Evaluation of the relative importance of coalbed reservoir

parameters for prediction of methane inflow rates during mining

of longwall development entries

 ̈ C.O. Karacan

Pittsburgh Research Laboratory, National Institute for Occupational Safety and Health, Pittsburgh, PA 15236, USA

Abstract

This study presents a reservoir modeling approach to investigate the relative effects of different coalbed parameters on

the migration of methane into development entries. A base coalbed reservoir model of a three-entry development section,

where grids were dynamically controlled to simulate the advance of mining at a constant section advance rate, was created

and calibrated for a Pittsburgh Coalbed mine in the Southwestern Pennsylvania section of the Northern Appalachian

Basin. The values of coalbed parameters were varied to evaluate their effects on predicted methane emissions for various

development distances.

The results of these parametric simulations were then used to derive linear expressions relating these parameters to

methane emissions into the workings. These models were analyzed to assess their significance and adequacy for predictive

purposes. This work shows that coupling reservoir simulations with linear modeling yield a technique that can be

applicable to different coalbeds. The reservoir parameters used by the linear models (coalbed thickness, pressure, sorption

time constant, Langmuir parameters, permeability) can be determined by running relatively simple laboratory tests, such

as adsorption equilibrium and permeability determination, on coal samples obtained either from the mining operation or

from the exploratory boreholes drilled ahead of mining.

1. Introduction

High methane liberation rates experienced during

development mining can result from the intrinsic

properties of the coalbed reservoir or from properties of the mining operation such as mining rate,

mining height, and entry length, to name a few. In

the case of unexpectedly high methane emissions

and subsequent increases in methane levels, mining

activity must be either slowed or stopped until these

high levels are diluted and removed from the active

workings by the ventilation airflow. Unfortunately,

the emission rates are controlled not only by

changes in mining parameters, but also by changes

in the coalbed reservoir parameters. Other than

increasing ventilation airflow, there are few means

available for offsetting the effects of high methane

Tel.: +1 412 386 4008; fax: +1 412 386 6595.

E mail address: cok6@cdc.gov
emissions originating as a result of the intrinsic

properties of the coalbed. Since all coalbeds differ in

their gas storage and flow characteristics, the ability

to predict the methane emissions based on a wide

range of coalbed reservoir parameters can lead to

more efficient ventilation system designs.

The recognition of methane in coalbeds as a

valuable resource has led to the development of

different numerical approaches for modeling the

storage and flow mechanisms of gas and water in

coal seams (King and Ertekin, 1991). The gas

storage and transport mechanisms of coalbeds are

complex and interacting. In order to simplify these

mechanisms and the resultant model, Gilman and

Beckie (2000) developed a coalbed methane model

whose parameters were combined into a few

dimensionless parameters. They used that model

to evaluate the importance of some coalbed parameters on methane migration. Due to the complexity and non-linearity of the equations, Zhao and

Valliappan (1995) have proposed a finite-element

approach instead of the commonly used finitedifference schemes where the pressure and concentration of methane due to gas migration in the

coalbeds were simulated (Valliappan and Wohua,

1996). However, finite-difference-based, pseudosteady and unsteady-state models described by King

and Ertekin (1991) continue to be the most widely

accepted and applied techniques for simulating the

complex storage and transport processes in coalbeds, since these type of models can realistically

represent the complex matrix-fracture transport

processes in the coalbeds.

The application of reservoir models for predicting

field performance of production wells was proven to

be successful in different field cases and helped

develop this additional energy resource (Ertekin

et al., 1988; Zuber, 1998; Young et al., 1991). These

models offered advanced predictive capabilities for

the benefit of the mining industry through evaluation and design of degasification wells (King et al.,

1986; Brunner et al., 1997; Maricic et al., 2005). The

reservoir modeling techniques, incorporating strata

disturbances and moving boundary conditions have

also been applied to the complex situations of

methane control from gob areas and for predicting

the performances of gob gas ventholes under

different completion and panel design situations

(Karacan et al., 2005, 2007). Reservoir modeling

was also demonstrated as a versatile technique for

prediction of methane inflow into development

entries (Zuber, 1997). Karacan (2007) used a

coalbed reservoir modeling approach with moving

boundary formulation to optimize ventilation air

requirements with and without degasification boreholes in the case of development mining and

integrated the results with artificial neural network

approach as an optimization method. As an

alternative approach, Lunarzewski (1998) developed and used the ‘‘Lunagas’’ method of gassiness

prediction based on research results and on

empirical results of the intensity of gas release per

unit area of exposed coal and the decay of gas

release with time.

Field demonstrations of coalbed methane reservoir simulators for project development and economics led to investigations into the impacts of

various coalbed parameters as controlling factors

for the performance of production wells. The

impacts of coalbed parameters on methane production were investigated using commercial and research reservoir simulators (Zuber et al., 1987;

Young, 1998; Remner et al., 1986; Young et al.,

1992). It was reported that some parameters were

more influential than others. As a result of their

parametric studies on a field case, Zuber and

Olszewski (1992, 1993) stated that the coalbed

parameters with the greatest impact on methane

simulation forecasts were adsorbed gas content,

desorption isotherm, water saturation, coalbed

thickness, permeability, and porosity.

Similar parametric studies have not been conducted for determining the relative importance of

coalbed parameters for controlling methane on

longwall or development mining sections. Reservoir

models can be extended to include the properties of

the mining environment and can define the effects of

each coalbed parameter or combination of parameters on methane inflow into mine workings. Such

simulations can help answer specific questions

related to mine ventilation. However, reservoir

modeling may require sophisticated simulation

packages and expertise to use and interpret them,

which may not be available to most mine operators.

Simpler, yet predictive, models will be helpful to

mine operators to quantify emissions into mine

entries from a coalbed whose critical properties can

be determined through simple laboratory testing.

Thus, multiple-factor linear models augmented by

reservoir simulations can be valuable tools for

predicting methane inflow into entries during

development mining. Such models allow the assessment of the relationships between methane inflow

rates and several independent coalbed parameters.
During the analysis, a linear combination of

coalbed parameters that is maximally correlated

with the methane inflow rates is developed. This

gives a linear equation that predicts methane inflows

using available coalbed parameters.

Multiple regression analysis allows assessment of

the relationship between one dependent variable

and several independent variables. However, when

multiple independent variables contribute to the

same dependent variable, it is sometimes difficult to

predict how the dependent variable will change

based on the changes in the independent variables.

Also, the independent variables should be uncorrelated. In the case of highly correlated independent

variables, large changes in the estimated regression

parameters may occur when a variable is added or

deleted (Sokal and Rohlf, 1994; Devore and Peck,

2001). It is also important to include significant

variables and to exclude the non-significant ones

that may mask the interpretation of the importance

of the independent variables. Backward elimination

is one of the multiple regression techniques that

judges the importance of each independent variable

based on its contribution to the dependent variable.

This technique has an advantage over forward

selection and stepwise regression because it is

possible for a set of variables to have considerable

predictive capability even though any subset of

them does not. Forward selection and stepwise

regression may fail to identify them. Because the

variables do not predict well individually, they may

never enter the model to have their joint behavior

evaluated. Backwards elimination starts with all

independent variables in the model, so their joint

predictive capability can be evaluated (Motulsky

and Christopoulos, 2004).

The objective of this work is to develop simple-touse, yet accurate, predictive models for methane

inflow into the entries during longwall development

mining of coal seams by using reservoir simulation

and multiple regression analysis techniques. This

objective quantifies the sensitivity of methane inflow

to different coalbed parameters and extends the

predictions of the base model to other three-entry

developments operating in different coalbeds as well

as evaluating their significance and adequacy for

predictions.

2. Reservoir modeling of development mining and

methane emissions

The reservoir model was constructed using

Computer Modeling Group’s (Computer Modeling

Group Ltd., 2003) compositional reservoir simulator (GEM) to simulate development mining of a

three-entry tailgate and headgate and calibrated

using the methane emission data measured in a mine

operating in the Pittsburgh Coalbed (Fig. 1)

operating in the Southwestern Pennsylvania section

of the Northern Appalachian Basin. The grid values

were controlled and the models were run ‘‘dynamically’’ to simulate advancing entry development.

