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Sorption kinetics of CH4 and CO2 diffusion in coal: Theoretical and Experimental study Paul Naveen, Mohammad Asif, Keka Ojha, D C Panigrahi, and Haribabu Vuthaluru Energy Fuels, Just Accepted Manuscript • Publication Date (Web): 25 May 2017 Downloaded from http://pubs.acs.org on May 30, 2017
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Sorption kinetics of CH4 and CO2 diffusion in coal: Theoretical and Experimental study Paul Naveena, Mohammad Asifb, Keka Ojhaa,1, D. C. Panigrahib and H. B. Vuthaluruc a
Department of Petroleum Engineering, Indian School of Mines Dhanbad, Jharkhand 826004, India b
c
Department of Mining Engineering, Indian School of Mines Dhanbad, Jharkhand 826004, India
School of Chemical and Petroleum Engineering, Australia – India Joint Research Centre for Coal and Energy Technology, Curtin University, GPO Box U1987, Perth 6845, Western Australia, Australia
ABSTRACT Experimental and theoretical analyses with empirical correlations were framed for diffusion of gas species, CH4 and CO2 in coal samples from Jharia coal fields, India, considering the intrinsic pore parameters. Co-efficient of diffusion (D) and diffusivity (Deff) for single and binary component coal–gas system were estimated by adopting unipore gas kinetic models for gas flow on the integration of Fick’s law and Langmuir relation. The rigorous study was carried out in estimating crossover pressure, which is dominant in distinguishing flow regime for two primary types of diffusion - Knudsen, Molecular as well as the transition between two regimes. Investigation reveals that experimental values of coefficients of diffusion of CH4 and CO2 in random homogeneous isotropic sphere packing of coal samples are in good agreement with the results of theoretical calculations. For the pressure range investigated, variation of co-efficient of diffusion was found to follow dual nature with the stable trend at pressures above 3500 kPa and increasing trend for lower pressures. The practical implication of the investigation for the pressures that are characteristically encountered in the Jharia coalfields is a positive finding for the concomitant recovery of CBM with CO2 sequestration. Additionally, dynamic relation between sorption-diffusion reveals that the co-efficient of diffusion significantly depends on the pore structure and pore size distribution, exhibiting a negative relationship with pressure variation. Keywords: Langmuir Relation, Flow regime, Uni-pore gas-kinetic model, Coefficient of diffusion
1
Corresponding author’s E-mail address:
[email protected] (Keka Ojha)
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Nomenclature
λ
Gas mean free path, m
nCH4 , nCO2
Number density of gases, cm-3
πσCO ,CH
Scattering cross section, cm
2
4
MCH4 , MCO2 Molecular weights of gases, g/mol p
Pressure, kPa
kB
Boltzmann constant (1.3807 × 10 −23 J/K)
T
Temperature, ܭ
Kn
Knudsen number
dp
Pore diameter, m
dg
Kinetic diameter of a gas molecule, m
DCO2K
Knudsen diffusion coefficient of CO2, m2/s
DCH4K
Knudsen diffusion coefficient of CH4, m2/s
DCO2 ,CO2
Molecular diffusion coefficient of CO2, m2/s
1 DCO 2 ,CO2
Effective diffusion coefficient of gas species CO2 and CH4, m2/s
t DCO 2
Total (Knudsen + molecular) diffusion coefficient of CO2 gas, m2/s
t DCH 4
Total (Knudsen + molecular) diffusion coefficient of CH4 gas, m2/s
τ
Tortuosity of the porous media
ΩCO2 ,CO2
CO2 (molecule – molecule) collision Integral, dimensionless
φ
Sample porosity, fraction
rs
Spherical particle radius, m
Vcell
Volume of sample cell, cm3
Vref
Volume of reference cell, cm3
Vv
Void volume, cm3
Egr1
Expansion factor of gas for initial reference cell pressure
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Egr2
Expansion factor of gas for final reference cell pressure
Egv1
Expansion factor of gas for initial sample cell pressure
Egv2
Expansion factor of gas for final sample cell pressure
Vstd
Volume of crystals in the sample cell, cm3
Ec
Expansion factor of gas for charged pressure
Ee
Expansion factor of gas for equilibrium pressure
Ec1
Expansion factor of gas on crystals for charged pressure
Ee1
Expansion factor of gas on crystals for equilibrium pressure
Egr1
Expansion factor of gas for initial reference cell pressure
