Simulation of an enhanced gas recovery field trial for coal mine gas management

International Journal of Coal Geology 85 (2011) 247–256

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International Journal of Coal Geology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i j c o a l g e o

Simulation of an enhanced gas recovery field trial for coal mine gas management Russell Packham a,⁎, Yildiray Cinar b, Roy Moreby a a b

School of Mining Engineering, University of New South Wales, Sydney, NSW 2052, Australia School of Petroleum Engineering, University of New South Wales, Sydney, NSW 2052, Australia

a r t i c l e

i n f o

Article history: Received 30 September 2010 Received in revised form 27 November 2010 Accepted 27 November 2010 Available online 13 December 2010 Keywords: Enhanced gas recovery Coal mine gas management Pre-drainage Methane drainage Nitrogen

a b s t r a c t Coal mine gas management has evolved from being predominantly dependant on mine ventilation systems to utilising sophisticated surface based directional drilling for pre-drainage of coal seams. However the advent of enhanced gas recovery techniques in the coalbed methane industry has provided an opportunity to address gas management objectives hitherto impractical. Specifically: achieving very low residual gas contents to mitigate against frictional ignitions and fugitive emissions; the means to accelerate gas drainage to accommodate mine schedule changes; and to enable pre-drainage of coal reserves with very low permeability. This article examines a possible enhanced gas recovery field trial at an Australian mine site. Production data from four surface to inseam medium radius gas drainage boreholes was modelled and history matched. The resulting reservoir characteristics were then used to model the performance of the boreholes using an enhanced recovery technique. One of the boreholes is modelled as an (nitrogen) injection well and two flanking wells are modelled as production wells. The model results suggest that accelerated gas flow rates as well as very low residual gas contents are achievable using typical coal mine gas drainage infrastructure and goaf inertisation systems. © 2010 Elsevier B.V. All rights reserved.

1. Introduction As underground coal production rates increase, and the seams worked become deeper and gassier, the practise of gas drainage has been progressively adopted. Gas drainage involves capturing the seam gases, before they enter the mine ventilation system, and using a reticulation system to dispose of the gases safely. Gas drainage includes pre-drainage of gas prior to mining commencing and postdrainage (also known as goaf or gob drainage) of gas from fractured and de-stressed strata associated with coal extraction. Adoption of medium radius drilling for surface pre-drainage of coal seams has allowed drainage lead times in excess of 3 years (Humphries et al., 2006). Typically this degree of pre-drainage achieves residual gas levels that do not impede mining operations. There are, however, some scenarios that still provide difficulties from a coal mine gas management perspective: • Localised regions of low permeability requiring extended drainage time not compatible with mine development and extraction schedules. • Changes in mine development schedules requiring accelerated drainage. • Lowering residual gas levels to very low levels as a possible mitigation of frictional ignitions and fugitive emissions.

⁎ Corresponding author. Tel.: +61 2 9385 4517; fax: +61 2 9313 7269. E-mail address: [email protected] (R. Packham). 0166-5162/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.coal.2010.11.013

A promising technique referred to as “enhanced gas recovery” was described by Puri and Yee (1990). The technique was proposed for use in the coalbed methane industry to both increase cumulative production of methane from coal seams and to improve the rate of recovery. Recognition of the potential value of this technique with respect to coal mining has largely been overlooked by coal mining industry although two references to the possibilities have been found (Brunner and Schwoebel, 2007; Thakur, 2006). The technique involves injecting a gas, which is different to the seam gas, into the coal seam to stimulate methane (or other seam gas) production. The injectant is introduced into the coal seam via an injector borehole and the seam gas is collected at separate production borehole(s). Four field trials involving using nitrogen as an injectant gas have been identified. The Tiffany unit trial (Reeves and Oudinot, 2004) which ran for 3 years demonstrated a 5-fold increase in gas flow rate arising during the trial. The Alberta Fenn Big Valley micro pilot trial (Mavor et al., 2004) demonstrated increases of absolute permeability from initial conditions of 1.2 mD to 13.8 mD resulting from nitrogen injection. During the Yubari CO2 sequestration trial (Shi et al., 2008), in an attempt to improve the CO2 injection rate, N2 was introduced to the reservoir. Modelling of the results indicated that an improvement in well block permeability of 0.1 mD to 40 mD accrued. One trial involving nitrogen injection has been conducted at an underground coal mine in China (Yang et al., 2010). The trial involved injection of nitrogen at 500 kPa into closely spaced, 15–20 m long gas drainage boreholes at the face of a development heading. The gas flow

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rate from the production boreholes demonstrated a 2 fold increase after 16 h of injection. The stimulation of the gas production and seam permeability is brought about by several mechanisms which are described below. The objective of this paper is to determine whether enhanced gas recovery can be applied to coal mine gas drainage systems, theoretically and practically. The specific research questions are: • Can enhanced gas recovery be used to lower residual seam gas content to negligible levels? • Can enhanced gas recovery be used to significantly increase gas drainage recovery rate? 2. Background – fluid flow in coal 2.1. Coal structure

−0:6615

τ = 3:1014 × IRD30

Gas in coal exists predominantly as molecules adsorbed on the internal surface of the coal matrix (Zuber, 1996). The adsorbed gas exists within the coal matrix at near liquid density (Yee et al., 1993). Unlike natural gas reservoirs in which gas exists in the pore space of the reservoir, coal seams can store comparatively large volumes of gas at low pressures. Coal seams also demonstrate an orthogonal fracture system known as cleat. The cleat system is comprised of face cleat and butt cleat, which typically exists at 90° to face cleat. Butt cleat is terminated by face cleat and both orientations tend to be normal to the bedding plane horizon. The cleat system provides a transport route for gas migrating through the seam. It should be acknowledged that two separate processes control the flow of gas from a coal seam reservoir to a gas drainage system: diffusion of gas from adsorbed state in the coal matrix to the cleat fracture system, and flow through the cleat fracture system as free gas. The cleat system is generally saturated with water before the gas drainage process begins. In order to explain the process of enhanced gas recovery it is desirable to understand the mechanisms affecting ‘primary’ gas recovery. Two laws that control the rate of gas recovery from a coal seam are the Darcy's law which governs gas and water flow through the cleat system and the Fick's Law which models the gas diffusion from the coal matrix into the cleat system. 2.2. Diffusion – Fick's law and adsorption isotherms The mechanism by which gas migrates from the very small pores of the coal matrix to the cleat system is diffusion. Three types of diffusion can contribute to the overall diffusion rate namely, bulk diffusion, surface diffusion and Knudsen diffusion (Cui et al., 2004; Zuber, 1996). The diffusion coefficient, D, is a composite of these three type of diffusion. Diffusion of gas from the coal matrix into the cleat system is described by the modified Fick's law (Zuber, 1996): qgm =