The models were calibrated for various entry

lengths using in-mine measurements of methane

inflow rates obtained during tailgate and headgate

entry developments. In collecting this data, monthly

averaged ventilation flow rates and air quantities

were measured by mine personnel using methanometers and anemometers at the monitoring locations in belt and return entries shown in Fig. 1.

Monitoring points

Tailgate entries

Headgate entries

Direction of development

Start of monitoring End of monitoring W E

N

S

Ventilation

airflow

direction

Direction of development

Bleeder

Fig. 1. Modeled longwall panel showing entry sections where mining and ventilation data were gathered during development mining.

Using airflow rate and methane concentrations in

both sets of data, they calculated monthly averaged

methane inflow rates during mining of headgate and

tailgate entries. They also reported total linear

distances advanced during mining and the clean

and raw tonnages produced. The length of each
entry section was around 11,000 ft (3353 m) and

took 8 9 months to mine.

2.1. Coalbed reservoir and modeling parameters

The base model was a coalbed methane reservoir

model where a single-layer coalbed was modeled in

cartesian coordinates to simulate fluid flow in the

unmined sections of the coalbed. In model construction, the base parameters given in Table 1 were

used for the Pittsburgh Coalbed. These base

parameters were used to match the predicted

methane emissions during mining with the in-mine

measurements.

Table 1

Coalbed properties and their ranges used in simulations of

development mining and statistical analysis of results

Parameter Regression

variable name

Values used in

predictions

Coalbed thickness (ft) Thick 5, 6a

, 7

Coalbed pressure (psi) Pres 90a

, 200, 400

Sorption time (days) S.Time 20a

, 125, 250

Permeability anisotropy

(Kx/Ky)

Anisot. 4a

, 8

Face cleat permeability

Kx (md)

Kx 4a

, 20, 40

Butt cleat permeability Ky

(md)

Ky 0.5, 1a

, 2.5, 5,

10

Langmuir volume (scf/ton) L.Vol. 200, 392, 490a

,

600

Langmuir pressure (psi) L.Pres. 126, 326a

, 526

Initial water saturation

Swi (%)

W.Sat. 40, 60a

, 100

Effective porosity (%) Por. 0.5, 2, 4a

, 5

Irreducible water

saturation Swirr (%)

Irr.W.Sat. 10, 30, 40a

, 58

Relative permeability to gas

(Krg) at Sg 1 Swirr

G.Rel.Perm. 0.35a, 0.5, 0.7,

0.9

a

Base reservoir values used in developing the base simulation

model.

The gas content and adsorption related data for

the Pittsburgh Coalbed was obtained from the

results of methane adsorption and direct method

of gas content determination tests on various coal

samples (Diamond et al., 1986). The spatial distributions of fracture permeabilities of the Pittsburgh

Coalbed have not been previously established or

reported. However, based on a large-scale modeling

study involving estimation of some coalbed parameters (Karacan et al., 2005, 2007), the average

permeabilities for the Pittsburgh coalbed were

estimated to be 4 md in the face cleat direction

and 1 md in the butt cleat direction. In the

simulations, these values were taken to be uniform

throughout the layer.

Hunt and Steele (1991) indicated that the

coalbeds in the Central and Northern Appalachian

Basin are desaturated and depressurized due to

geological history, extensive coal mining, and the

presence of many oil and gas wells. Thus, initial

water saturation and pressure of the Pittsburgh

Coalbed in the Northern Appalachian Basin were

estimated to be 60% and 90 psia (6120 kPa) for this

study, respectively. These numbers correspond to

60% of the available coalbed porosity, mainly cleat

porosity, as water saturated and 90 psia (6120 kPa)

as the initial fluid pressure in the coalbed.

The gas relative permeability curve of the coalbed

was estimated by matching the average gas production rate from the simulated boreholes in the models

to the reported average methane production rates of

three horizontal degasification boreholes in the

mining area [8.42 scf/day/ft (0.782 m3

/day/m) from

simulations vs. 8.70 scf/day/ft (0.807 m3

/day/m)

from field measurements]. A similar field-data-based

adjustment could not be made to the water relative

permeability curve because no data was available.

Thus, the relative permeability of water at initial

water saturation was set low so the wells would

experience low amounts of water [0.0016 bbl/day/ft

(0.0015 m3

/day/m)] as saturation changes. Although

this is an assumption for a desaturated coalbed and

the number may not be exact for water production

in this specific field, the real-life practice in the study

mines proved that there was not a major water

inflow or accumulation problem in the entries

during longwall mining or during development

mining.

In the Pittsburgh Coalbed in the Northern

Appalachian Basin, face and butt cleats are

perpendicular and parallel, respectively, to the fold

axis. In this mine, in the plane of mine roof, the

major horizontal principle stress is 2370 psi at North

781 East, and the minor horizontal principle stress is

2200 psi. The gate road orientation and sequencing

of longwall panel extraction relative to the in situ

horizontal stress field can have a major impact on

the gate road stability. Thus, mining direction is

approximately in the E W direction in the study

mine. Furthermore, in this field face cleats were

oriented nearly in the E W direction and butt cleats

nearly in the N S direction. This information

indicates that the direction of mine advance is

approximately parallel to the face cleats and
perpendicular to butt cleats. When positioning the

simulation grids and assigning the permeabilities,

attention was given to cleat directions.

2.2. Modeling of development mining process and

performing the simulations

For modeling advances of tailgate and headgate

entries, a three-entry development model around a

longwall panel was studied. Fig. 2a shows a

snapshot of mining advance, pillar layout, and

ventilation scheme. The middle entry was modeled

as the ‘‘track’’ or haulage, and intake entry, where

intake air flowed to the mining area. In this entry,

ventilation air injection and mine pressure assignments to the grids were performed using an injector

well. The entry to the left of ‘‘track’’ was designated

as the ‘‘belt’’ entry. The third entry was designated

as the ‘‘return’’ entry carrying away a majority

(490%) of the methane emissions and the methaneloaded ventilation air. The producer wells used in

these entries both assigned the mine pressures and

monitored the amount of methane in the produced

gas stream.

Return

Intake/

Track

Belt Direction

of advance

Monitoring

locations in 

the model

Pillar

Stopping

C

C

C

Stopping

Ventilation curtain

Monitoring Pillar

b c

d e

a

Fig. 2. A snapshot of mining advance, pillar layout and ventilation scheme in coalbed reservoir model. Ventilation arrows schematically

represent flow magnitude (thicker arrows represent higher flow). Locations where total methane inflow is monitored are also shown (a).

(b e) Progress of mining in coalbed between four successive section advance steps. Figures show entries, cross cuts, stoppings and location

of ‘‘curtains’’ dynamically created during simulations plus path of ventilation airflow occurring during simulations.

During mining of the headgate and tailgate developments, entries were extended and interconnected by
cross-cuts. The amount and rate of methane

emission into the developed entries depended upon

the extent of the continually created new surfaces.

As the continuous mining machine advanced, new

volumes were created that required ventilation,

while new surfaces were created that liberated gas

into that volume. This constituted a moving

boundary value problem, which was handled using

‘‘restart’’ model runs. These models were run

sequentially, with each run characterizing an

advance in entry development using a specified

development rate. Coalbed properties were replaced

with the assigned properties of the entries in the

models, and ventilation-related features were constructed as required. Each restart run was performed so that entries would advance on a

determined rate. This approach was used by

Karacan (2007) to model development mining in

coal seams to estimate ventilation air requirement

with and without degasification/shielding boreholes

drilled along the entries. Karacan et al. (2005, 2007)

also used this approach to model the longwall

mining process and the performances of gob gas

ventholes, which are drilled from the surface on the

active mine panel to control methane emissions into

the mine as a result of extensive fracturing of the

overlying strata.