Egr2
Expansion factor of gas for final reference cell pressure
Egv1
Expansion factor of gas for initial sample cell pressure
Egv2
Expansion factor of gas for final sample cell pressure
mC
Mass of coal sample, g
∆VS
Change in gas storage capacity during pressure step, m3/ton
z
Coefficient of compressibility factor of gas, dimensionless, dimensionless
v
Volume of gas sorbed, m3/ton
vL
Langmuir volume (gas storage capacity), m3/ton
ad
Ash fraction (dry basis), (Wt. %)
pL
Langmuir pressure, kPa
C
Concentration of gas, g/cm3
γg
Specific gravity of gas, dimensionless
ρc
Density of coal sample, g/cm3
CDa
Dimensionless average concentration (fraction of gas sorbed), fraction
tD
Dimensionless time
D
Coefficient of diffusion of gas, m2/s
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D eff
Effective diffusion coefficient of gases, s-1
t
Elapsed time for each step, s
b
Slope
1. INTRODUCTION In recent years major advancement has been made concerning the exploration and exploitation of unconventional gas resources due to rising demand and the declining output of oil and gas, which has landed the global energy and economy in crisis. In this aspect, coalbed methane (CBM) gas has gained its prominence in commercial scale in countries such as – USA, Australia, China, Russia, and Canada, due to its competence as an alternative energy resource in mitigating the global energy crunch and also a potential source for carbon capture and sequestration. 1 A comprehensive and reliable statistics on gas transport and sorption, plus the inter-reliant interaction between these properties are required for the practical development of CBM, CO2 enhanced CBM (CO2 – ECBM) production and CO2 storage in coal reservoir. In order to design effective and reliable strategies for the development of CBM and retaining the CO2 or sequestration at the full scale, one needs to understand the sorption and diffusion properties of gases: CH4 and CO2. To investigate these properties, characterization studies are a prerequisite in conjunction with theoretical modeling efforts. Integration of theory and experimental studies will allow for the relevant sorption kinetics of CH4 and CO2 in coal reservoirs. Coal reservoirs exhibit multi-scale heterogeneity by distinctive matrix pore structure involving macropores and micropores 2, which can be treated with a bimodal (bidisperse) pore size distribution. Practically, in the porous medium of high permeability (or hydraulic conductivity) such as fractures, transport by advection dominates, while diffusion dominates in coal matrix of low permeability. The matrix pore structure, specifically due to the relative abundance of micro-/meso-/macroporous volume, provides an extremely large internal surface area with strong affinity to certain gases (e.g., CH4 and CO2). It has been estimated that ~95% of total in-place gas available in coal matrix is in adsorbed form.3 It is significantly established that there is a preference of adsorption of different gases onto the surface of coal, the order from low to high being N2, CH4, CO2 (1:1.5:2.6) and the actual quantities in the
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proportion vary for different coals.4-5 The adsorption of CO2 is mainly due to the van der Waals forces, accompanied by long-range London dispersion forces, short range intermolecular repulsion, strong electrostatic adsorption and weak hydrogen bond adsorption. Similarly, the adsorption of CH4 was due mainly to the van der Waals force (weaker than that in CO2 adsorption), with no hydrogen bond adsorption 6, and the adsorption is governed by the interplay between the strength of gas – pore wall, gas-gas interactions as well as the influence of confined pore volume on the state and thermodynamic stability of gases. Sorption isotherm relates the gas storage capacity of a coal to pressure and depends on the rank, temperature and moisture content of the coal. Transport and sorption of CH4 and CO2 in the coal matrix is strongly influenced by morphology, pore sizes and shape and surface characteristics.7 The measured values of gas sorption are generally controlled by two processes: the sorption process (sorption characteristics of the coal); and the diffusion process (diffusion of gas through coal matrix). These two processes are usually lumped together and described by elapsed time during adsorption process which is used in analytical modeling for estimating diffusion coefficient. 