8πDVm ðCm −C ðpÞÞ s2f

ð1Þ

where the gas production rate qgm, is a function of matrix volume, Vm, and the difference between the matrix gas concentration, Cm, less the equilibrium concentration at the matrix cleat boundary C(p). The diffusion coefficient, D, and fracture spacing, sf, are normally lumped together through the use of desorption time, τ, which may be derived from a gas content testing. τ=

s2f 8πD

derived from the gas content of a coal sample measured using a slow desorption method. Most Australian coal mines conduct pre-drainage for mitigation of potential outburst hazards. The outburst hazard is assessed during routine mine operation by gas content testing for which a fast desorption method is generally used. τ cannot be directly determined from a fast desorption gas content test. However a common feature of slow and fast desorption gas content testing is the measurement of initial desorption rate to determine lost gas (“Q1”). From the initial desorption rate of the core the volume of gas desorbed in the first 30 min after the core was deemed to have started desorption is measured. This volume, referred to as “IRD30” in fast desorption testing, has been used to provide a correlation to τ (Williams and Yurakov, 2003, pp. 71–72):

ð2Þ

τ is defined as the time taken for 63.2% of the total gas to diffuse at constant pressure from a coal sample (King et al., 1986). τ can be

ð3Þ

This correlation has been used to provide an indicative τ for the seam gas at the mine site subject to this investigation. The use of τ to characterise the desorption behaviour of the reservoir is simplistic. The simplification arises from the assumption that the fracture spacing of cleat and shape factor of the matrix in the coal sample are representative of the whole reservoir. The diffusion coefficient, D, is related to the pore size within the matrix and the mean free path of the gas molecule (Cui et al., 2004). Thus where an injectant gas is used to stimulate diffusion of a seam gas, a separate desorption time must be identified for each gas if the process is to be modelled. The concentration of gas in the coal matrix is defined by the coal's characteristic adsorption isotherm and has a non-linear relationship with pressure. Yee et al. (1993) provide a good description of the various models available for defining isotherms. Pan and Connell (2008) have discussed the problems associated with various adsorption models in relation to potential errors and practicality of application. Of the models the Langmuir isotherm model is widely used for primary gas drainage modelling and can be modified to create binary or ternary gas mixture isotherms from pure gas isotherms as is necessary when examining the effects of multiple gas species adsorbing and desorbing in a coal matrix. The Langmuir model is described by (Zuber, 1996):

V=

VL βp βp + 1

ð4Þ

where V is the coal gas content at pressure p in equilibrium, β is the Langmuir constant, and VL is the Langmuir volume defining the adsorption isotherm for a single gas in a specific coal seam. Where the Langmuir model is used in a mixed gas environment (such as enhanced gas recovery or where the seam gas composition is a variable mixture of methane and carbon dioxide) the Extended Langmuir Model (ELM) may be applied:

VEi =

VLi pYi βi 1 + p∑nc j = 1 Yj βj

ð5Þ

such that , VEi is the extended Langmuir storage capacity of component i, VLi is the Langmuir volume for pure component i; Yi, is the mole fraction of component i; nc is number of components, and βi is the Langmuir constant for component i. There is an assumption in the use of ELM that there is no interaction between the different gas species arising from counter-diffusion as would occur in an enhanced recovery process.

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the coal matrix in enhanced gas drainage). Assuming the pressure of the free gas in the cleat is in equilibrium with the adsorbed gas, then:

2.3. Darcy's Law For a 1-D, single phase flow through a porous medium (coal seam) in the following manner Darcy's Law is described by:   kx ∂P ∂D −ρgx μ ∂x ∂x

vx = −

249

ð6Þ

Volumetric flux in the x direction, vx, is a function of seam permeability, kx, the fluid viscosity, μ, and the incremental pressure drop. The pressure drop relates to the difference in pressure at the gas drainage borehole and the seam gas pore pressure. In Australian longwall mining environments the coal seams are typically almost level, as a consequence gravitational effects on gas flow are negligible. Seam permeability is a dominant parameter for gas production rates. 2.4. Permeability variations Permeability is known to be sensitive to effective (horizontal) stress brought about either by local tectonic or geological structures and also by the shrinkage or swelling of the coal matrix due to desorption or adsorption of gas. Gray (1987) described permeability of a coal seam in relation to the changes in effective stress in the coal seam, where, if water is removed from the cleat, the matrix blocks are less constrained and tend to compress the cleat. This process, referred to as cleat compression, leads to a reduction in permeability. As the fluid pressure in the cleat system falls, gas desorption occurs. The subsequent release of gas from the matrix into the cleat causes the matrix to shrink and a reduction in effective horizontal stress. In terms of permeability changes, the two processes, cleat compression and matrix shrinkage tend to cancel each other. Several analytical models have been developed to interpret the effect of cleat compression and matrix shrinkage on reservoir permeability. Palmer (2008) provides an exposition of the analytical models and discusses how the reservoir permeability may be determined from either change in volumetric strain/porosity or effective horizontal stress. Seidle et al. (1992) described how coal seam permeability changes in effective horizontal stress: −3cf ðσ−σo Þ

Δεs = αs ðV−V0 Þ

ð10Þ

where αs is the volumetric shrinkage/swelling coefficient for a specific gas (i.e. a seam gas, methane or an injectant gas such as nitrogen), V corresponds to the gas content at the reservoir pressure, p; Vo is the gas content at the initial reservoir pressure po. V and Vo can be determined using the Langmuir isotherm (see Eq. (4)). This allows the change in effective horizontal stress to be determined resulting from cleat compression and matrix shrinkage or swelling due to change in pore pressure: ðσ−σo Þ = −