In building the restart models, all three entries

were developed simultaneously to a specific distance in a predefined amount of time, allowing calculation of the mining advance rate. For

different rates, the times in the recurrent data

set were changed. Thus, the rates reported in this

study are not linear mining rates, but instead

represent the rates that the mine section advanced. Based on this approach, a 150 ft (45.7 m)

section advance corresponded to 570 ft (173.7 m)

of linear mining distance in the model, which

included developing three entries and required

cross-cuts.

As the entries advanced, the pillars and cross-cuts

were simultaneously developed. The pillars between

the entries were 125 ft (38.1 m) in length and 75 ft

(22.9 m) in width and were assumed to have the

same properties as the coalbed. During the development of entries, each of which was 20 ft (6.1 m) in

width and the same height as the coalbed, the

permeability was replaced with a high permeability

[109 md (10 6 m2

)] in all three directions. Also, the

coal-matrix pressures in the mined grids were

assigned to atmospheric pressures to simulate the

mining process.

The development of the cross-cuts was modeled

the same way as the entries. However, during each

simulation run only the last set of cross-cuts was left

fully open for ventilation airflow. In the model,

stoppings (block walls) between track-belt and

track-return were automatically constructed between the restart runs to force ventilation flow

through the last open cross-cuts at each section

advance. A permeability of 100 md was assigned to

the stoppings to represent a low leakage, a common

occurrence in underground mining. This value was

selected in the absence of measured permeability

data for the stoppings. A ‘‘curtain’’ resistance

created in the last section of the ‘‘intake’’, or

‘‘track’’, diverted some of the intake air towards

the ‘‘belt’’ entry to ventilate both belt and face

(Figs. 2c e) as it happens in the mining environment. Figs. 2b e show the progress of mining between four successive section advance steps. These

figures show the entries, cross-cuts, stoppings and

the location of the ‘‘curtains’’ created during

simulations plus the path of the ventilation airflow

during simulations.

2.3. Matching reservoir model predictions of

methane inflow with in-mine measurements

Various factors control methane emissions during

development mining. Among these factors, coalbed

parameters and mining parameters are probably the

most important. In this study, the base coalbed

parameters for the Pittsburgh seam (Table 1) and

the mining parameters reported by the mine were

used to calibrate and test the capability of the

developed model for predicting the monthly, averaged in-mine methane emissions.

During mining, the linear advance distances and

lengths of exposed rib were reported as monthly

totals. The mining distances were reported as linear

distances mined (including entries and cross-cuts),

which were around 4500 6500 ft (1372 1981 m) per

month, rather than the daily advance rate of the

three-entry sections. In order to establish a comparison between measured data and the reservoir model

formulation, linear mining distances were converted

to net advance of the section. For this purpose, a

ratio was calculated using the measured lengths of

cross-cuts and entries and the net monthly advance

of the entries determined from the mine maps. This

approach revealed a ratio of 0.27 (1 section ft 1⁄4 3.7

linear ft) between these two-length scales. Thus, the

linear mining distances were converted to distances
in the direction of mine advance. The advance rates,

using the lengths in the direction of mine advance,

were calculated based on two eight-hour production

shifts and one maintenance shift per day for six days

per week. The majority of calculated section

advance rates were between 70 and 110 ft/day

(21.3 33.5 m/day) during production shifts and

working days. The average rate of mining to

develop both sections to full length was approximately 80 ft/day (24.4 m/day).

The predictive performance of the reservoir

model was compared with in-mine measurements

of methane inflow, reported as monthly averages,

during development of the tailgate and headgate

entries. The simulation results using the base

reservoir data (Table 1) and calculated advance

rates of 70 and 110 ft/day for 2000 12,000 ft

(610 3658 m) development distances were compared

with the in-mine methane inflow rates.

Fig. 3 shows the simulator predictions and

measured methane inflows into the headgate and

tailgate entries. The solid markers and the trendlines show the simulator predictions for methane

emissions with the upper and lower advance rates as

a function of development distance. Since the

simulations use constant mining and coalbed parameters, its methane inflows show a continuous

increase with distance, as opposed to the scattered

increase in measured data. However, the developed

base model closely predicts the range of the

measured data.

3. Effect of coalbed parameters on methane inflow

into entries during development mining

0

100000

200000

300000

400000

500000

600000

700000

800000

900000

1000000

0 2000 4000 6000 8000 10000 14000

Entry Length (ft)

Methane Inf ow (scf/day)

Tailgate Entries - Measured

Headgate Entries - Measured

70 ft/day - Model

110 ft/day - Model

12000

Fig. 3. Comparison of measured methane inflow into mine and reservoir simulator (GEM) predictions at two different average daily

mining rates practiced during development of entries.

This study investigated the impacts of selected

coalbed properties on methane inflows for 2000,

6000, 10,000 and 12,000-ft-long (610, 1830, 3050,

and 3660 m) development distances. For the parametric analyses, the values of key coalbed properties were varied around their base values that were

used to match the field measurements as shown in

Table 1.

For the parametric analyses, the calibrated

reservoir model was run with 50 ft/day (15.3

m/day) section advance rate rather than the 70 or

110 ft/day rate mentioned previously in model

calibration discussions for the study mine. The

reason for simulating a lower mining rate is that

most mining operations run their continuous

mining machines fewer days per week or with fewer

production shifts than the study mine of the base

case. Mining fewer days a week or less number of

hours within a day reduces the average daily section

advance rate. This means that a section length to be

mined takes longer time for when mining machines

operate shorter periods, which is equivalent to

decreasing linear advance rate in numerical models.

Since the purpose of the study is to develop models

with a more general applicability, a lower average

daily section advance rate was selected. The following sections discuss the changes in methane inflow

data resulting from variations (i.e., all other values
remaining constant at the base values) in coalbed

parameters.

3.1. Effect of coalbed permeability and permeability

anisotropy on methane inflow into development

entries

Permeability is an intrinsic property of porous

formations that relates to pressure drop and flow

rate. In coalbeds, vertical permeability is usually

significantly lower than horizontal permeability

because of the presence of bedding. Thus, horizontal permeability and its direction (anisotropy) are

more important in coalbed reservoirs. Horizontal

permeability and its anisotropy in coalbeds are

characterized with two orthogonal permeability

components that run in the direction of characteristic fractures within the coalbed. These are termed

the face and butt cleats. Face cleats are continuous

and can extend for long distances. However, butt

cleats are short and discontinuous, usually terminating at face cleats. Because of the nature of these

two cleat systems, face cleats are more permeable to

gas and water flow. The permeability anisotropy can

be defined as the ratio of face cleat (Kx) to butt cleat

(Ky) permeabilities.

The presence or lack, and direction of permeability has a profound effect on methane inflow into

the wellbores (Remner et al., 1986), suggesting that

any horizontal drilling in coalbeds should account

for directional permeability. The average permeability for flow in coalbeds can be defined as

Ka 1⁄4 pKxKy, (1)

where Ka is the average permeability and Kx and Ky

are the directional permeabilities of the cleats.

Direction and magnitude of permeability is

important for control of methane emissions during

mining. When mining advances perpendicular to the

face cleats, where permeability is higher, much more

gas is emitted into mine workings than when the

advance is parallel to the face cleat. In fact, in one

area of a mine operating in the Pittsburgh coalbed,

the methane emissions from the solid ribs were

significantly higher than the emissions from the

working face as a result of the ribs intersecting the

face cleats (McCulloch et al., 1975).

In this study, mining advance was oriented

parallel to the face cleats to mimic the modeled

mine. The effects of permeability anisotropy and

directional cleat permeabilities on methane emissions into the development entries were evaluated.

Both face and butt cleat permeabilities were varied

between minimum and maximum values shown in

Table 1. Permeability anisotropies were increased by

decreasing the butt cleat permeability. Anisotropies

could have been increased by increasing face cleat

permeability rather than decreasing butt cleat

permeability. However, since mining was parallel

with face cleat permeability, the effect of this change

would have been less compared to the changes

obtained by varying butt cleat permeability, which

were perpendicular to entries in this case. This

argument is further supported by statistical analysis

presented in the following sections.

