N2 in coals: insights from modeling of experimental gas adsorption data. Fuel 83, 293-303. 28. Seidle, J. P., Jeansonne, D. J., Erickson, D. J., 1992. Application of matchstick geometry to stress dependent permeability in coals. SPE Rocky mountain regional meeting. Paper 24361, 18–21. 29. Coal Mine Outburst Mechanism, Thresholds and Prediction Techniques, 2006. Australian Coal Association Research Program C14032. 30. Fredericks, L., 2008. Bulli seam permeability data files-2003 to 2006, BHP Billtion Illawarra coal exploration—confidential test report. 31. Laubach, S.E., Tremain, C.M., Ayers, W.B. Jr., 1991. Coal fracture studies: Guides for coalbed methane exploration and development. Journal of Coal Quality. 10, 81–88. 32. Dawson, G. K. W., Esterle, J. S., 2010. Controls on coal cleat spacing. International Journal of Coal Geology 82, 213–218. 33. Paul, S., Chatterjee, R., 2011. Determination of in-situ stress direction from cleat orientation mapping for coal bed methane exploration in south-eastern part of Jharia coalfield, India. International Journal of Coal Geology 87, 87-96. 34. Mazumder, S., Wolf, K., Elewaut, K., Ephraim, R., 2006. Application of X-ray computed tomography for analyzing cleat spacing and cleat aperture in coal samples. International Journal of Coal Geology 68, 205222. 35. Prinz, D., Littke, R., 2005. Development of the micro- and ultramicroporous structure of coals with rank as deduced from the accessibility to water. Fuel 84, 1645-1652. 36. Hol, S., Gensterblum Y, Spiers, C. J., 2013. Direct determination of total CO2 uptake by coal: A new technique compared with the manometric method. Fuel 105, 192-205. 37. Liu, J, 2016. Mechanical effects of sorption processes in coal and implications for coalbed methane recovery. Utrecht University. 38. Bergen, F., Hol, S., Spiers, C., 2011. Stress– strain response of pre-compacted granular coal samples exposed to CO2, CH4, He and Ar. International Journal of Coal Geology 86, 241-253.


Prediction of Coalbed Methane (CBM) Production Considering

Recommend Documents