4 Transport mechanism of gases in coal reservoirs is commonly considered to take place in three stages: sorption in from internal pore surfaces, gas diffusion in coal matrix and Darcy flow through the cleat system.8 Concentration gradient driven gas diffusion during the sorption and desorption processes is well demonstrated by Fick’s second law of diffusion.9 Typically, diffusion mechanism can be combination of in three distinct phenomena in coal matrix: (1) Knudsen diffusion by collisions between gas molecules and pore walls, It is relevant when the diffusion is through small pore sizes and low pressures; (2) Surface/viscous diffusion, where physically sorbed molecules move along the pore surface; (3) Bulk/Molecular/Continuum diffusion, where inter-molecular collisions between gas molecules (Brownian motion) dominates.10,11 Earlier studies by researcher have shown significant progress estimating Diffusion coefficient using unipore and bi-disperse models, where few studies prove the positive relationship between D and pressure. 2,12-13 While other few studies witness negative relationship
22, 23
. Higher diffusion coefficient for CO2 than for
CH4 (for dry coals) is especially due to the physio-chemical characteristics of the molecules, such as kinetic diameter, polarity, and gas –gas, gas – solid interaction in coal. Though bi-disperse diffusion model is used extensively for modelling of gas diffusion in coal by some researchers 14, 15, this model encounters few setbacks such as significant misfit when compared experiment values 16 due to the assumption constant pore diameters for micro- and
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macro-pores, which is not reliable because of persistent changes in void volume during adsorption/desorption process. To the best of our knowledge, the present work is the first study of investigating the total effective gas diffusivity for coal samples from Jharia coalfield in India which is the major CBM producing area of the country. This field presently is under development stage and requires proper understanding of fluid flow mechanism for efficient production. In order to understand gas transport mechanism during primary and possible enhance recovery in the field, a detailed investigation was conducted on the diffusion of CH4 and CO2 gases which effectively control overall production rate and the flow regime prevailing at the reservoir pressure and temperature conditions. In the present study, the unipore diffusion model was rather used in order to eliminate the errors of the bi-dispersive model and to simplify the process of determining the diffusion coefficient (D) for the individual as well as mixed gases. For CH4 and CO2, diffusion in the grains determines the kinetics of the process of accumulation and the release of sorbate. Due to the low permeability of coal matrix, it is difficult to experimentally investigate the transport processes inside coals as well as to accurately measure the transport properties. A theoretical model is then employed to simulate fluid flow considering Knudsen diffusion coefficient, binary diffusion coefficient, the total diffusivity of CH4 and CO2 incorporating tortuosity factor. Also, Numbers of experiments have been carried out to determine the diffusion coefficients and sorption isotherm parameters. 2. MATERIALS AND METHODS 2.1. Sample collection The two reservoir samples for analysis were obtained from currently-active CBM plays of Jharia coalfield and other two samples from Phularitandi collieries (Barora area/ Area – 1). The coal samples, hereafter referred to as JH#101, JH#102, PH#90, and PH#80 were selected from the single well of different seams for the analytical and theoretical studies to evaluate the diffusion properties and kinetics of CH4 and CO2 gas. The coal from Jharia coalfields is mainly of Barakar formation – Gondwana basin, which constitutes about 99% of the total coal reserves of India and the formation mainly consists of grit, medium to coarse sandstone, and grey shale is overlain by a thin layer of alluvium other than thick strata of coal which have cumulative coal thickness and equally high gas content in place.17 Depths of the