Fig. 4 presents the simulated average methane

inflow rates as a function of permeability anisotropy, average permeability calculated using Eq. (1),

and development distance. This figure shows that

increasing average permeability, while keeping the

anisotropy constant, increases methane inflow into

the entries. On the other hand, doubling anisotropy

decreases methane inflow even though the face cleat

permeability is unchanged. This is due to lower flow

from the decreased butt cleat permeability, which is

perpendicular to the entries in this study. Also, this

figure shows that the effects of anisotropy or

changes in butt cleat permeability are more pronounced for longer development distances. In a

more general sense, the effect of butt cleat permeability observed in this study should be interpreted

as the effect of coalbed permeability perpendicular

to the entries, based on orientation of mining. Thus,

cleats perpendicular to entries are more important

than parallel ones for contributing to methane

inflow.

3.2. Effect of porosity on methane inflow into

development entries

The fracture or cleat system is the main source of

porosity in coalbeds. Gas can exist as free gas in the

fractures and cleat network or in a sorbed state in

the coal matrices. However, cleat porosity is usually

small and the amount of methane residing in the

cleats as free gas is much less compared to the

sorbed gas. The fine micropore structure of coal has

a very high storage capacity for methane compared

to a fracture volume of the same size (Zuber, 1996).

Porosity in coalbeds is related mainly to water

storage capacity (Young et al., 1992).

Fig. 5 shows the effects of changing coalbed

porosity on methane inflow into the entries. The

data in this figure show that increasing porosity
slightly decreases average methane inflow into the

entries. As porosity is increased in a constant

reservoir volume, the fraction of the volume

previously occupied by the high methane storage

capacity matrices is replaced by fractures whose

methane content is less. This is equivalent to

decreasing the gas-in-place of the coalbed, which

causes average flow rate to decrease. Fig. 5 also

shows that the effect of increased porosity on

methane inflow rate is greater when mining longer

entries [12,000 ft (3660 m)] than when mining shorter entries [2000 ft (610 m)]. As longer entries are

mined, more gas flows from the coalbed because of

an increased drainage area and pressure sink. As a

result, the impact of decreased methane in-place is

more pronounced.

0

100000

200000

300000

400000

500000

600000

700000

0 10 15 20

Average Permeability (md)

Methane Inf ow (scf/day)

2000 ft- Kx/Ky = 4 2000 ft- Kx/Ky = 8

6000 ft- Kx/Ky = 4 6000 ft- Kx/Ky = 8

10000 ft- Kx/Ky = 4 10000 ft- Kx/Ky = 8

12000 ft- Kx/Ky = 4 12000 ft- Kx/Ky = 8

5 25

Fig. 4. Reservoir model simulations of methane inflow variability with permeability, permeability anisotropy, and development distance.

0

0123456

100000

200000

300000

400000

500000

600000

Porosity (%)

Methane Inf ow (scf/day)

2000 ft

6000 ft

10000 ft

12000 ft

Fig. 5. Reservoir model simulations of methane inflow variability with cleat porosity and development distance.

3.3. Effect of Langmuir volume, Langmuir pressure,

and coalbed pressure on methane inflow into

development entries

In coalbeds, the major portion of the gas exists in

adsorbed state, rather than in a free state. As the

pressure is lowered due to fluid production from the
cleats, gas starts to desorb from the micropore

surfaces and diffuse into the macropores (Remner

et al., 1986). Adsorption and desorption of methane

from coal is described by a Langmuir isotherm,

which defines the relationship of coalbed pressure to

the capacity of a given coal to hold gas at a constant

temperature. More specifically, the Langmuir isotherm for coals relates matrix gas content, V(P), to

the coalbed cleat pressure, P, according to

VL VðP  P Þ 1⁄4 , (2) ðP þ PLÞ

where VL is the Langmuir volume or maximum

amount of gas that can be adsorbed. PL is the

Langmuir pressure or a characteristic measure of

residence time for a gas molecule on the surface and

represents the pressure at which gas storage capacity

is half of the maximum storage capacity, VL

(Young, 1998). Both VL and PL can be determined

from gas sorption measurements on the coal core

samples. The Langmuir Eq. (2) provides a necessary

boundary condition at the matrix cleat interface

(Young, 1998). For non-equilibrium diffusion sorption models, it is assumed that the concentration of

methane at the surface of the micropore matrix

blocks is in equilibrium with the free gas pressure in

the cleats. This implies that the external boundary

condition of the micropore equation is the equilibrium sorption isotherm (King et al., 1986).

The shape of this isotherm is important for

manipulating the boundary condition between

matrix and cleats and to control desorption of gas

from coal. The shape of the isotherm is largely

affected by VL and PL. These two quantities dictate

the gas content of the coal at a certain cleat pressure

and gas release rate as pressure decreases.

Cleat pressure is also important for determining

the gas content of the coalbed for a given VL and

PL. However, it should be noted that, initially, the

actual amount of gas in the coalbed (gas content)

may not be on the desorption curve defined by the

Langmuir isotherm and may be below this curve. In

this case, coalbed cleat pressure needs to be reduced

further until it reaches a critical desorption pressure

where gas starts to desorb and gas release follows

the Langmuir isotherm as pressure declines. VL and

PL also determine how quickly the critical desorption pressure is going to be reached at such a

condition.

0

0 100 300

200000

400000

600000

800000

1000000

1200000

1400000

1600000

1800000

2000000

200 400 500

Coalbed Pressure (psi)

Methane Inf ow (scf/day)

2000 ft

6000 ft

10000 ft

12000 ft

Fig. 6. Reservoir simulations of methane inflow variability with coalbed pressure and development distance.

Fig. 6 shows the effect of coalbed pressure on

methane inflow during development mining of

entries. Since coalbed pressure is related directly to

the methane content, higher pressure results in

higher methane inflow rates at constant values of VL

and PL. The dependency of inflow rate on pressure

is nearly linear for each of the entry length studied.

Also, it should be noted that the inflow rate is

higher when mining longer entries, as expected,

since longer entries create a larger drainage area

into which gas can flow. Furthermore, a much

larger portion of the coal seam is depressurized

sooner which triggers gas desorption from greater

distances, a similar phenomena observed in longer

horizontal production wells (Ertekin et al., 1988;
King et al., 1986). A steeper slope of the graph for

longer entries can be explained by the same reasons.

The effects of VL and PL on simulated methane

inflow into the entries during development mining

are shown in Fig. 7. This figure shows that methane

inflow rate is almost a linear function of VL. Since

VL represents the maximum gas capacity of coal,

higher VL ensures the availability of more methane

and promotes higher methane emissions when

pressure and PL are kept constant.

The effects of PL on methane inflow rates show

inverse relations (Fig. 7) when both VL and coalbed

pressure are constant. The slope of the isotherm, or

the change of gas capacity with pressure, is largely

controlled by PL. If PL is high, then the isotherm

will be flatter compared to the isotherm with a lower

PL value, especially where V(P)oVL/2. This means

that when mining a coalbed with a higher PL, the

change in gas capacity or change in gas desorption

from the coal will be less compared to a seam with a

lower PL for the same pressure drop. Thus, the rates

of desorption and methane inflow into entries in a

higher-PL coalbed decrease as development distances increase.

0

100000

200000

300000

400000

500000

600000

700000

800000

100 200 300 500 700

Langmuir Volume (scf/ton) and Langmuir Pressure (psia)

Methane Inf ow (scf/day)

2000 ft - VL

10000 ft - VL

2000 ft - PL

10000 ft -PL

6000 ft - VL

12000 ft - VL

6000 ft - PL

12000 ft - PL

400 600

Fig. 7. Reservoir simulations of methane inflow variability with Langmuir pressure (PL) and Langmuir volume (VL) and development

distance.

