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1.7 RETENTION OF METHANE Retention of methane in the coal beds occurs by any of the following ways: I. As adsorbed gas molecules on internal surfaces or absorbed within the molecular structure of the coal. II. As gas molecules held within the matrix porosity (micro or macro) III. As free gas within cleat and fracture net work of coal seam, and IV. As gas dissolved in ground water within the coal bed. 1.8 COALIFICATION AND GENERATION OF METHANE Methane is generated during the formation of coal through “coalfication process” of vegetable matter. The generation of CBM during coal formation occurs in two principal ways: I. By metabolic activities of biological agencies (biological process), and II. By thermal cracking of hydrogen rich substances (thermogenic process). Methane generated at shallow depths (< 10 m) and low temperature (< 50 O C) by the first process in low rank stage of coalification (sub bituminous) is termed as biogenic or diagenetic methane. Methane generated under relatively low energy (pressure > 10 m depth, and temperature > 50-170 O C) conditions in the second step (catagenesis and metagenesis) is called as thermogenic methane. Biogenic methane constitutes only about 10 % of the total methane whereas themogenic methane constitutes the rest of bulk CBM generated in subsequent steps of coalification. Methane generated by biogenic process is dry while it is wet / dry when generated by thermogenic processes (catagenetic / metagenetic). Vast quantities of methane rich gas are generated during coalification. As much as 250 m 3 of gas is generated for each ton of coal while maturation from lignite to anthracite. Most of the gases generated in the early biogenic stage escaped due to poor gas retention capacity of low rank coals and shallow depth of burial. Gases generated in the succeeding thermogenic stage could not 1

Properties of Coal

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Page 1: Properties of Coal

1.7 RETENTION OF METHANE

Retention of methane in the coal beds occurs by any of the following ways: I. As adsorbed gas molecules on internal surfaces or absorbed within the molecular structure of

the coal. II. As gas molecules held within the matrix porosity (micro or macro)

III. As free gas within cleat and fracture net work of coal seam, and IV. As gas dissolved in ground water within the coal bed.

1.8 COALIFICATION AND GENERATION OF METHANEMethane is generated during the formation of coal through “coalfication process” of vegetable matter. The generation of CBM during coal formation occurs in two principal ways:

I. By metabolic activities of biological agencies (biological process), and II. By thermal cracking of hydrogen rich substances (thermogenic process).

Methane generated at shallow depths (< 10 m) and low temperature (< 50O C) by the first process in low rank stage of coalification (sub bituminous) is termed as biogenic or diagenetic methane.Methane generated under relatively low energy (pressure > 10 m depth, and temperature > 50-170OC) conditions in the second step (catagenesis and metagenesis) is called as thermogenic methane.Biogenic methane constitutes only about 10 % of the total methane whereas themogenic methane constitutes the rest of bulk CBM generated in subsequent steps of coalification. Methane generated by biogenic process is dry while it is wet / dry when generated by thermogenic processes (catagenetic / metagenetic). Vast quantities of methane rich gas are generated during coalification. As much as 250 m3 of gas is generated for each ton of coal while maturation from lignite to anthracite. Most of the gases generated in the early biogenic stage escaped due to poor gas retention capacity of low rank coals and shallow depth of burial. Gases generated in the succeeding thermogenic stage could not migrate as a result of high-pressure regimes and remained stored in the coal. Generation of large amount of methane takes place during HV A-Bituminus to LV-Bituminus coal stage, however, part of methane generated is retained in coal beds / seams due to prevailing high pressures and the excess above retention capacity of the coal bed, tend to migrate to the surrounding reservoir rock (e.g. sandstone). It exists as monomolecular layer within the micro-pores of the coal. Most available coalbeds have in-situ gas contents of 1 - 20 m3/t.1.10 COMPOSTION OF CBM GASAlthough methane (CH4) is the major component of coal gases, other gases such as ethane (C2H6), propane (C3H8), butane (C4H10), carbon-di-oxide (CO2), nitrogen (N2), and water are released during coalification. Total amount of methane generated during the coal formation (Ro max 0.5 - 1.8 %) approximately range between 2000 - 5000 scft/ton.

