Bureau of Mines Report of Investigations/l982 

Probability of Encountering Coalbed 

Discontinuities During Vertical 

and Horizontal Borehole Drilling 

By David W. Houseknecht 

UNITED STATES DEPARTMENT OF THE INTERIOR 
Report of Investigations 8665 

Probability of Encountering Coalbed 

Discontinuities During Vertical 

and Horizontal Borehole Drilling 

By David W. Houseknecht 

UNITED STATES DEPARTMENT OF THE INTERIOR 

James G. Watt, Secretary 

BUREAU OF MINES 

Robert C. Horton, Director 
This publication has been cataloged as follows: 

Houseknecht, David W 

Probability of encountering coalbed discontinuities during 

vertical and horizontal borehole drilling. 

(Report of investigations / US. Dept. of Interior, Bureau of 

Mines ; 8665) 

BibIiography : p. 20-2 1. 

Supt. of Llocs. no.: I 28.23:8665. 

1. Boring. 2. Methane. 3. Coal mines and mining. I. Title. 11. Series: Report of investigations (United States. Bureau of Mines) ; 8665. 
CONTENTS 

Page 

Abstract ....................................................................... Introduction ................................................................... Acknowledgments ................................................................ The Beckley Coalbed ............................................................ Quantification of discontinuities .............................................. Working definition ........................................................ Sources of data ........................................................... Definition and measurement of size. shape and orientation .....ma.......... 

Probability of encountering discontinuities during vertical drilling ........... Probability analysis ...................................................... Assumptions and variables ............................................ Determination of probabilities for the Beckley Coalbed ............... Drilling grid pattern. .......................................... Discontinuity distribution and orientation ...................... Discontinuity shape ............................................. Discontinuity size and borehole spacing ......................... Application of probabilities: Hypothetical drilling program for vertical 

boreholes ............................................................... Description of hypothetical program .................................. Results .............................................................. Discussion of results ................................................ Probability of encountering discontinuities during horizontal drilling ......... Probability calculation ................................................... Considerations ...............................................m....... 

Method of calculation ........m....................................... 

Application of probability calculation method: Hypothetical drilling program for horizontal boreholes ........................................... Summary and conclusions ........................................................ References ..................................................................... 

ILLUSTRATIONS 

Generalized stratigraphic column showing position of Beckley Coalbed ...... Map of study area showing mines that have encountered discontinuities in 

the Beckley Coalbed ..................................................... Location of approximately 300 boreholes drilled within the study area for 

exploratory and/or developmental purposes ............................... Map of Beckley Coalbed discontinuities compiled from individual mine maps . Definition of discontinuity size. shape. and orientation .................. Examples of discontinuities of various shapes with a-axes of equal lengths 

Orientations of Beckley Coalbed discontinuities ........................... Size versus shape of Beckley Coalbed discontinuities ...................... Beckley Coalbed discontinuity map showing locations of hypothetical vertical boreholes ........................................................... Method of calculating probabilities of encountering discontinuities with 

horizontal boreholes of various lengths ................................. Horizontal borehole length versus probability of encountering a discontinuity in the Beckley Coalbed ............................................ 
TABLES 

Page 

1. Characteristics of coalbed discontinuities in study area of Beckley Coalbed 

and results of hypothetical vertical drilling program.................... 9 

2. Probabilities of encountering discontinuities of various shapes during vertical drilling. ..........e.eeeee.e.eee.....eee..eeee..e..e.ee.eee..e.e.ee 13 

3. Horizontal borehole length and probability of encountering a discontinuity 

for hypothetical horizontal drilling program............e...eeeee.e..ee.. 19 
PROBABILITY OF ENCOUNTERING COALBED DISCONTINUITIES DURING VERTICAL 

AND HORIZONTAL BOREHOLE DRILLING 

By David We Houseknecht' 

ABSTRACT 

Probabilities of encountering coalbed discontinuities during vertical or horizontal drilling in a specific coalbed can be estimated based 

on analysis of mined-out areas of the coalbed where the size, shape, 

orientation, and distribution of discontinuities are known. The resultant probability estimates can be applied to cost-risk evaluations of 

drilling programs proposed for exploratory, developmental, or methane 

drainage purposes in undeveloped areas of that coalbed. 