3.4. Effect of sorption time constant on methane

inflow

Once methane desorbs from the micropore surfaces of the coal matrix, it flows towards the cleat

system in response to a methane concentration

gradient defined by a combination of Knudsen,

bulk and surface diffusion processes (Smith and

Williams, 1984; Kolesar and Ertekin, 1986). In

coalbed modeling, unsteady-state diffusion effects

can be quantified by determining a sorption time, t

(days), which is proportional to cleat spacing, sf,

and the diffusion coefficient, D, that can be

determined by laboratory tests:

s2

t f . (3) D

In effect, t is the time constant that regulates the

rate at which gas is released from the micropores

into the macropore system. For small values of t, or

larger values of D, the diffusion and sorption

process is faster and a higher cumulative gas

production and a higher production rate peak is

observed at degasification boreholes (Remner et al.,

1986; Spencer et al., 1987). Later in the life of the

coalbed methane reservoir, sorption time, together

with desorption, may also act as an internal pressure

maintenance mechanism.

Instead of separately investigating the effects of

cleat spacing and diffusion coefficient on methane

inflow into entries, the effect of t was evaluated. The

simulated effects of different sorption times, shown

in Fig. 8, demonstrate that small sorption times

cause higher methane inflow rates, a phenomenon

observed in coalbed gas production using horizontal

boreholes (Remner et al., 1986). It is also evident

that the change in inflow rates between short and

long sorption times is more significant for longer

entries than shorter ones (2000 vs. 12,000 ft).
This may be related to regulation of the rate of gas

release from micropores to cleats and pressure

maintenance in the reservoir while mining is

progressing. During mining of shorter entries, the

pressure disturbance within the coalbed is limited

and the area of drainage is less. A short sorption

time, t, results in high flow rates from the areas

surrounding the entries and from the areas that

pressure transients can propagate. In the case of

longer sorption times with other reservoir parameters being constant, the flow rate will be less due

to slow diffusion from the coal matrices into the

cleats. Also, the pressure transients will travel

further since there will not be enough pressure

maintenance in the coalbed. However, when the

sorption time is even longer, its effect is less

pronounced since there will be a semi-steady-state

condition established between diffusion/desorption,

cleat pressure, and flow rate at the existing coalbed

permeability.

When mining longer entries, the inflow rates are

higher because the pressure disturbance affects a

larger area for a longer time and a larger surface

area is exposed. The methane inflow with a short

sorption time constant is higher. However, with a

longer sorption time constant, the flow rate is less

due to slower diffusion rates into the cleats. This

causes the pressure transients to propagate further

due to the lack of sufficient pressure maintenance

within the reservoir. Mining longer entries affects

larger areas for longer periods, increasing sorption

time, and reducing average flow rates even further.

0

0

50000

100000

150000

200000

250000

300000

350000

400000

450000

500000

150 250

Sorption Time Constant (days)

Methane Inf ow (scf/day)

2000 ft 6000 ft

10000 ft 12000 ft

50 100 200 300

Fig. 8. Reservoir simulations of methane inflow variability with sorption time constant and development distance.

3.5. Effect of coalbed thickness on methane inflow

Fig. 9 shows that the methane inflow rates

increase almost linearly with the coalbed thickness.

The figure also shows that, as expected, mining

longer entries in thicker coalbeds results in higher

inflow rates. This is due to a combination of the two

factors suggested by Ertekin et al. (1988) for

fracture-stimulated horizontal boreholes: larger

reservoir volumes and the increased surface area

for flow in horizontal boreholes stimulated by

hydraulic fractures whose lengths are equal to the

coalbed thickness. They report that methane production from horizontal boreholes increases as the

coalbed thickness increases even if the borehole

surface area is the same due to larger volumes of

reserves encountered due to the presence of

hydraulic fractures. Also, in the case of fracturestimulated boreholes, the flow rates are even higher

compared to the non-fractured counterparts due

to the increases in surface area (Ertekin et al.,

1988).

During development mining in thicker coalbeds,

larger volumes of methane reserves are encountered.

Also, the increased thickness of the coalbed results

in an increased area of flow, which is a similar to

and even more significant than vertical fractures

in the boreholes. Thus, mining longer entries in

thicker coalbeds increases both the size of the

methane reservoir encountered and the surface area

created, which increases methane inflow rates even

further.
0

100000

200000

300000

400000

500000

600000

4.5 5.5 6.5 7.5

Coalbed Thickness (ft)

Methane Inf ow (scf/day)

2000 ft

6000 ft

10000 ft

12000 ft

567

Fig. 9. Reservoir simulations of methane inflow variability with coalbed thickness and development distance.

3.6. Effect of initial and irreducible water saturation

of the coalbed on methane inflow

The saturation of a given phase or fluid in any

porous medium represents the fraction of the total

pore volume occupied by that phase or fluid.

Coalbeds are almost always partially or completely

saturated with water. However, since the porosity

and permeability of coal matrices are extremely low,

almost all of the water resides in fractures and cleats

in the coalbed. Thus, any water saturation for

coalbeds represents the fraction of cleat porosity

that is occupied by water. Since this saturation

definition is based on the total pore volume of

cleats, part of the pore volume may be occupied by

immobile water, where water saturation cannot be

reduced further. Thus, water saturation in cleats

may vary between a minimum value (immobile

water saturation) and a maximum of 100% saturation, at which water has maximum relative permeability and mobility. Intermediate values denote

mobile saturation where water can flow in the cleats.

Besides decreasing the available cleat volume for

methane, saturations are particularly important for

affecting the permeabilities of the coalbed to water

and methane. If there are two fluids flowing

simultaneously through a porous medium, then

each fluid has its own effective permeability. These

permeabilities are dependent on the saturations of

each fluid (Dake, 1978). When water saturation, Sw,

is equal to one, then the cleats are entirely filled with

water and the effective permeability to water is

equal to the absolute cleat permeability and the

effective permeability to gas is zero. Likewise, if the

saturation of water is at irreducible water saturation

(Sw ) here water is immobile, then the effective irr

permeability of water is zero and the effective

permeability of gas is a maximum. The practical

range of variations of gas saturation, Sg, is

SgirrpSgp1 Sw . (4) irr

However, irreducible gas saturation ðSgirrÞ is not

appreciable in the cleats and gas saturation may

change between 0 and 1 Sw . Critical gas satura- irr

tion where gas becomes mobile may be important;

however, this value is expected to be small, or equal

to irreducible gas saturation.

Effective permeability can be normalized to absolute permeability to give relative permeability, which

is commonly used for mathematical convenience

(Dake, 1978). Relative permeabilities of each phase

as a function of their saturations can be interpreted

the same way as the effective permeabilities.

In methane production from coalbeds using

boreholes, increases in initial free gas saturation

result in recovery that is greater than the additional

gas volume stored in the cleats alone due to the

impact of saturation on relative permeability

(Young et al., 1992). As the initial free gas

saturation is increased (and water saturation is

decreased), reservoir conditions favor gas flow over

water flow since the relative permeability to gas

increases with increasing gas saturation. Similarly,

as the irreducible water saturation is decreased,
more water is allowed (or considered mobile in a

wider saturation range) to flow in the cleats, which

potentially can reduce relative permeability to gas.

Thus, gas and water flow at different initial and

immobile water saturation conditions and follow

distinctly different ‘‘paths’’ on the relative permeability functions.

Initial water saturations were changed while

keeping the irreducible water saturation constant,

and irreducible water saturations were changed

while keeping the initial water saturation constant

to evaluate the possible effects of water saturations (and thus gas saturations) on methane

inflow. Fig. 10 displays simulated methane

inflow rates at different initial and irreducible

water saturations and shows that reducing

irreducible water saturation to 10% for a development distance of 2000 ft reduced the methane

inflow rate. For other irreducible saturation levels

and entry lengths, reducing irreducible water

saturation did not make any significant difference

in gas inflow.