2.1 COAL PETROGRAPHY Coal petrography enables us to determine the relative abundance of different maceral and mineral matter in coal. Macerals are the smallest microscopically recognizable entities in coal. Coal consists

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of three main maceral groups: Vitrinite, Inertine & Liptinite (Exinite). These are all sub divided into maceral sub groups and macerals. Minerals are the impurities in coal. The high Vitrinite content and very low Liptinite content of coal suggest that it is a gas–prone source rock. During coalification the generated coalbed gases are stored in macerals of coal mostly in adsorbed form with subordinate amount occurring as free gas within cleats and fractures and a small amount may be dissolved in water.

Vitrinite is the principle gas sorbet maceral in coal and have the largest surface area for Methane adsorption. Dominance of Vitrinite (> 60%) results in high surface area in coals and thereby increasing Methane adsorption capacity. Vitrinite rich coals (bright coal) have greater Methane adsorption capacity than Inertinite rich coals (dull coals) of equivalent rank. This is due to Vitrinite having predominantly micro-pores (< 20Å or 2nm) compared to Inertinite which supposedly has the dominance of meso-(> 2nm – 50nm) and macro- pores (> 50nm). So coals with higher Vitrinite content are likely to have higher gas content, providing other parameters are also favorable (Hunt 1992). Thus coal petrography plays an important role in CBM exploration.

2.1.1 COAL RANK

The rank of a coal indicate degree of coalification, the organic matter was subjected to. It is a particular stage in the maturation path of coal from peat to anthracite. Major rank parameters of coal include volatile matter content, fixed carbon content, moisture and Vitrinite Reflectance, these are known as rank parameters. Gas/Methane content of coal increases proportionally with the rank of a coal (Eddy& Right mire, 1982 Fig.15).

2.1.2 CALORIFIC VALUE (CV)The Calorific Value or Heating Value of coal (Fig.18) is defined as the amount of heat evolved when a unit weight of coal is completely burned and the products of combustion are cooled to a standard temperature of 298°K. It is usually expressed as Gross Calorific Value (GCV) or Higher Heating Value (HHV) or Net Calorific Value (NCV) etc. Calculation of Calorific values of coal:UHV kcal/kg = (8900-138×[percentage of ash content + percentage of moisture content])Empirical Relationship of GCV, UHV, and NCVUHV: Useful heat value = 8900 - 138(A+M)GCV: Gross Calorific Value = (UHV + 3645 -75.4 M)/1.466NCV: Net Calorific Value = GCV - 10.02MUHV, GCV, NCV in Kcal/Kg, “A” is %age Ash; “M” is %age Moisture. 2.1.3 GRADE OF COAL The grade of a coal refers to its degree of impurity. The major grade parameters affecting the sorption capacity of coal is mineral matter content. The dominant forms of mineral matter in coals are clay minerals, quartz, pyrite and calcite. Proximate and ultimate analyses of coals generate the key grade parameters (Levine, 1993). These analyses report ash, which include the non-combustible residue of mineral matter and sulfur forms like pyretic sulfur and organic sulfur. Low grade coals have less adsorptive capacity for gases. Coal industry use grade parameters to decide utilization of a particular coal.