  ν Eαs VL βp βp0 − ðp−po Þ + 1−ν 3ð1−νÞ 1 + βp 1 + βp0

ð11Þ

In an enhanced gas drainage process using nitrogen as an injectant, the coal matrix desorbs one gas, generally methane or carbon dioxide, and adsorbs nitrogen. The net matrix shrinkage effect is thus determined by the volumetric shrinkage coefficients, αs and the mixed gas adsorption isotherm characteristics for the desorbing and adsorbing gasses as may be determined from the extended Langmuir model, Eq. (5). 2.5. Gas-water relative permeability Gas drainage from coal seams includes typically gas and water. The water exists predominantly in the cleat space (pore volume) whereas the gas exists initially in an adsorbed state in the matrix. As desorption occurs gas becomes present as ‘free gas’ in the cleat space thereby creating the second phase within the cleat system. Gas may also be dissolved in water. The solution of gas is negligible for methane in water but may be significant for carbon dioxide in water. At initial conditions the cleat space is typically saturated with water and the effective permeability of the cleat to gas is zero. In order for gas to flow, the water saturation must be reduced. This is achieved by ‘drawdown’ of the gas drainage well. Drawdown refers to pumping water out of a gas well and progressively reducing the well pressure to enable water to flow to the well and subsequently gas, see Fig. 1.

ð7Þ

k = ko e

where ko is the initial permeability, cf is the cleat-volume compressibility and σ is the horizontal stress. Shi and Durucan (2004) developed a relationship to enable the calculation of change in horizontal effective stress resulting from changes in reservoir pressure and desorption of gas from the coal: ðσ−σo Þ = −

  ν E p p0 εl ðp−po Þ + − 1−ν 3ð1−νÞ p + Pε p0 + Pε

ð8Þ

where εl and Pε are the matrix shrinkage constants, ν and E are the Poisson's ratio and Young's Modulus of the coal, respectively. Initial or reference horizontal stress and pore pressure are σ0 and p0, respectively. The two terms on the right hand side of the equation relate to cleat compression and matrix shrinkage respectively. Volumetric shrinkage strain, Δεs, is considered in the Shi/Durucan formulation to be related to the Langmuir type relationship of matrix strain at the maximum adsorbed gas content and the gas content pressure at which half of the maximum strain occurs:  Δεs = εl

p p0 − p + Pε p0 + Pε

 ð9Þ

Shi and Durucan (2005) further developed this relationship to account for matrix swelling (as may occur where a gas adsorbs onto

Fig. 1. Schematic depiction of coal seam relative permeability (Koenig, 1990).

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Underground gas drainage holes achieve ‘drawdown’ by drilling the hole from seam horizon at atmospheric pressure whereas surface gas drainage boreholes achieve drawdown by pumping water from the well. Relative permeability is important in relation to gas drainage from coal seams as the characteristic of the relative permeability curves determine how much water (%) must be removed from the seam before gas begins to flow. The gas flow, desorption/diffusion and permeability relationships referred to above may be modelled by means of finite difference numerical modelling (King et al., 1986). Several coal-bed-methane simulators are available to model these behaviours. Law et al (2002) compare 5 simulators as part of an investigation into improvements for enhanced coalbed methane modelling. One of the simulators, Simed2, has been used in this research (the windows version – SimedWin). 2.6. Primary production Primary production thus is brought about by pressure reduction at a production well causing fluid flow through the cleat system to the well. Fluid flow in turn causes a pressure reduction at the cleat/matrix interface resulting in desorption of gas within the matrix and diffusion of the gas to the cleat interface. The pressure at which desorption occurs is determined by the adsorption isotherm. The gas flow rate is controlled by the reservoir absolute permeability, relative permeability and desorption pressure. Relative permeability is dependent on the cleat water saturation which also affects initial cleat compression. Primary gas production inevitably results in a falling flow rate as reservoir gas content is reduced. Enhanced gas recovery, through the use of nitrogen as an injectant gas, affects: • Gas flow rate by maintaining higher differential pressure between the reservoir and production well – δp/δx in Eq. (6). • Residual gas content by maintaining a high concentration gradient between the coal matrix and cleat interface, Cm−C(p) in Eq. (1). • Pore pressure induced permeability effects by controlling cleat compression whilst enabling matrix shrinkage, Eq. (11). 3. Hypothesis The hypothesis speculates that a goaf inertisation nitrogen membrane system, already used at some Australian mine sites, with a capacity of 43,200 sm3/d at up to 1 MPa (abs), may also be used to introduce an injectant into a gas drainage borehole. When flanked by similar boreholes, this may stimulate recovery of residual methane from the coal seam. The objectives are to: 1. demonstrate the ability of enhanced gas recovery to increase gas flow rates in a coal mine gas drainage environment and 2. reduce the gas content of the coal matrix to a level that would result in negligible methane emission upon mining, thus eliminating fugitive gas emissions and frictional ignition hazards. The sections that follow describe how the hypothesis is tested by means of numerical modelling of an existing coalmine gas drainage system.

4. Well details 4.1. SIS wells Production data for 10 horizontal surface to inseam (SIS) wells for methane pre-drainage has been provided by an Australian coal mine co-operating with ACARP Project 17055. The production data spans a period of five years between April 2004 and April 2009. The production data was collected from a well management system and includes down hole pressure (bottomhole pressure), casing pressure (at the surface), surface temperature, surface differential pressure (from the flow device), and down hole pump speed (derived from surface motor speed). From this primary data, drainage performance characteristics such as the water level in the vertical well (and well block pore pressure), gas flow rate, and water flow rate were derived. Ten horizontal SIS holes were drilled over a 12 month period to pre-drain three longwall blocks. The holes, referred to as SIS21-30, average 2500 m long with a maximum length of 2806 m. A further 8 holes (SIS34-41) were drilled in 2008 to drain two more longwall blocks. All holes were drilled to a finished diameter of 147 mm. The details of the SIS holes used in the production history matching are shown in Table 1. All SIS holes intersected a vertical production well at the deepest point of the lateral. In addition a secondary ‘service’ well closer to the end of the lateral was intersected (Fig. 2). Both the build section of the lateral wells and the vertical wells were cased to within 3 m of the coal seam (a 3 m interval is maintained to avoid interaction between mining equipment and the casing steel). The lateral surface collar and service well surface collar are fitted with isolation valves and mechanical pressure gauges. Gas and water production were managed from the vertical production well; the service well was used for pressure monitoring and lateral flushing as necessary. SIS21 to SIS30 are essentially parallel and drilled due north from similar collar northings. The East/West separation of the wells varies from 97 m to 130 m. It can be seen from Table 1 that the initial down-hole pressure is significantly less than that which would be expected from the hydrostatic head. The operation of the wells differs slightly from standard CBM approach in that the wells are connected to a vacuum plant (at a utilisation facility), and in the latter stages of the well production the well operating pressure is reduced to atmospheric pressure or slight partial vacuum. The implication is that the ultimate residual gas content of the reservoir will not be lower than gas content at atmospheric pressure (~1.3 m3/t). 4.2. Piezometer wells In addition to the SIS lateral and vertical wells, seven piezometer wells (PZ1–PZ7) were drilled within the region influenced by drainage from SIS28–SIS30. Cores were taken from each well for gas content analysis (by a fast desorption method). Six of the wells successfully had vibrating wire piezometers installed at the coal seam horizon. A description of piezometer installation is provided by Doyle and Poole (2006). The piezometers began monitoring pore pressure at