Data compiled from mine maps of the Beckley Coalbed in southern 

West Virginia were used to estimate the probabilities that discontinuities would be encountered in two illustrative hypothetical drilling 

programs--one for drilling vertical boreholes and the other for drilling 

horizontal boreholes. Analysis based on a mined-out area of the Beckley 

Coalbed indicated that vertical methane drainage boreholes spaced 

1,000 feet apart in a square grid pattern would each have a 29 percent 

probability of encountering a discontinuity in a geologically unexplored 

area of the coalbed. It was also determined that exploratory vertical 

drilling could locate most of the discontinuities if a borehole spacing 

of 2,500 feet were used. For horizontal drainage boreholes in the Beckley Coalbed, the analysis indicated a linear relationship between hole 

length and the probability of encountering a discontinuity. 

'~eolo~ist, Department of Geology, University of Missouri, Columbia, Mo. ; faculty 

advisor with the Bureau of Mines, Pittsburgh Research Center, Pittsburgh Pa. 
INTRODUCTION 

Coalbed discontinuities are a major 

problem encountered during the drilling 

of methane drainage boreholes and during 

all phases of coal exploration and development. Specific problems related to 

discontinuities are numerous. The 

presence of undetected discontinuities 

can result in overestimation of a property's reserve and production potential. 

Discontinuities encountered during developmental mining can result in delays in 

entry development and in the completion 

of ventilation circuits. In certain geologic settings, natural gas may be 

emitted from discontinuities into a mine 

atmosphere (6) .2 Discontinuities can 

obstruct methane drainage borehole 

drilling and block anticipated gas migration paths to methane drainage boreholes. 

Roof instability and the presence of 

excess water are often related to lithologic facies changes in roof strata 

associated with discontinuities (6). - 

As part of its methane control 

program, the Bureau of Mines has 

addressed the problem of anticipating 

coalbed discontinuities because these 

discontinuities frequently have adverse 

effects on methane drainage drilling 

programs. This report summarizes a 

method for estimating probabilities 

of encountering discontinuities during 

drilling so that cost and risk factors 

can be more thoroughly analyzed in 

advance of major drilling programs, 

whether they are for methane drainage, 

exploratory, or developmental purposes. 

The procedure described can be completed 

with a modest investment of time and 

money, and yet it provides a quantitative 

estimate of the probabilities of 

encountering discontinuities when various vertical borehole spacings and 

various horizontal borehole lengths are 

used. 

ACKNOWLEDGMENTS 

Mine maps and other information per- Piney Creek Coal Co., and Westmoreland 

taining to Beckley Coalbed discontinu- Coal Co. 

ities were provided by The New River Co., 

THE BECKLEY COALBED 

The Beckley Coalbed of southern West 

Virginia is used as a model for this 

study. This coalbed lies within the New 

River Formation of the Pottsville Group 

(fig. 1) and attains a minable thickness 

in large areas of West Virginia's 

Raleigh, Wyoming, and McDowell Counties 

(1). Beckley coal is a high-quality 

metallurgical coal, typically ranging 

between low- and medium-volatile bituminous rank with the following average 

2~nderlined numbers in parentheses 

refer to items in the list of references 

at the end of this report. 

characteristics: Fixed carbon, 74 to 

77 percent; volatile matter, 16 to 

18 percent; total sulfur, less than 

1 percent; total ash, 3 to 6 percent; 

calorific value, 14,500 to 15,000 Btu/lb; 

and mean vitrinite reflectance, 1.50 to 

1.55 percent. 

Mining operations in the Beckley 

Coalbed have long been plagued by severe 

mining problems, including coalbed discontinuities, roof instability, excessive 

methane emission from the coalbed and 

enclosing strata (!), and. excessive 

ground water migration into mine entries 
FIGURE 1.  Generalized stratigraphic column showing position of Beckley Coalbed (modified 

from reference 5). 

from enclosing strata. Continuous mining 

activity since early in this century has 

resulted in large mined-out areas, most 

of which were accurately mapped as mining 

progressed. The coalbed's mining problems (especially the discontinuities) and 

the existence of accurate maps of the 

mined-out areas make the Beckley an ideal 

coalbed to use as an example of how to 

estimate the probability of encountering 

discontinuities during drilling. 

Figure 2 is a map of a large area 

in portions of the Beckley, Crab 

Orchard, Lester, and Eccles 7-112-minute 

quadrangles of southern West Virginia. 