2.1.4 LABORATORY STUDIES FOR CBM PROSPECT EVALUATION

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For evaluation of any Coalbed Methane (CBM) prospect various laboratory studies (e.g., canister desorption tests, petrographic studies, proximate analysis, ultimate/elemental analysis, adsorption isotherm studies, etc.) are carried out during the initial phase of exploration. Coal quality parameters, including grade, chemical composition, maceral composition, rank, physico- mechanical properties, gas content and gas saturation and storage capacity (summarized in Table no-5) have significant impact on reservoir characteristics and gas flow potential of coal (Kim, 1977; Eddy & Rightmire, 1982; Levine, 1993; Lamberson & Bustin 1993; Bustin & Clarkson 1998). 2.1.5 PROXIMATE ANALYSISProximate analysis is the study of physico-chemical parameters of coal and can be used to establish the grade and rank of coals. Chemical characteristics of coal are an important parameter that dictates the sorption potential of coal. For the present study Indian Standard procedures (BIS Standard: 1350, Part-1, 1995) were carried following to determine moisture, ash and volatile matter content of coals. 2.1.5.1 Determination of moisture: About 1 g of the powdered air dried sample was spread uniformly in a petridish which is pre-heated at 1080C, cooled and weighed. The uncovered petridish containing the sample is weighed and heated in a drying oven at 1080C±20C for 1-1.5 hours until there is no further loss in mass. The petridish is covered, cooled in a desiccator and weighed again. The loss in mass on oven drying expressed as a percentage of the total mass of sample is reported as the percentage of moisture content in the sample.2.1.5.2 Determination of ash: About 0.25-0.5 g of the powdered air dried sample is taken in a clean platinum crucible of known weight. The uncovered vessel containing the sample is weighed and inserted into a muffle furnace and heated in air to 5000C in 30 minutes. The temperature is raised from 5000C to 8150C±100C for a further 30-60 minutes and maintained at this temperature for another 60 minutes until there is no further loss in mass. The crucible is covered with a lid, removed from the muffle furnace and cooled in a desiccator. The cooled vessel is weighed. The mass of ash produced expressed as a percentage of the total mass of sample is reported as the percentage of ash yield in the sample.2.1.5.3 Determination of volatile matter: About 0.5g of the powdered air dried sample is taken clean platinum crucible of known weight. The covered vessel containing the sample is weighed, inserted into a muffle furnace and heated out of contact with air at 9000C ±100C for 7 minutes. The covered vessel is removed from the furnace, cooled in a desiccator and weighed. The difference between loss in mass on heating expressed as a percentage of the total mass of sample is reported as the percentage of volatlile matter in the sample.2.1.5.4 Determination of fixed Carbon: Percentage of Fixed carbon is obtained by difference of the %moisture, %ash, and %Volatile Matter from 100.2.1.6. Calculation of vitrinite reflectance:The value of vitrinite reflectance (Ro%) gives idea about the coal rank and grade. In the present study, the vitrinite reflectance (Ro %) is calculated by using the formula by Rice using the formula data from proximate analysis. The formula is as follows: Ro %= -2.712 × log (VM) + 5.092

2.2 GAS CONTENT DETERMINATION:

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2.2.1 In situ Gas content measurements by Canister Desorption Tests:Gas content measurements were determined by carrying out canister desorption tests at the well site by adopting modified USBM Direct Method. The total gas content of recovered coal core samples desorbed in canister is arrived by adding the three components viz. calculated Lost Gas volume, measured Desorbed Gas volume and measured Residual Gas volume. Gas content is reported at NTP conditions in units of cc/g.Lost Gas volume denoted by (Q1) is the volume of gas lost by core sample since its extraction from the undisturbed coal seam to its confinement in the desorption canister. Based on the relationship that the initial values of gas desorbed is proportional to the square root of desorption time, it is estimated by backward extrapolation of a statistically valid number of measured cumulative desorbed gas volumes against the square root of elapsed time for the initial two hours of the desorption tests. Desorbed gas volume is measured periodically by keeping the samples in canister under controlled reservoir temperature and allowing positive pressure in the canister to bleed into an appropriate displacement apparatus maintained at ambient conditions. Desorbed gas volumes are measured frequently such that pressure in canister are not allowed to build up, till the released gas volume was found in the range of 0.05 cc/g/day. Ambient temperature and pressure were recorded at the time of taking each reading for correction of gas volume to normal temperature and pressure. Cumulative volume of gas desorbed gave desorbed gas volume (Q2) for the coal samples.Residual gas volume The Residual Gas is measured by crushing about 300g of the desorbed sample to grain size of ~200 mesh BSS in about 40 minutes. The volume of residual gas released on crushing was measured by water displacement method. From the measured volume of gas obtained after crushing the coal, the residual gas volume (Q3) was calculated for the total weight of the coal sample desorbed.2.2.1.1 Lost gas calculation:The lost gas is calculated by graphical method based on the relationship that for the first few hours of emission, the volume of gas given off is proportional to the square root of the desorption time. A plot of the cumulative emission after each reading against the square root of the time is drawn. .A straight line is obtained which when interpolated to the Y axis gives us an intercept which is the calculated lost gas.A Lost gas calculation graph is shown below:

Fig1: Lost gas calculation

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2.2.1.2 SORPTION TIMESorption Time ( τ Tau ) provides an indication of the rate that gas diffuses out of the coal. It is the time in hours required to desorb 63.2% of initial gas volume. Errors in sorption time estimates can effect prediction of reserves and production rates. The total amount of desorbed gas is calculated by adding up all the volumes of the gas observed throughout the desorption process at successive time intervals. The sorption time is the value of the cumulative time at that point when the fraction of volume desorbed has a value of 0.635Sorption time can also be calculated from cleat spacing and difusion co-fficient by the given formula.τ = s2/8πDCleat Spacing (s in ft)Diffusion coefficient (D ft2/day)Normally it is difficult to determine the cleat spacing(s) and difusion co-officient (D), so overall property, sorption time(τ) is determined from gas content measurement which is directly used as input parameter for reservoir simulation.