Table 1 SIS well specifications. SIS well

Total length (m)

Total inseam (m)

Seam intersection (m)

Plan length inseam (m)

Depth to coal (m)

Drilling started

Pumping operational

Initial DHP (kPa)

Desorption date

Desorption pressure (kPag)

27 28 29 30

2685 2595 2604 2806

2729 3045 3053 3766

338 398 379 406

2346 2197 2226 2399

162 173 169 171

2/06/06 18/11/06 3/01/07 16/01/07

26/07/06 28/04/07 28/04/07 28/04/07

857 650 807 841

26/07/06 4/05/07 30/04/07 29/04/07

857 584 793 793

R. Packham et al. / International Journal of Coal Geology 85 (2011) 247–256

251

Fig. 2. Schematic depiction of an SIS drainage installation.

the end of 2006. Due to the location of the piezometer wells and the proximity of the mine site inertisation facility, SIS29 was chosen as a potential enhanced gas drainage injection site. The general arrangement of the SIS and piezometer wells is shown in Fig. 3.

5. Model development 5.1. Reservoir simulation Gas drainage at coal mining operations behaves in the same manner as at coal-bed-methane operations although there are some aspects of the mining process which affect the larger gas reservoir. Longwall coal extraction results in extensive fracturing (and thus permeability and porosity changes) to superjacent strata, including non-extracted coal seams. In addition, stress relief of subjacent strata caused by the longwall may also result in gas desorption and flow from beneath the longwall panel. Management of gas liberated by these processes is referred to as post-drainage (also goaf or gob drainage). The dominant mechanism in post-drainage is the roof and floor stress re-distribution, and subsequent permeability stimulation. Pre-drainage of gas within a coal mine lease using surface to inseam drilling, in preparation for development drivage, is generally

Fig. 3. Mine plan showing the location of SIS holes and piezometer wells.

conducted in areas which are not subject to the superjacent and subjacent stress regimes associated with longwall operations. An exception to this is multi-seam longwall extraction, which, whilst common in Europe, China and Russia is comparatively uncommon in Australia. With this caveat, modelling of methane pre-drainage at coal mines may be satisfactorily achieved using coal-bed-methane simulators. There are two features associated with coal mine operations which may reasonably be considered to have implications for pre-drainage which would not be present in standard CBM operations: 1. Hydrological effects caused by the presence of mine workings (situated in the coal seam in which pre-drainage activities are conducted). Mine workings, roadways and regions of completed extraction, exist at near atmospheric pressure, as such the workings form a low pressure sink within the gas reservoir. Where the reservoir is (gas) under-saturated, the migration of water is likely to occur to the workings. Relative permeability effects will tend to limit the twin phase flow of gas and water once desorption pressure has been reached. However it may reasonably be assumed that the effect of mine workings would result in reduced hydrostatic gradient and earlier onset of gas desorption than would otherwise occur. 2. Stress abutments associated with mine workings. Re-distribution of vertical load associated with longwall extraction and to a lesser extent development drivage may be expected to have localized influence on effective horizontal stress. Increasing effective horizontal stress in turn reduces permeability. In flat coal seams these effects would be expected to extend no further than 50– 100 m from the periphery of the longwall (significantly less for development roadways). Pre-drainage operations undertaken in excess of 1 km from longwall activity may reasonably be considered immune to these stress abutment permeability effects. SimedWin is a coal seam methane reservoir simulator providing a multi-component (methane, nitrogen and CO2), two phase (gas and water), dual porosity (Fickian and Darcian flow) and fully implicit model (Stevenson and Pinczewski, 2006). As such Simedwin is considered suitable for modelling gas drainage (both primary and enhanced) at coal mines. SimedWin also incorporates a feature specifically relevant to coal mine operation, namely the facility to model gas emissions into a mine roadway as the drivage advances within the seam and as the reservoir age increases. This facility could be used to model the impact of mine workings as an atmospheric pressure ‘sink’ within the reservoir. Initial attempts to model the region bounded by SIS28 and SIS30 using the production details of SIS28, SIS29 and SIS30, proved unsatisfactory in terms of the bottom hole pressures and desorption pressures. In an attempt to simulate the reservoir conditioning

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brought about by the operation of wells 21–27(and possibly the effect of mine workings), a four well model including SIS27 to 30 was established. An exponential grid was created to model the horizontal wells within the reservoir, the grid spacing being narrower closer to the horizontal wells. The grid has 3132 blocks (Fig. 4). SIS27 began operation approximately 9 months prior to SIS28 and had the effect of reducing the pore pressure at wells 28–30 such that desorption began almost immediately upon drawdown. It is feasible that the effect of the mine workings and preliminary operation of SIS21–27 cumulatively brought the reservoir pressure at SIS28–30 to below desorption pressure prior to the start of drawdown operations, unfortunately piezometer data is not available to define this. It can be seen from Fig. 4 that the reservoir model dimension is large, 2000 m by 3500 m. The size of the model is largely driven by the SIS hole geometry, and the attempt to minimize boundary effects.

pressure started to rise and desorption pressure could be deduced from the bottomhole pressure (accommodating the position of the sensor beneath the seam) at the time the casing pressure starts to increase. The reservoir desorption pressure is thus only related to the highest gas content along the immediate wellbore. 5.4. Relative permeability Modelling of methane drainage from the coal seam requires an interpretation of the gas-water relative permeability. SimedWin offers three relative permeability curve sets and the facility to create specific curves. During the modelling process several relative permeability curve sets were tried, the set adopted is shown in Fig. 5. The set chosen provided the best match for bottomhole pressure and peak gas flow.