0

5000

100000

150000

200000

250000

300000

350000

400000

450000

500000

0 0

Irreducible (Swirr) and Initial (Swi

) Water Sat. (%)

Methane Inf ow (scf/day)

2000 ft - Swirr 6000 ft - Swirr 10000 ft - Swirr

12000 ft - Swirr 2000 ft - Swi 6000 ft - Swi

10000 ft - Swi 12000 ft - Swi

20 40 60 80 100

Fig. 10. Reservoir simulations of methane inflow variability with irreducible ðSwirr Þ and initial water ðSwiÞ saturations and development

distance.

Fig. 10 shows that increasing initial water

saturation, while keeping irreducible water and

other parameters constant at their base values,

had a more significant effect on methane inflow

rates. With development distances of 2000 ft (610 m)

and 6000 ft (1830 m), increasing initial water saturation decreased the methane inflow rate mostly due

to decreased initial gas saturations and gas relative

permeabilities. A similar decrease was observed in

the longer entries when initial water saturation was

changed from 40% to 80%. Increasing water

saturation puts the reservoir initially in an unfavorable situation for gas flow. However, when mining

10,000 and 12,000-ft (3050 and 3660-m) long entries,

gas inflow rate started to increase when water

saturation increased from 80% to 100%. When

mining begins in a coalbed that is 100% saturated

with water, first water will start flow into the entries

rapidly and trigger a high initial gas desorption and

the ‘‘negative decline’’ period as observed in the

production wells, thus increasing average inflow

rate into the entries. These high-methane-inflow

periods are repeated as the mine face is progressively advanced in the coalbed for longer distances

in the reservoir. Shorter entry developments may

not experience the repeated effect of these periods

and methane inflow remains at lower values.

However, mining longer entries gives enough time,

longer coalbed exposure and more face-advance

steps for the initial high gas inflow rates and

negative declines to impact average methane inflow

rates, as seen when progressively extending entry

lengths in Fig. 10. Overall, initial water saturation seems to be more influential and negatively

correlated with methane inflow for shorter entry

developments.

12
3.7. Effect of end-point-relative permeability of gas

on methane inflow into entries

The maximum relative permeability to gas that

can naturally occur at the irreducible water saturation is called the end-point relative permeability,

K0

rg, and is defined as (Dake, 1978)

K0

rg 1⁄4 Krgðat Sw 1⁄4 Sw or Sg 1⁄4 1 irr Sw (5) irrÞ.

In this definition, Krg is the relative permeability

to gas. End-point relative permeabilities can be

determined by core-flow tests (Crotti et al., 1998;

Gash, 1991).

Fig. 11 shows the impact of different end-point

relative permeability values on methane inflow. The

simulation data shows that, although the impact of

end-point relative permeability value for gas flow

increases slightly for longer entries; in general, this

factor does not have a significant effect on the

methane inflow rates. However, it should be

mentioned that the effect of relative permeability

‘‘curves’’ on the whole saturation range, relative

permeability path and how it changes with saturation, may be more important than the effect of only

end-point relative permeability values (Price and

Ancell, 1993; Young et al., 1992).

0.2

0

100000

200000

300000

400000

500000

600000

0.6 1

Gas Relative Permeabiity (Sg@1-Swirr)

Methane Inf ow (scf/day)

2000 ft 6000 ft 10000 ft 12000 ft

0.4 0.8

Fig. 11. Reservoir simulations of methane inflow variability with end point gas relative permeability and development distance.

4. Multilinear models for prediction of methane

inflows and their diagnostics for utility and adequacy

In this paper, the main coalbed parameters shown

in Table 1 that control gas storage and flow in

coalbed reservoirs and that may have significant

effects on the methane inflow were considered as the

independent parameters. The importance of each

parameter from a coalbed reservoir engineering, gas

flow, and gas storage point of view and the relative

importance of each on simulated methane inflows

were evaluated in the previous sections. These data

showed that these changes usually created linear or

close-to-linear relations with respect to methane

inflow with no significant non-linearities for the

various development lengths.

The dependent variables used for these regressions were the simulated methane inflow rates into

the 2000, 6000, 10,000, and 12,000 ft developments

using a calibrated reservoir model with a 50 ft/day

(15.3 m/day) section advance rate. By using 11

coalbed parameters, 57 observations (simulations)

were created for each of these development distances by changing the values of individual coalbed parameters within the range of values listed in

Table 1 while keeping the others at their base values.

A separate regression analysis for methane inflow

prediction was carried out for each development

distance. Table 1 shows the symbolic names of all

variables used in multiple regression analysis.

The methane inflows were modeled by including

many parameters in the simulations, since the

outputs were expected to mimic a number of

reservoir and mining conditions. In this modeling

study, the independent variables investigated were

those major gas flow and storage-related coalbed

properties impacting methane inflow. However,
a predictive model may not contain variables whose

statistics prove them to be insignificant in the

presence of the other significant ones. Using a

variety of techniques, insignificant variables are

excluded so that the final models are composed only

of significant variables. Apart from a statistical

point of view, this is important from a practical

point of view since fewer significant variables will

make data collection easier and more economical.

In this study, backward elimination was used, due

to its advantages over forward selection and

stepwise regression to evaluate joint predictive

capability (Motulsky and Christopoulos, 2004), as

the multiple regression technique to judge the

importance of each independent variable based on

its contribution to the dependent variable. This

technique was used to develop a linear model to

predict methane inflows using 57 observations for

each of the four development distances (2000, 6000,

10,000 and 12,000 ft). In selecting the coalbed

parameters for their relative importance on methane

inflow, care was taken to ensure that there would

not be a high degree of correlation between them.

For this reason, face cleat and butt cleat permeabilities were selected in lieu of anisotropy, which is

defined by the ratio of these two variables. Thus,

multiple regressions were performed with 11 independent variables shown in Table 1, by excluding

permeability anisotropy. During these analyses, the

significance cutoff value, a, and the confidence

interval of regression were set as 0.05 and 95%,

respectively.

4.1. Model equations, analysis of multiple

determination coefficients, and ANOVA

Table 2

Linear models for predicting methane inflow rates into development entries of various lengths using key coalbed reservoir parameters

Development

length (ft)

Methane inflow ratea (scf/day) R R2 aR2 F

2000 9025.0349+(18,676.8392  Thick)+

(1367.1790 Pres)+( 581.1950 S.Time)+

(13,100.6770  Ky)+(121.6918  L.Vol.)+

( 197.1251 L.Pres.) +( 1280.3404 W.Sat.)

0.9597 0.9209 0.9096 81.538

6000 193,021.3700+(49,697.1335  Thick)+

(2734.4987 Pres)+( 997.3667 S.Time)+

(19,103.2963  Ky)+(298.3296  L.Vol.)+

( 544.3628 L.Pres.)

0.9493 0.9011 0.8893 75.945

10,000 256,242.0600+(73,838.2649  Thick)+

(3764.7566 Pres)+( 1256.0067  S.Time)+

(21,052.8924  Ky)+(457.1441  L.Vol.)+

( 867.7456 L.Pres.)

0.9432 0.8896 0.8764 67.169

12,000 283,185.5900+(85,055.0763  Thick)+

(4219.7519 Pres)+( 1357.3077  S.Time)+

(21,403.8583  Ky)+(532.4142  L.Vol.)+

( 1023.3603  L.Pres.)

0.9404 0.8844 0.8705 63.736

(Thick: thickness; Pres: pressure; S.Time: sorption time constant; Ky: butt cleat permeability in this study, but can be interpreted as cleat

permeability perpendicular to entries; L.Vol: Langmuir volume; L.Pres: Langmuir pressure; W.Sat: water saturation). Multiple, squared

multiple and adjusted multiple determinations coefficients as well as F test results are also shown. a

The units of coalbed parameters are as presented in Table 1. The calculated inflow rates using these linear models are compared with

simulator predictions in Fig. 12.