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analyzed coal samples were at 925 m (JH#101), 950m (JH#102), 90m (PH#90) and 80m (PH#80) with a temperature of 328 K, 335 K, 321 K and 318 K respectively. 2.2. Sample preparation Coal samples (as-received) obtained from the Jharia field were priory ground to exclude the cleats and fractures following ‘Particle method’. Samples were initially broken into half-inch lumps and then proceeded to mechanical size reduction using jaw crusher with adjustable jaw openings. Sample particles were then introduced to a Hammer mill for further size reduction to less than 2.36 mm (-8 ASTM). Finally based upon the desired analyses, perquisite samples were ground and sieved to mesh size of (60/70 ASTM). 2, 14, 21 For the most of the analyses and experiments, average particle diameter (60/70 ASTM) i.e. 230µm was used, except for petrographic analysis and porosity-permeability determination. Prior to the analyses and experiments, approximately 120g of powdered sample was kept in the isolated environment for ~48hrs at temperatures at 378.15 K to ensure equilibrated condition of sample. 2.3. Sample characterization 2.3.1. Proximate and Ultimate Analyses The Advanced Research Instrument Proximate Analyser (APA-2) using the gravimetric technique in accordance to standard (ASTM D3172-07a or ISO 17246:2005) was used to perform the proximate analysis. Elementar-Vario MICRO cube was used to conduct CHNSO-Elemental analysis in accordance with standard ASTM D3176-89(2002) or ISO (17247:2005). 2.3.2. Vitrinite Reflectance (Vro) The vitrinite reflectance properties were measured in according to ISO 7404 – 5 and ASTM D2798 method using microscope made of CRAIC Technologies (Microspectra 1 CoalPro). 2.4. Low-pressure adsorption using N2 (LPA-N2) The measurement of surface area and porosity properties of the coal samples were conducted on an Automated Gas Sorption instrument (Quantachrome Instruments - Quantachrome® ASiQwin™) using liquefied N2 gas. The pore size distribution, pore volume, and surface area
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thus obtained are representing mainly large micropores and mesopores. The samples (~0.124g each) were first degassed under vacuum at 373.15K for 10.1h on the degassing port of the equipment prior to adsorption analysis at 77.4 K in a liquid nitrogen environment. All the LPA experiments following the test procedure (ISO 9277:2010 and ISO 15901-2:2006) were repeated three times and the final result is the average value of three independent tests. 2.5. Porosity and Permeability determination The porosity of samples was analyzed using Advanced Automated Porosimeter, Permeater APP -10K-A-1, to measure the direct grain volume and pore volume in an auxiliary cell at isothermal conditions. The instrument is controlled by a computer-based technique capable of performing automatic data acquisition analysis of analyzed coal core plug (Diameter 25mm & Length of 80mm), processing pore volume, grain volume, grain density, bulk volume, porosity at ambient as well as at reservoir conditions, overburden pressure up to 5000kPa. The porosity and permeability of coal core samples under reservoir simulated confining pressures of 9107.97 kPa, 9328.61 kPa for JH#101, JH#102 respectively and 6011.19 kPa, 4609.97 kPa for PH#90, PH#80 respectively. 2.6. High-pressure adsorption isotherm (AI) experimental set-up Adsorption-desorption study was carried out in an indigenously fabricated set-up as shown in Figure 1. The setup is based on the manometric method of gas expansion technique (Boyle’s law). The system consists of fixed volume stainless steel sample cell (SC) and reference cell (RC), both capable of withstanding high pressures separated by a two-way ball valve (Flow operation valve). The RC is connected to a high precision pressure transducer (Make –Druck & Leicester, UK; Maximum pressure – 25 Mpa, Sensitivity – 2.5%; 0.05% of full scale). Care is taken to maintain isothermal conditions during experiments by equipping constant temperature water bath with an accuracy of ±0.1ºC. Micro filters are placed at the inlet & outlet of sample cells to prevent blockage of pipelines by powdered coal particles during abrupt pressure changes. The sample cell was packed with 100gm of coal sample with the help of a vacuum pump for each experimental run. 2.7. Setup calibration and procedure Construction of an adsorption isotherm using manometric method is followed in three steps. At first, the empty volume of the sample cell