5.2. Water production Each vertical production well is fitted with a progressive cavity pump with its inlet in a sump approximately 10 m beneath the seam. The rate of water production from individual horizontal wells was inferred from the pump motor run time record, the pump motor speed, and pump efficiency. Motor run time and speed were recorded continuously by the well management system and stored as hourly data. Pump efficiency was determined by conducting weekly ‘bucket tests’ of the pump flow rate at a fixed operating speed. Normal operating pump speed was automatically controlled to maintain a set water level in the vertical well. Due to the automated control of the pump, the average pump speed changed daily. To model the water production rate, ten day average pump speed (expressed as a flow rate) were defined for each well in the model. 5.3. Desorption pressure Desorption pressure (Table 1) was estimated by comparing the bottom hole pressure and surface casing pressure during drawdown. The gas production line on the vertical production wells were shut-in during initial drawdown; as the water level in the well fell as a result of pump operation the casing pressure also fell slightly (due to the partial vacuum in the casing). When desorption began the casing

5.5. Adsorption isotherms Langmuir isotherm tests for CO2, CH4 and N2 were conducted for four samples from one borehole. In addition, data from a further twelve methane isotherms from seven separate boreholes was considered in relation to the model isotherms. The methane isotherms, adjusted to 12.5% ash and a test temperature of 31 °C, are shown in Fig. 6. It can be seen that a wide range of isotherms characteristics exist for the same seam. Samples used for testing isotherms had ash contents varying between 5.2 and 15.1% ash. An average seam ash of 12.5% was used for the isotherm selection. 5.6. Desorption time, τ From the seven piezometer wells, 25 separate core samples were tested for gas content using a fast desorption technique. The average desorption time, τ, derived using Eq. (3) and the “IRD30” values of the gas content tests was 4.34 days. The gas composition for the cores was predominantly methane (~ 97%). Desorption time for nitrogen was estimated to be 3 days. Due to the empirical nature of the derivation of tau, the model simulations were run with several combinations of desorption time for CH4 and N2.

Fig. 4. Numerical model grid design.

Relative permeability

R. Packham et al. / International Journal of Coal Geology 85 (2011) 247–256

1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.00

253

Table 2 History matched model parameters.

krwt krgt

0.20

0.40

0.60

0.80

1.00

Water saturation Fig. 5. Gas-water relative permeability curves used in the simulations.

Parameter

Value

Source

Seam thickness Gas content Langmuir volume CH4 Langmuir volume N2 Langmuir pressure CH4 Langmuir pressure N2 Permeability (x and y) Poisson's ratio Young's modulus Max sorption strain Cleat compressibility Porosity Desorption time CH4 Desorption time N2

2.7 m 6.75 m3/t 28.51 m3/t 27.93 m3/t 2258 kPa (abs) 5722 kPa (abs) 5 mD 0.35 2.62e6 kPa 7.98e−3 1.16e−4 kPa−1 0.85% 10 days 7 days

Site data Site data Lab' report GeoGAS 2008-538 Sample OC12297 12.5% ash at 31 °C Site data, variable. (Shi et al., 2008)

Variable Variable

5.7. Reservoir geology Longwall coal extraction requires benign geological conditions to achieve satisfactory economic outcomes. Geological structures such as full seam displacement faults, dykes, sills, washouts and seam interburden can present impediments to longwall operations and are investigated prior to longwall panel design. For this reason the degree of geological definition at coal mine sites is often better than that at CBM operations. The implication for gas drainage at this site is that there is confidence that SIS wells are situated within a reservoir which is largely unaffected by structures which may have significant localised effects on permeability or gas-in-place. Survey details from the SIS wells indicate a gentle anticline structure trending East West near the service well locations. The coal does not have inter-burden capable of influencing vertical permeability within the seam. 6. History matching 6.1. Matched parameters In order to test the hypothesis prior to a site trial, the numerical reservoir simulator SimedWin was used to history match production data for the period between April 2006 and April 2009. History matching involved fixing the water production rates as per site records and modifying other reservoir parameters to achieve an acceptable match to SIS29 methane production rate and bottomhole pressure. The parameters modified included permeability and porosity, seam thickness, seam gas content, adsorption isotherm, Young's modulus and Poisson ratio, cleat compression and matrix shrinkage coefficients. The permeability response to change in reservoir pressure has been treated in terms of effective horizontal stress in relation to sorption strain and cleat compression as described by Shi and Durucan (2004). The parameters used in the final matched model are given in Table 2.

SIS27 began drawdown at day 0, SIS29 began at day 276. The model is matched to the well water production and defaults to the minimum bottomhole pressure where the water rate cannot be achieved. The model runs to day 987 (8th April 2009). Two discrepancies are evident: 1. It can be seen from Fig. 7, that SIS27 has drawn down the pore pressure at SIS29 to desorption pressure of 707 kPa by day 276. This implies that the pore pressure at SIS29 was not 900 kPa at day 0. However in order to honour the Langmuir isotherm desorption values and indicated average reservoir gas content (6.75 m3/t) the match has been accepted. A desorption pressure of 900 kPa(abs) would require a gas content of ~8.2 m3/t, the effect of this on the model is to increase the peak and ongoing gas flow rates. The discrepancy is a feature of this model which has used uniform gas content for the entire reservoir rather than a variable gas content that would allow higher gas contents and desorption pressures around parts of the SIS well. 2. After approximately day 400 the bottomhole pressure in the history match model is higher than actual. It was found that reducing both the porosity and permeability helped bring the model closer to actual. However the permeability used of 5 mD is considered at the low end of the acceptable range and the porosity of 0.85% appropriate. Reducing porosity independent of permeability results in increasing the well gas flow rates. Fig. 8 shows a comparison of SIS29 actual and modelled flow rates. Matching peak flow may be improved by reducing gas content or permeability, however as stated above, 5 mD is considered reasonable and reducing gas content has the effect of lowering the desorption pressure. A closer match may be achieved by modifying the relative permeability curves, however within the limitations of uniform gas content, seam depth and seam thickness, and to test the hypothesis, the model is considered adequate.