2.2.1.3 Diffusivity coefficient:Eleven coal samples of Well-I were obtained and their desorbed gas was measured from volumetric displacement apparatus as a function of time. For calculating effective diffusivity, a graph was plotted between fraction of volume sorbed and √t. Fraction of volume desorbed is obtained by:

Fraction of Vol . sorbed=Cumm . DesorbedVol . at NTP (cc )at a time interval ,t

Total gasdesorbed (Cummulative gas desorbed+Lost gas )√t = Square root of cumulative time, min.The slope of the curve is measured from the graph plotted and, by using bi-disperse model (Eq. 2), Effective Diffusivity is calculated.

Where,

2.2.2 INDIRECT METHOD OF GAS CAPACITY ESTIMATION:

Most of the gas in coal is adsorbed on the internal surface of micropores and varies directly with pressure and inversely with temperature. The relationship between the volume of adsorbed gas with pressure and temperature based on the moisture and ash content of coal samples was estimated by Kim’s empirical equation (Kim 1977),

Gsaf= (0.75 )(1−a−wc )[K o(0.095 d )no−0.14 ( 1.8 d100

+11)]5

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Ko=0.8x fc

xvm

+5.6, no=0.315−0.01x fc

xvm

Where,Gsaf = Dry ash free gas storage capacity, cm3/g; a = Ash content, weight fractionwc = moisture content, weight fraction; d = Sample depth, m(feet/3.28)xfc = Fixed carbon, weight fraction; xvm= Volatile matter, weight fraction

2.3 MODELLING OF COAL BED METHANE SORPTION DATA:

Various isotherms for adsorption of gases on solids have been analyzed using different approaches such as Langmuir theory, BET theory,Freundlich theory and Dubinin Astakhov thoery. In addition, there are several semi-empirical approaches to describe the adsorption of gases on solids. 2.3.1 Langmuir isotherm However, the most commonly used model is Langmuir model that describes Type I isotherm and has been extensively used for adsorption of methane and CO2 on coal. Langmuir model is based on the assumption that there exists a fixed adsorption sites on the surface of the solid and only one gas molecule is adsorbed at a single adsorption site. Moreover the adsorbent surface is energetically homogeneous and that the energy of adsorption is constant for all sites with no interaction between the adjacent adsorbate molecules. The equation for the Langmuir isotherm is given as:

Where, V is the adsorbed volume at equilibrium pressure P, b is the pressure constant, VL is the Langmuir volume and PL is known as Langmuir pressure. This model has been used to describe methane adsorption data on coals over a wide range of temperatures and pressures with a good fit (Yee et al., 1993). As per the Langmuir model it is believed that the surface of the solid should be energetically homogeneous, which is not so in the case of coal. Hence this model has limited application to CO2 adsorption on coal.

2.3.2 BET isotherm In 1938, Brunauer et al., modified some of the assumption of Langmuir model and provided an extended Langmuir model for multilayer adsorption popularly known as the Brunauer, Emmet, and Teller (BET) model. This model assumes that the surface of the adsorbent is energetically homogeneous with no interaction between the adsorbed molecules. Moreover, the heat of adsorption is equal to the molar heat of condensation in all layers except for the first layer which acts as a stack. At saturated vapor pressure, the adsorbate condenses to liquid on the surface of the solid leading to infinite layers. The BET isotherm equation is given as:

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where, Vm is the monolayer volume, C is a constant, Po is the saturation vapor pressure, and the remaining variables have their usual meaning. Although BET equation does not entirely fit into the experimental data, yet it is a useful tool that provides a theoretical foundation for the various isotherms shapes (Lowell and Shields, 1984). The validity for the BET model ranges between relative pressure values of 0.05 to 0.35 (Gregg and Sing, 1982).