Vcell is estimated which is followed by
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measurement of adsorbent volume and the free volume (void volume, Vv ) remaining in the sample cell after packing with the sample. These two volumes are usually measured using helium (He) gas displacement. In the third step, tests were performed by injecting gases (CH4 and CO2) with increasing pressure steps. Before beginning, the pressure in the sample container was neutralized by a vacuum pump. At each pressure step, the volume of adsorbed gas is calculated incorporating the compressibility factor of gases at particular pressure and temperature. Berndt Wischnewski’s Peace software was used for the calculation of thermodynamic state variables of methane and carbon dioxide. For helium, compressibility factor was calculated using the equation from technical note 631 of the National Bureau of Standards for Helium (1972). The error involved in estimating adsorption capacity was minimized using standard method.18
Figure 1. Experimental setup for Gas adsorption and diffusion
Benchmarking and calibration of the experimental setup were done adopting dual gas expansion method was used for this purpose to enhance the accuracy compared to conventional liquid filling calibration methods
19,20
. The method involves the determination
of volume the sample cell, reference cell and void space in the sample container using a nonadsorbing gas (helium). Firstly, Helium gas inside the reference cell at pressure, Pc, is expanded into the sample cell. When equilibrium is reached, the system pressure, Pe, is measured. Volume of the cell is given by
Vcell = Vref
(Ec − Ee ) Ee
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(1)
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For second expansion step, a known volume of non-adsorbent (standard volume, glass marbles in the present case) is placed in the sample cell. Then, same procedures were followed as stated in the first step. Thus,
Vcell − Vstd = Vref
( Ec1 − Ee1 ) Ee1
(2)
Solving above equations (1) and (2) for Vref : Vref =
Vstd ( E − Ee ) ( Ec1 − Ee1 ) [ c − ] Ee Ee1
(3)
Thus, solving equations (1) and (3), exact volumes of the sample cell and reference cells are determined. 3. MODELLING APPROACH 3.1. Diffusion mechanisms in coal porous media Micropore, macropore and fracture diffusion of gas molecules involves molecular interactions between gas molecules as well as collisions between gas molecules and porous media
21
. The pore size and pore structure of coal are related directly to the diffusion
mechanisms as illustrated in Figure 2. As the gas molecules progress through the porous media, depending on the characteristic of the diffusing gas species and the intrinsic microstructure of the porous media. There are usually combinations of three types of diffusion: (i) Knudsen; (ii) surface/viscous and; (iii) bulk/molecular/continuum as mentioned earlier.
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Figure 2. Diffusion mechanisms of gas species through the porous media. a) Molecular diffusion; b) Knudsen diffusion; c) Knudsen + Molecular diffusion and d) Tortuous pore paths 3.2. Mean free path ( λ ) and Knudsen number ( Kn ) The mean free path of CO2 diffusing-in in a porous medium at the dynamic condition, when porous medium is composed of binary gases (CH4 and CO2) is given by. 22
λCO = 2
2nCO2 πσ
Where, n =
2 CO2
1 M CO2 2 )nCH4 πσ CO + ( 1+ 2 ,CH 4 M CH4
(4)
p ; kB is the Boltzmann constant (1.3807 × 10 −23 J/K), the collision diameter kBT
σ CO ,CO is given in (Å) is the arithmetic average of the molecular radii two gas species 2
σ CO
2
2
, CH 4
=
1 (σ CO 2 + σ CH 4 ) . Knudsen number ( Kn ), which is the ratio of gas mean free path ( 2
λ ) to the pore diameter ( dp ) of the porous media, is typically used to differentiate the regimes23. Based on the value of Kn , flow regimes were classified Darcy flow as ( Kn