20

1000

Gas content m3/t

16 methane isotherm used in model 14

}

12 10

900

CH4 N2

8 6

SIS 29 history match

700 600 500 400 300

4

nitrogen isotherm used in model

2 0

SIS 29 Actual

800

BHP kPaa

}

18

0

500

1000

1500

2000

2500

200

SIS27 100 operational 3000

Pressure kPa

0

0

100

200

300

SIS29 operational 400 500 600

700

Production day Fig. 6. CH4 and N2 isotherms, corrected for ash content and temperature (reported at 20 °C and 1 atm).

Fig. 7. SIS29 bottomhole pressure.

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900 1000

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1000

16000

SIS 29 Actual

14000

SIS 29 History match

12000 10000 8000 6000 4000 2000 0

0

100

200

300

400

500

600

700

800

Bottomhole pressure kPa

Gas Flow rate m3/day

18000

900

4.84 mD, 0.85% ø. R22

700 600

8.24 mD, 0.76% ø. R76

500 1.61 mD, 0.78% ø. R13

400 300 200 100 0

900 1000

6.04 mD, 0.99% ø. R24

800

0

200

The effect of varying the desorption time parameter for methane was investigated (Table 3). It can be seen that tau appears to have a noticeable difference on the peak flow rate for VW29 but a small effect on cumulative methane recovery. 6.2. Stochastic simulations A Monte Carlo model was used to generate simulations using random combinations of permeability and porosity from a predefined distribution. A total of 118 realisations of the model were conducted. Two specific features were observed. Firstly, a “bounce” in the bottomhole pressure was predicted in a large number of realizations. The bounce occurs as a result of a low permeability being applied, an example of this is shown in Fig. 9, realisation R13. In this example the well-bore pressure quickly declines in the early stages of pumping when pumping rates are comparatively high. Then as the pumping rates fall, the well-bore pressure increased suggesting that the pumping rate did not match the water inflow rate. A further feature was the high peak gas flow predicted by a large number of the realizations (Fig. 10). Actual peak gas flow was around 15,000 m3/day (Fig. 8). High peak flow requires low porosity and high to average permeability, the effect of porosity on peak flow can be seen in realisations, R22, R24 and R76 in Fig. 9. This effect is interpreted as a combination of absolute permeability, relative permeability and porosity. Specifically, with a fixed pumping rate, lower porosity results in a comparatively larger region of reduced water saturation around the well bore. In turn the reduced water saturation results in higher relative (gas) permeability and enables higher gas flows to occur. The stochastic simulations support the choice of the permeability as 5 mD and porosity as 0.85%. 7. Injection model Using the reservoir parameters established by the history match and stochastic simulations, an injection model was built to predict the effects of enhanced recovery on the reservoir behaviour. The model was matched up to day 987, then projected in drawdown only, up to day 1071 when nitrogen injection was initiated. The injection model was set to allow injection at 43,200 sm3/d until a BHP of 1 MPa

Table 3 Effect of varying methane desorption time on peak flow and cumulative methane recovery. Tau, methane, in days. 4.34 10 20

VW29 peak flow m3/d

VW29 cumulative CH4, drawdown to day 987, m3

18,493 16,516 16,838

4,639,702 4,667,842 4,682,407

600

800

1000

Fig. 9. Monte Carlo simulations of bottomhole pressure at VW29 with variable porosity and permeability.

(abs) then continue injection at a maximum of 1 MPa (abs). Nitrogen injection is continued until day 1320 when the injection well is shut-in and the model run until day 1756. The model assumes a sweep efficiency of 100%, i.e. that the injected nitrogen does not follow preferential flow paths or regions of higher permeability between the injection well and production wells. In relation to the condition of the reservoir at the end of injection, day 1320, it can be seen that: 1. In the enhanced drainage model the methane content around the injection well SIS29 is close to zero (Fig. 11). 2. A region of increased methane content has developed due to the flushing of gas toward the adjacent production wells SIS28 and SIS30 (“Day 1320, Enhanced” Fig. 11). This is attributed to the increased reservoir pressure brought about by the nitrogen injection (Fig. 12). 3. The methane content at SIS28 has fallen below what would be expected at atmospheric pressure (well operating pressure) presumably due to the stimulated diffusion effects of nitrogen flowing towards the well (Figs. 11 and 12). The reservoir pressure increase in the region between SIS28 and SIS30 represents a significant ‘energising’ of the reservoir. An implication of the increased reservoir pressure caused by the injection (and adsorption) of nitrogen (Fig. 12) and the reduced methane content at SIS28 caused by enhanced diffusion of CH4 from the matrix (Fig. 11), is that the region will experience further enhanced recovery after injection at SIS29 is suspended (assuming that SIS29 is shutin). This is evident from the reduced methane content shown in the enhanced model as compared to the drawdown model for day 1756 (Fig. 11) and the reduction in reservoir pressure at day 1756 (Fig. 12). A comparison of the cumulative methane production from the region bounded between SIS28 and SIS30 (Fig. 13, Table 4) shows that

30000

Gas Flow rate m3/d

Fig. 8. SIS29 comparative gas flow rates.

400

Model Days

Production day

8.24 mD, 0.76% ø. R76

25000

4.84 mD, 0.85% ø. R22

20000

6.04 mD, 0.99% ø. R24

15000

1.6 mD, 0.78% ø. R131

10000 5000 0 0

200

400

600

800

1000

Model Day Fig. 10. Monte Carlo simulation of gas flow rate at VW29 with variable porosity and permeability.