Table 2 shows the linear models of methane

inflow rates for the four development distances

derived using backward elimination. The table also

shows the multiple determination coefficient, R, the

square of multiple determination coefficient, 2 R ,

and the adjusted determination coefficient, 2 aR , for

the regression models presented. These coefficients

are high for each model, indicating successful fitting

of the models to the observations. The value of 2 aR

is adjusted for the number of parameters in the

equation and the number of data observations

(Motulsky and Christopoulos, 2004). Thus, it is a

more conservative estimate of the percent of

variance, especially in the case of many independent

variables. This parameter ranges between 0.9096

and 0.8705, for 2000 ft (610 m) and 12,000 ft

(3660 m) models. In other words, the models

account for roughly 0.91 and 0.87 of the variance,
respectively, and suggest that these formulations are

reasonably good.

Table 2 also presents the utility of the model using

ANOVA (analysis of variance) tests. The reported

‘‘F’’ statistics and the ‘‘Prob F’’ values test the

overall significance of the regression model. The

probability value of F is the probability that the null

hypothesis for the full model is true. More

specifically, it tests the null hypothesis that all of

the regression coefficients are equal to zero in the

model (Devore and Peck, 2001). A low probability

value for F (o0.05 in this study) implies the high

possibility of having non-zero coefficients and that

the regression equation does have validity in fitting

the data. In this study, ‘‘Prob F’’ values for all linear

models were computed to be zero, which suggests

that all models have very high possibility of having

non-zero coefficients for the independent variables

and thus they have validity in fitting the data.

Table 3

Coefficients of independent variables in models, tolerance of independent variables, beta (b) weights, correlation coefficients, semi partial

correlations, t value, and probability t for testing the significance of model variables for different entry lengths

Development

length (ft)

Variables Model

coefficients

Tolerance b Corr. Semi partial

corr.

t Prob t

2000 Thickness 18,676.8392 0.9574 0.1041 0.1117 0.1019 2.536 0.0145

Pressure 1367.1790 0.8897 0.9172 0.8204 0.8651 21.537 0.0000

S.Time 581.1950 0.9021 0.4525 0.1699 0.0863 10.698 0.0000

Ky 13,100.6770 0.9415 0.2407 0.0449 0.2336 5.815 0.0000

L.Vol. 121.6918 0.8700 0.0885 0.2244 0.0825 2.055 0.0453

L.Pres. 197.1251 0.8732 0.1438 0.2587 0.1344 3.345 0.0016

W.Sat. 1280.3404 0.9685 0.0877 0.1377 0.4297 2.150 0.0366

6000 Thickness 49,697.1335 0.9829 0.1359 0.1437 0.1347 3.030 0.0039

Pressure 2734.4987 0.8923 0.9001 0.8369 0.8503 19.121 0.0000

S.Time 997.3667 0.9025 0.3810 0.1029 0.3619 8.139 0.0000

Ky 19,103.2963 0.9441 0.1722 0.0164 0.1674 3.763 0.0004

L.Vol. 298.3296 0.8704 0.1064 0.2690 0.0993 2.233 0.0301

L.Pres. 544.3628 0.8736 0.1948 0.3248 0.1821 4.095 0.0002

10,000 Thickness 73,838.2649 0.9829 0.1435 0.1587 0.1423 3.029 0.0039

Pressure 3764.7566 0.8923 0.8808 0.8380 0.8321 17.710 0.0000

S.Time 1256.0067 0.9025 0.3410 0.0663 0.3240 6.896 0.0000

Ky 21,052.8924 0.9441 0.1349 0.0459 0.1311 2.790 0.0074

L.Vol. 457.1441 0.8704 0.1159 0.2901 0.1081 2.302 0.0255

L.Pres. 867.7456 0.8736 0.2207 0.3565 0.2063 4.391 0.0001

12,000 Thickness 85,055.0763 0.9829 0.1461 0.1639 0.1448 3.011 0.0041

Pressure 4219.7519 0.8923 0.8723 0.8370 0.8240 17.134 0.0000

S.Time 1357.3077 0.9025 0.2300 0.0525 0.3093 4.470 0.0000

Ky 21,403.8583 0.9441 0.1212 0.0564 0.1178 2.449 0.0179

L.Vol. 532.4142 0.8704 0.1193 0.2975 0.1113 2.314 0.0248

L.Pres. 1023.3603 0.8736 0.3256 0.3677 0.2150 6.432 0.0000

The models presented in Table 2 do not contain all of the initially selected coalbed parameters.

For instance, the model for the 2000 ft (610 m)

case does not contain four of these parameters,

namely porosity, irreducible water saturation, endpoint relative permeability to gas, and face cleat

permeability. Due to their low significance, they

were eliminated from the set of independents

during the backward elimination process. However,

it may be surprising to see that face cleat permeability is not as important for methane inflow

during development mining. This is because for

this study the entries advance parallel to the face

cleats, which makes butt cleat permeability

more significant for controlling methane inflows.

For longer development distances, water saturation is also eliminated from the independent

variables.

4.2. Significance tests and analysis of results

In order to further test the validity of these

equations and the significance of the regressions
coefficients, ‘‘t’’ tests were performed on the mode

equations presented in Table 2. Table 3 presents th

coefficients of independent variables in the models

tolerance of independent variables, beta (b) weights

correlation coefficients, semi-partial correlations,

values, and probabilities.

The tolerances represent the regression of th

corresponding independent variable on all the othe

independent variables, ignoring the dependent vari

able. The higher the intercorrelation of the inde

pendents, the more the tolerance will approach zer

(Lewis-Beck, 1980). Generally, if tolerance is les

than 0.20, a problem with multicollinearity i

indicated. Table 3 shows that the tolerances excee

0.85 for all independent variables. This indicates th

absence of multicollinearity between the indepen

dent variables, which is one of the prerequisites o

multiple regression analysis.

The beta weights, b, presented in Table 3 for eac

independent variable, are the average amounts (i

standard deviations) that the dependent variabl

increases when a specific independent variabl

increases one standard deviation and other inde

pendent variables are held constant. The higher th

b value, the greater the impact of that independen

variable is on the dependent variable. Thus for

2000 ft (610 m) development length, the b values i

this analysis show that pressure, sorption tim

constant, butt cleat permeability, and Langmui

pressure are the more important independen

variables for prediction than Langmuir volum

and coalbed thickness. But sorption time an

Langmuir pressure are negatively correlated wit

methane emissions rates, since increasing values o

these two variables results in slower diffusion rate

and desorption rates, respectively. Water saturatio

is also negatively correlated with methane emissio

rates, as discussed before, indicating that highe

cleat saturations impede gas flow in mining shorte

entries.

Furthermore, the b weights show that th

predictive importance of the independent variable

changes with increasing entry length. For instance

the b value for pressure is 0.91 for a 2000 f

(610 m) development distance compared to 0.8

for a 12,000 ft (3660 m) distance, suggesting

decrease in the importance of coalbed pressure o

methane inflow for longer developments. A greate

decrease in the relative influence of sorption tim

(b values from 0.45 to 0.23) is also observe

between 2000 and 12,000 ft (610 and 3660 m) entr

lengths. On the other hand, the importance o

l

e

,

,

t

e

r

-

-

o

s

s

d

e

-

f

h

n

e

e

-

e

t

a

n

e

r

t

e

d

h

f

s

n

n

r

r

e

s

,

t

7

a

n

r

e

d

y

f

coalbed thickness and Langmuir pressure on

methane emissions increases with entry length,

suggesting that the shape of the adsorption isotherm

and the area of exposed coal surfaces are becoming

more important.

The correlation coefficient reported in Table 3 is

the percent of variance in the methane inflow data

explained by the corresponding independent variable when all other independent variables are

allowed to vary. This value is different than b

weights. Statistically, the magnitude of correlation

includes not only the covariance it shares with the

dependent variable, but also the covariance shared

with other independents in the model and its

uncontrolled effects on the dependent variable. A

correlation value 40.90, or several values 40.7,

may be indicative of multicollinearity, which is a

concern as it inflates standard errors and makes

assessment of the relative importance of the

independents unreliable using b values (Devore

and Peck, 2001). The correlation values given in

Table 3 show that the independent variables do not

fall into this category.