2.3.3 Freundlich Isotherm:

The Freundlich equation or Freundlich adsorption isotherm is an adsorption isotherm, which is a curve relating the concentration of a solute on the surface of an adsorbent, to the concentration of the solute in the liquid with which it is in contact. In 1909, Freundlich gave an empirical expression representing the isothermal variation of Adsorption of a quantity of gas adsorbed by unit mass of solid adsorbent with pressure. This equation is known as Freundlich Adsorption Isotherm or Freundlich Adsorption equation. There are basically two well established types of adsorption isotherm: the Freundlich adsorption isotherm and the Langmuir adsorption isotherm. Here the amount of mass that is adsorbed is plotted against the temperature which gives an idea about the variation of adsorption with temperature.

x = mass of adsorbate

m = mass of adsorbent

K and n are constants for a given adsorbate and adsorbent at a particular temperature.

2.3.4 Dubinin Astakhov isotherm:

In 1967, Dubinin described adsorption on microporous adsorbents and proposed a new theory known as the theory of volume filling of micropore (TVFM). Coal being a microporous adsorbent as its pore size ranges below 20 nanometer. Thus the mechanism by which adsorption of microporous solid occurs is restricted to volume rather than their surface. Dubinin (1975) thus introduced a new theory called the Theory of Volume Filling of Micropore that postulates that, in micropores, the adsorbate occupies the pore volume by the mechanism of volume filling, and does not form discrete layers in the pores. In 1995, Dubinin and Astakhov proposed an equation based on this theory that represented the isotherms that obeyed the TVFM. The Dubinin- Astakhov (D-A) equation, it is expressed as follows:

where, V is the amount adsorbed, Vo is the micropore volume, n is the structural heterogeneity parameter that varies between 1 and 4, D=(RT/βE)n is a constant, where, E is the characteristic energy of the adsorption system, T is the absolute temperature, R is the Universal Gas Constant, and β is the adsorbate affinity coefficient. D is a constant for a particular adsorbent-adsorbate system, and is determined experimentally. Po is the saturation vapor pressure of the adsorbate at temperature T, and P is the equilibrium free gas pressure.

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2.4 ADSORPTION ISOTHERM

2.4.1 Adsorption Isotherm Measurement

Adsorption isotherm test is used to determine the gas storage capacity of a coal sample i.e., how much gas could the coal hold at reservoir temperature and pressure.

Adsorption test is essentially the reverse of a desorption test. In the adsorption test the coal sample is crushed to a very grain size, releasing any gas still present. The sample is then brought to equilibrium moisture content at estimated reservoir temperature and then placed in the adsorption apparatus to determine how much gas can be adsorbed.Methane adsorption Isotherm analyses were conducted according to procedures outlined by Moore and Crossdale (2006). The instrument used to determine adsorption isotherm of coal samples consist of a water bath, control panel, sample bombs, reference bombs, and vacuum pump. The principle underlying operation in an Adsorption isotherm unit is a known quantity of adsorbent (methane) is introduced to an adsorbate (coal sample) and the amount of gas adsorbed by the coal can be calculated by measuring the drop in pressure of the system. At reservoir temperature and equilibrium moisture conditions, methane adsorption curves were produced using the Langmuir equation assuming a mono-layer gas adsorption mechanism.In the adsorption device the reference cell is filled with a precisely known volume of gas to a pressure greater than the desired stabilized pressure. The gas in the reference cell is then released into a sample cell packed with a known mass of prepared coal sample. All components of the test system are maintained at constant temperature (usually at the estimated reservoir temperature) by immersion in a temperature regulated oil bath. The pressure is progressively increased and held at several levels. The pressure at each step is held constant for a period long enough for the adsorption of test gas to equilibrate and the volume of gas adsorbed at that pressure is recorded. The gas capacity and pressure data derived from the test generate an adsorption curve which is steep at lower pressures and then becomes flatter at higher temperatures The test gas can be a mixture of gases equivalent to the reservoir gas composition or alternatively, isotherms of the pure gas components can be determined and the isotherm for reservoir gas calculated.

Typically, six point adsorption isotherms are obtained at evenly spaced pressure increments, at constant reservoir temperature. Gas storage capacity of a coal sample, as measured by a Langmuir Isotherm, is an indirect method for predicting maximum gas storage capacity.

II.4.2 Langmuir Isotherm

The most commonly used equation to describe the adsorption of gases on a solid is that of Langmuir, who developed the theory in 1918. The major assumptions in deriving the equation are as follows:

One gas molecule is adsorbed at a single adsorption site.

An adsorbed molecule does not affect the molecule on the neighboring site.

Sites are indistinguishable by the gas molecules.