Day 1320, Enhanced Day 1320, Drawdown

3

Day 1756, Enhanced 2.5

Day 1756, Drawdown

2 1.5 1 0.5 0

SIS27

790

SIS29

SIS28

840

890

940

990

1040

SIS30

1090

1140

1190

East West cross section, meters

a net increase in cumulative gas production was brought about by the nitrogen injection process after day 1235 and that the increased rate of methane recovery continues after injection stops. The initial falloff in methane production is due to SIS29 well being converted from a production well to an injection well. The composition of the produced gases is shown in Fig. 14. By the end of injection at day 1320, the nitrogen component of the produced gas at VW28 and VW30 is 56% and 31% respectively. This level of nitrogen breakthrough would represent a significant contaminant in a CBM operation. It is common at Australian mines for pre-drained gas to be used to generate power in reciprocating engines. The engines are capable of operating on a wide range of methane concentrations, the composition of the produced gas would not be a problem. The recovery in the methane cut after injection is stopped, for SIS30 and to a lesser extent SIS28, is considered to result from methane draining from outside the region bounded by SIS28 and SIS30. The improvement in incremental recovery (Table 4) between the end of injection, day 1320, and the end of the model run, day 1756, is significant. However the recovery has required 5 Mm3 of nitrogen and an extra 436 days drainage. A means by which the methane may be recovered more quickly would be to increase the differential pressure between the reservoir and the production wells. As the production wells are operating at or slightly below atmospheric pressure there is little scope for achieving this at the production wells. However if the injection pressure were increased the flow rates may reasonably be expected to increase. There is scope to increase injection pressure up to a maximum outlet pressure of the membrane filter (without additional booster compressors) of 1.3 MPa abs (personal communication, S.Joseph, 2010). A further opportunity to reduce the drainage time would be to start nitrogen injection before day 1070. The choice of day 1070 as the start of

1000 Day 1070, start of injection Day 1320, end of injection

800

kPa (abs)

700

13.0

Injection started

6.0

Injection ended

5.0

12.5 12.0

4.0

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Model Day

Fig. 11. Reservoir CH4 content at days 1320 and 1756, enhanced drainage and drawdown only models.

900

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Cumulative injected nitrogen Mm3

Methane content, m3/t

3.5

Cumulative produced methane Mm3

R. Packham et al. / International Journal of Coal Geology 85 (2011) 247–256

Day 1756.

600 500

Fig. 13. Comparison of cumulative methane production from the region bounded by SIS28 and SIS30.

an enhanced recovery trial represented the earliest feasible injection date at the specific site. The significant factors for an injection start date would be that the reservoir had been established, through drawdown, in a two phase flow condition and that the injection pressure was significantly higher than the maximum reservoir pressure. Injection of nitrogen at higher pressures would be expected to result in higher reservoir pressure around the injection well, with nitrogen stored in the reservoir in the form of adsorbed gas. An initial elevation of methane content within the reservoir, as shown in Fig. 11 may be expected. This is due to the movement of methane toward the production wells at higher pressure and subsequent re-adsorption at higher gas content. However if the production wells are maintained at atmospheric pressure the elevated methane would ultimately drain. The rate at which the enhanced recovery occurs is related to the injection pressure. The amount of enhanced recovery that may be achieved is related to the volume of nitrogen injected. Where the reservoir has a very high permeability such that the injected gas passes through to the production well rapidly or where the coal desorption time is very high, the diffusivity of the coal may be a controlling factor. This condition would be identified as early breakthrough of nitrogen with little associated methane. In these circumstances the ‘residence’ time of the nitrogen within the reservoir should be increased by increasing the operating pressure of the production wells. The effectiveness of the nitrogen injection is dependent on certain conditions: • The coal seam is not layered with significant variation in permeability between layers. If this were the case preferential flow of nitrogen may be expected in the high permeability layers resulting in early nitrogen breakthrough and reduced recovery. Stevenson et al (1993) examine the economics of multi layered permeability variation. • Injection of nitrogen should not occur before adequate dewatering by drawdown has been achieved. If injection starts before water saturation has been reduced sufficiently to achieve high relative gas permeability, viscous fingering may arise (Meaney and Paterson, 1996). Viscous fingering may result in trapped regions of water within the reservoir and associated reduced methane recovery.

400 300 Table 4 Cumulative methane production in the region between SIS28 and SIS30, drawdown and enhanced models.

200 100 SIS27

0 790

SIS28

840

890

940

SIS29

990

1040

SIS30

1090

1140

1190

East-Westcross section, meters Fig. 12. Comparative reservoir pressure at days 1070, 1320 and 1756.

Model

Day 1070

Day 1320

Day 1756

Drawdown model, cumulative CH4 m3 Enhanced model, cumulative CH4 m3 Incremental CH4 m3

9,515,114 9,515,114 0

10,470,780 10,755,731 284,951

11,542,492 12,570,364 1,027,872

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Gas Component fraction

1

the SimedWin modelling. John Weissman, Brandon McCowan, Paul Bannerman, and Jordan Allen must also be acknowledged for their help in relation to the mine site production data.

nitrogen injection stopped

0.9 0.8 0.7 0.6

VW28 N2

0.5

VW28 CH4

0.4 0.3

References

VW30 CH4 VW30 N2

0.2 0.1 0 1000

1100

1200

1300

1400

1500

1600

1700

1800

Model Day Fig. 14. Gas component fraction at VW28 and VW30.

8. Conclusions In relation to the initial hypothesis it is apparent that the region immediately around SIS29 has been stripped of methane and as such could eliminate a frictional ignition hazard for the development drivage. This condition has extended to SIS28 by day 1756 although part of the region between SIS29 and SIS30 has a methane content above that which would occur at atmospheric pressure (~1.3 m3/t). In relation to fugitive emissions, assuming the incremental methane recovered through the use of enhanced recovery would otherwise contribute to a greenhouse emission, and that the cost of carbon (equivalent) emissions were Aus$25 per tonne, and that nitrogen cost were Aus$0.07 per m3 (Brady et al., 2008). Then the cost of the nitrogen injection is Aus$352,777 and the offset carbon tax, Aus$377,743. It is feasible that enhanced recovery techniques may find a role in the management of fugitive emissions from underground coal mines. With regard to accelerated gas flow rates and reduced drainage times, it is evident that flow rates are likely to be improved through the use of nitrogen injection although injection pressure, reservoir volume, desorption time may be limiting factors. Based on a reservoir model calibrated through history matching, enhanced gas recovery utilizing existing SIS gas drainage wells and a nitrogen membrane filter in a depleted reservoir is achievable. Enhanced gas flow rates are to be expected through the use of nitrogen injection in the reservoir described. Furthermore a significant reduction in the residual methane content around the injection well occurs as a result of nitrogen injection and it is reasonable to consider this will have a mitigating affect on fugitive emissions and the potential for frictional ignitions during development drivage. Reducing the methane content of the entire reservoir (between boreholes SIS28 and SIS29) however, requires a prolonged drainage period due to the size of the reservoir and the injection pressure of the nitrogen plant. Based on the modelling results an enhanced drainage trial at the site is justified to test and demonstrate the model findings. An enhanced recovery trial based on this modelling began on 6th July 2010. Acknowledgements The first author wishes to acknowledge the Australian Coal Association Research Program (ACARP) for support of this research through ACARP scholarship C18003 and ACARP project C17055. In addition we thank Xstrata Coal for the provision of SIS well data and the facilities to conduct the trial. The author also wishes to thank Luke Connell of CSIRO Petroleum for his suggestions and assistance with