The relative importance of the independent

variables on the dependent variable can be assessed

by computing the semi-partial correlations. The

linear effects of the other independents are removed

from the given independent variable before computing the remaining correlation of this variable with

the dependent variable. Interpreting the relative

importance of coalbed parameters on methane

inflow, in conjunction with the b weights, shows

the same importance grouping between coalbed

parameters considered; that is, pressure, sorption

time constant, butt cleat permeability and Langmuir

pressure are highly correlated with methane inflows

and their importance changes with entry length as

discussed before.

The ‘‘t’’ and ‘‘Prob t’’ values give an indication of

the significance or impact of each predictor variable.

The smaller the value of Prob t, the more significant

the parameter is and the less likely that the actual

parameter value is zero. In other words, the terms of

the regression equations containing the independent

parameter having a low ‘‘Prob t’’ cannot be eliminated without significantly affecting the accuracy of

the regression (Devore and Peck, 2001). As seen in

Table 3, the probability t values for all the coalbed

variables are smaller than the cutoff a, 0.05, indicating that all are significant and cannot be removed

from the models without significantly affecting the

accuracy.
4.3. Durbin– Watson test for autocorrelation

Absence of autocorrelation of residuals indicates

the independence of variables, which otherwise

leads to biased estimates of standard deviations

and significance. A Durbin Watson test is performed to check the autocorrelation (association

between successive residuals) of errors. The value of

the Durbin Watson coefficient (d) ranges from 0 to

4. Values of d close to 0 indicate high positive

autocorrelation, whereas d values close to 4 indicate

high negative autocorrelation. When d is close to 2,

the result indicates that there is no serial autocorrelation of errors (Savin and White, 1977).

The values of d between 1.5 and 2.5 indicate the

independence of observations. In this study, the

Durbin Watson coefficients were 1.8812, 1.7579,

1.7951, and 1.8101 for the methane inflow models

presented in Table 2 for development mining of

2000, 6000, 10,000, and 12,000-ft entries, respectively. The d values obtained for the models show

that there is no apparent autocorrelation problem.

4.4. Adequacy of multiple regression models

Figs. 12a d show the comparison of predicted

methane inflow rates using the GEM model with the

rates calculated from the linear models. These

figures indicate that the models can predict the

observations reasonably well for all the entry

lengths studied. However, some cases have more

residuals than others.

0

400000

800000

1200000

1600000

2000000

0

Observations

Methane Inf ow Rate (scf/day)

2000-ft Entry, Simulator Result

2000-ft Entry, Regression Model

0

400000

800000

1200000

1600000

2000000

Observations

Methane Inf ow Rate (scf/day)

6000-ft Entry, Simulator Result

6000-ft Entry, Regression Model

10000-ft Entry, Simulator Result

10000-ft Entry, Regression Model

0

400000

800000

1200000

1600000

Observations

Methane Inf ow Rate (scf/day)

2000000 12000-ft Entry, Simulator Result

12000-ft Entry, Regression Model

10 20 30 40 50 60

0

400000

800000

1200000

1600000

2000000

Methane Inf ow Rate (scf/day)

0 10 20 30 40 50 60

Observations

0 10 20 30 40 50

0

60

10 20 30 40 50 60

Fig. 12. (a d). Comparison of simulated methane inflow rates for different combination of coalbed parameters with the predictions of

linear equations for mining of different development distances.

A plot of standardized residuals against fitted

values is helpful in identifying unusual or highly

influential cases and gives an idea about the

adequacy of the proposed models (Devore and

Peck, 2001). While, in a perfect prediction, the value

of standardized residual is zero, in predictive

modeling it is nearly impossible to achieve this for

all observations. Thus, a desirable residual plot

exhibits no particular pattern and distributes points

randomly between 2 and 2. Any outside data may

be considered an error in measurement. Also, any

point on the plot that is very far from the rest of the

data in the horizontal direction may have had a
major influence in determining the fitted line

(Devore and Peck, 2001).

Figs. 13a d show the standardized residual plots

for each prediction model. These plots show that a

few of the observations exhibit values very close to

or slightly more than 72. However, even with these

data in the models, the values of the adjusted

regression coefficients and other statistical parameters were quite acceptable. Thus, they were kept

in the data set in order to include their effects in the

results.

A closer look at the residual plots for mining

10,000 and 12,000 ft (3050 and 3660 m) entries

(Figs. 13c and d) suggests that curvilinear models

may be better fits for these cases compared to linear

models presented in this study, possibly because of

the slightly curvilinear relations between some

coalbed parameters and calculated methane inflows.

However, considering the comparative graphs in

Figs. 12a d and the distribution of the residuals,

simpler linear models may be as helpful and

adequate for predicting the methane inflows.

5. Summary and conclusions

-3

-2

-1

0

1

2

3

0 1000000 1500000

Predicted Value (scf/day)

Standard zed Res dua

-3

-2

-1

0

1

2

3

0 1500000

Predicted Value (scf/day)

Standard zed Res dua

-3

-2

-1

0

1

2

3

0 500000 500000 2000000

Predicted Value (scf/day)

Standard zed Res dua

-3

-2

-1

0

1

2

3

0 1500000 2000000

Predicted Value (scf/day)

Standard zed Res dua

500000 2000000 500000

1000000 500000 1000000

1000000 2000000

Fig. 13. Plots of standardized residuals vs. predicted methane inflow values during mining using linear models developed for mining of

different development distances: (a) 2000 ft, (b) 6000 ft, (c) 10,000 ft, and (d) 12,000 ft.

This study coupled ‘‘dynamic’’ reservoir models

to linear models to predict methane inflows during

development mining of a coal seam. The base

reservoir models were developed for a typical threeentry system in the Northern Appalachian Basin

section of the Pittsburgh Coalbed. Model data and

reservoir simulation results were calibrated using

the in-mine measured methane inflows during

mining of the headgate and tailgate entries. The

base model that was developed for a 50 ft/day

(15.3 m/day) section advance rate was used to

predict methane inflows into these entries for

different coalbed reservoir conditions by varying
key reservoir parameters. Thus, 57 simulation cases

were performed for each of the 2000, 6000, 10,000,

and 12,000 ft (610, 1830, 3050, and 3660 m) development distances.

The methane inflow data were then used to

develop linear models using the backward elimination technique. The linear models predicted the

methane inflows by using these key coalbed

reservoir properties. The models and their parameters were analyzed to evaluate their significance

and adequacy for prediction.

This study made the following conclusions:

1. Reservoir simulation was used effectively for

modeling development mining in underground

coal mines. It predicted methane inflows into the

entries based on various coalbed and operating

parameters.

2. Methane inflow rate increased with entry length

because of increases in the surface area of the

coalbed exposed to the mine environment.

3. Among all the coalbed parameters evaluated,

coalbed thickness, pressure, sorption time constant, permeability perpendicular to entries and

adsorption parameters were found to be the most

influential on methane inflow rate. For shorter

development distances, initial water saturation

was also found to be influential too.

4. Statistical analyses to evaluate the significance of

the linear regression model parameters showed

that, for all development distances, pressure,

sorption time constant, butt cleat permeability,

and Langmuir pressure were the more important

independent variables for prediction rather than

Langmuir volume and coalbed thickness. For

shorter development distances, initial water

saturation was also found to be influential with

a lesser degree. It was further shown that as the

development distance increased, the relative

importance of coalbed variables changed.

5. Statistical tests suggested that the linear models

and their independent parameters did not reveal

any statistical problems that would indicate

autocorrelation or multicollinearity. Also, hypothesis testing showed that the models had

predictive significance.

6. Standardized residuals plotted against predicted

parameters indicated that there were only a few

data points outside 72 interval. In longer

development distances, slightly increasing nonlinearity was observed, suggesting that non-linear

models may be more appropriate.

7. Considering the results of all analyses, comparison of simulator and linear-model predicted

rates, low residuals, and high regression coefficients, linear models using influential coalbed

parameters can be adequate models and can be

used to predict methane inflows in entries during

development mining.

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