Adsorption is on an open surface, and there is no resistance to gas access to adsorption sites.

The assumption of an open surface is a troublesome one in the Langmuir theory because micropore throats leading to cavities in the coal may be thousands of molecular diameters long and only several

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molecular diameters wide. Therefore, the adsorbate does not have unrestricted access to the adsorption sites, which are far from comprising an open surface. The development of the Langmuir equation reveals how the faulty assumption still serves the true phenomenon.

At equilibrium for a given temperature, the rate of molecules of adsorbed gas leaving adsorption sites will equal the rate of those attaching to adsorption sites, somewhat similar to evaporation from the surface of liquid water.

The idealized monolayer adsorption of methane on coal matrix can be calculated by the equation:

Where V = quantity of gas adsorbed at equilibrium pressure on

coal matrix, VL = quantity of gas adsorbed at infinite pressure (Langmuir Volume), PL = pressure at which 0.5VL is obtained (Langmuir Pressure) and P = equilibrium pressure.The moisture content of coal substantially influences adsorption of gas. The gas content decreases significantly with an increase in the moisture content of the coal. If the gas content of dry coal is known, then the value for the moist coal can be approximated from the formula:

Where, H is moisture cont

2.4.3 Adsorption Isotherm dataMethane adsorption isotherm is used for describing gas content vs. pressure relationship, estimation of in-situ gas content at reservoir condition. The adsorption isotherm data as analysed when compared with measured in-situ gas content of the sample generally show under saturation.

The extent of gas saturation plays significant role in gas production. If gas saturation is high, sorbed gas from the coal will be produced much faster compared to coals having lesser degree of saturation. Adsorptive capacity of coals depends mainly on coal characteristics (e.g., coal lithotype, rank, moisture and mineral matter content) and temperature, pressure, in-situ stress, burial history and so on. Comparing the measured adsorptive capacity of the three coal samples with their respective gas content studied from the Well-I was found to vary from 60% to near saturation.

2.5 TRANSPORT PHENOMENON OF COAL BED METHANE

2.5.1 Cleats in Coal Cleats in coals are extensional fractures (Close, 1993) of genetic type. All Humic coals of sub-bituminous and above rank are characterized by two sets of orthogonal fractures where one set predates the other. The set formed earlier, are more prominent and continuous; these are called face cleats. The set formed later, are less prominent and discontinuous showing offset nature; these are called butt cleats (Fig-20). Cleats are usually filled with water. These cleats constitute the major part of a coal’s macro-porosity and permeability system. When gas flow from coal is initiated, the gas, which comes out of coal by diffusion, pushes the water in the cleats towards wellbore. Thus all CBM wells initially produce moderate to huge amount of water before a sustainable flow of gas is attained. This is called dewatering of a CBM production well. This is in contrast with a conventional reservoir like sand/sandstone (Fig.21) where water-cut is a late stage phenomenon in a producing well.2.5.2 Transport mechanism of methane in coal:

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Movement of gas in coalbeds involves three distinct steps: I. The first stage involves fuid flow through the natural fracture and cleat network caused by

decrease in the pressure on the coal seam.II. Desorption of gas at the cleat/matrix interfaces into natural fractures caused by pressure

differences.III. Finally in the third stage, the gas flows through the coal seam cleat network under Darcy flow

conditions. Although diffusion through the micropores and Darcy's flow through the interconnected fracture system in the coalbeds are separate and distinct phenomena, they are interdependent. If one of the steps is considerably slower than the other, the overall gas flow rate is determined by the magnitude of the slower step. The micropore transport of gas obeys Fick's law of diffusion:

Observation of some coals in the world indicates that the most important model of fluid transport is Darcy flow in the cleats. According to Darcy's law the flow of gas can be expressed as:

Where,K = Permeability, the property of the rock that allows fluid to flow through it, darcyq = Rate of flowA = Area of cross section of the coal core, cm2μ = viscosity of gas, cpPS = inlet pressure of the core, atmL = Length of core, cmThe gas transport equation must account for the gas slippage phenomenon. The correction for gas slippage usually takes the form of Klinkenberg equation

In other approach, the slip velocity is superimposed on to the Darcy velocity and is substituted directly into the transport equation after Fick's law. The advantage of this procedure is that the gas, which is slipping, can be treated as real gas (Klinkenberg equation was derived assuming ideal gas behaviour).

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Fig 2: Gas transport mechanism in coal

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