Brady, J.P., Burra, S., Calderwood, B.R., 2008. June 9-11 The Positive Pressure Chamber. Paper presented at the 12th U.S./North American Mine Ventilation Symposium 2008, Reno Nevada. Brunner, D., Schwoebel, J., 2007. In-mine methane drainage strategies. American Longwall, pp. 38–39. May. Cui, X., Bustin, R.M., Dipple, G., 2004. Selective transport of CO2 CH4 and N2 in coals: insights from modelling of experimental gas adsorption data. Fuel 83, 293–303 2004. Doyle, J., Poole, G., 2006. The use of downhole piezometers, implications for modern underground mines. Paper presented at the Coal Operators' Conference, University of Wollongong. URL: http://ro.uow.edu.au/coal/42. accessed 25/11/10. Gray, I., 1987. Reservoir engineering in coal seams: part 1–the physical process of gas storage and movement in coal seams. SPE Reservoir Eng. 2 (1), 28–34 SPE 12514-PA. Humphries, P., Ogden, A., Fusheng, L., 2006. Pre-mining gas drainage technologies optimisation: Australian Coal Association Research Program. Report C13020. King, G.R., Ertekin, T., Schwerer, F.C., 1986. Numerical simulation of the transient behavior of coal seam degasification wells. SPE Formation Eval. 1 (2), 165–183 SPE 12258-PA. Koenig, R.A., 1990. Well testing to determine two-phase flow properties of coal seams. In: Paterson, L. (Ed.), Methane Drainage from Coal. CSIRO, pp. 39–45. Law, D.H., van der Meer, L.G.H., Gunter, W.D., 2002. Numerical simulator comparison study for enhanced coalbed methane recovery processes, part I: pure carbon dioxide injection. Paper presented at the SPE Gas Technology Symposium, Calgary. SPE 75669. Mavor, M.J., Gunter, W.D., Robinson, J.R., 2004. Alberta multiwell micro-pilot testing for CBM properties, enhanced methane recovery and CO2 storage potential. 26-29 September Paper presented at the SPE Annual Technical Conference and Exhibition, Houston. SPE 90256. Meaney, K., Paterson, L., 1996. Relative permeability in coal. Paper presented at the SPE Asia Pacific Oil and Gas Conference. Adelaide, Australia. SPE 36986. Palmer, I., 2008. Permeability changes in coal: analytical modelling. Int. J. Coal Geol. 77, 119–126. Pan, Z., Connell, L.D., 2008. Comparison of adsorption models in reservoir simulation of enhanced coalbed methane recovery and CO2 sequestration in coal. Int. J. Greenhouse Gas Control 3 (1), 77–89. Puri, R., Yee, D., 1990. Enhanced coal bed methane recovery. Paper presented at the SPE 65th Annual Technical Conference and Exhibition, New Orleans. SPE 20732. Reeves, S., Oudinot, A., 2004. The Tiffany Unit N2 – ECBM Pilot: a reservoir modelling study. US DoE Topical report, DE-FC26-0NT40924. Seidle, J.P., Jeansonne, M.W., Erickson, D.J., 1992. Application of matchstick geometry to stress dependant permeability in coals. Paper presented at the SPE Rocky Mountain Regional Meeting, Casper, Wyoming. SPE 24361. Shi, J.Q., Durucan, S., 2004. Drawdown induced changes in permeability of coalbeds: a new interpretation of the reservoir response to primary recovery. Transp. Porous Media 56 (1), 1–16. Shi, J.Q., Durucan, S., 2005. A model for changes in coalbed permeability during primary and enhanced methane recovery. SPE Reservoir Eval. Eng. 8 (4), 291–299 SPE 87230-PA. Shi, J.Q., Durucan, S., Fujioka, M., 2008. A reservoir simulation study of CO2 injection and N2 flooding at the Ishikari coalfield CO2 storage pilot project, Japan. Int. J. Greenhouse Gas Control 2 (1), 47–57. Stevenson, M.D., Pinczewski, W.V., 2006. SIMEDWIN – multicomponent coalbed gas simulator, users manual: centre for petroleum engineering, University of New South Wales. CSIRO Petroleum. Stevenson, M.D., Pinczewski, W.V., Downey, R.A., Stevenson, M.D., Pinczewski, W.V., Downey, R.A., 1993. Economic evaluation of nitrogen injection for coalseam gas recovery. Paper presented at the SPE Gas Technology Symposium, Calgary. SPE 26199. Thakur, P.C., 2006. Coal seam degasification. In: Kissell, F. (Ed.), Handbook for Methane Control in Mining. National Institute for Occupational Safety and Health., Information Circular 9486, Pittsburgh, PA, p. 85. Williams, R.J., Yurakov, E., 2003. Improved application of gas reservoir parameters: Australian Coal Association Research Program. Report C10008. Yang, H., Zhang, T., Wang, Z., Zhao, C., 2010. Experimental study on technology of accelerating methane release by nitrogen injection in coalbed. J. China Coal Soc. 35 (5), 792–796. Yee, D., Seidle, J. P., and Hanson, W.B., (1993). Gas Sorption on Coal and Measurement of Gas Content. In Law and Rice (Eds.), Hydrocarbons from Coal (pp. 203-218): American Association of Petroleum Geologists. Zuber, M.D., 1996. Basic reservoir engineering for coal. In: Saulsberry, J., Schafer, L.P., S, Schraufnagel, R. (Eds.), A Guide to Coalbed Methane Reservoir Engineering, GRI-94/0397. Gas Research Institute, Chicago, pp. 3.4–3.5.