Within this area, the Beckley Coalbed has 

been mined out in five large mines, as 

shown on the map. Figure 3 shows the 

locations of approximately 300 boreholes 

which have been drilled into the Beckley 

Coalbed during exploration and development (in the same area as is shown in 

figure 2) since the early part of the 

century. Figure 4 is a map of discontinuities that have been delineated 

within the Beckley Coalbed (again in the 

same area), partly during mining and 

partly as a result of drilling. 
. . . 

. . . . . . .. . . 

. 

.a?.' 

. . *. . . :. . . . .. 

. . 

. *. 

. 

.. LEGEND o 1 rnt 

Exploratory and developmental o t-+--'l t 2km 

borehole locations Scale 

FIGURE 3. - Location of approximately 300 boreholes dril led within the 

study area for exploratory and/or developmental purposes, 
LEGEND 0 1 mi 

p:::::1 

. . . . . . . . , -....... . . . . . . . . I Discontinuity o I--+-% 1 2 km 

Scale 

FIGURE 4. - Map of Beckley Coalbed discontinuities compi led from individual mine maps. 
QUANTIFICATION OF DISCONTINUITIES 

Working Definition 

Discontinuities differ in mode of 

origin and physical dimensions. Unfortunately, detailed descriptions of discontinuities are generally not recorded on 

mine maps or in mine records. For this 

reason, an estimate must be made (for 

purposes of analysis), as to what has 

been considered to constitute a discontinuity on a specific mine property or 

within a specific coalbed. By inspecting 

coal thickness records and talking with 

mine personnel, it is usually possible to 

determine what has historically been considered a discontinuity on any specific 

property. 

In the case of the Beckley Coalbed, 

drilling. A few detailed mine maps also 

show coal thickness and/or lithologic 

descriptions in areas adjacent to discontinuities. It is advisable to make 

underground visits to verify the accuracy 

of mine maps, but this is seldom possible in extensively mined-out areas 

because mines may no longer be open or 

discontinuity areas may have been sealed 

off or may be unsafe to visit. 

After mine maps of large minedout areas have been compiled, all 

discontinuities should be clearly 

identified for measurement purposes. The 

assumption made in using data from minedout areas is that discontinuity size, 

shape, orientation, and distribution in 

mined-out areas are similar to those in 

coal thicknesses less than 28 inches have undeveloped areas of the coalbed. 

generally been mapped as discontinuities. 

Although these areas of thin coal are Definition and Measurement of Size, 

usually different in origin than discon- Shape, and Orientation 

tinuities in which coal is totally absent 

(channel-phase sandstone bodies, normal Discontinuity size, shape, and 

faults, etc.), the two are commonly not orientation are defined as illustrated in 

distinguished from one another on mine figure 5. Since discontinuities are 

maps. Because these two types of discon- usually irregular in shape, their sizes 

tinuities cannot easily be distinguished and shapes are not conveniently measured. 

using the available data, all areas To standardize measurement procedure and 

labeled as discontinuities on mine maps eliminate ambiguity in measurement tech- 

(wants, normal faults, etc.) are used in nique, a smallest possible tangential 

the following analysis, despite the fact 

that this procedure may result in considering unlike features as belonging to 

a single category. 

Sources of Data 

Maps from mined-out areas and borehole data serve as the primary sources of 

data for the calculation of probabilities 

of encountering discontinuities. Most of 

the mine maps include areas of discontinuities encountered during mining or 

during exploratory and/or developmental 

rectangle is constructed around each 

individual discontinuity on the discontinuity map (as shown in figure 5). Two 

axes are defined for measurement of size; 

the long axis of the rectangle is defined 

as the a-axis, and short axis is defined 

as the b-axis. These two axes can also 

be defined as the major and minor axes of 

an ellipse. Because the shape of most 

discontinuities approximates an ellipse, 

the long and short axes of the tangent 

rectangle are appropriate representatives 

of the actual discontinuity dimensions. 
mnwg 

P.Too(D 

09 (D 001 

C Y ocn 

Y(D c 

(D- Y 

O'd (D 

UY o a 

(DYY rt 

D 0 r 

d3 F (D 
FIGURE 6. - Examples of discontinuities of various shapes with a-axes of equal lengths. 

The numerical values be low each example are quantitative representat ions 

of shape (the ratio b-ax is/a-axis). 

a Measured orientations of long axes of discontinuities 

FIGURE 7. - Orientations of Beckley Coalbed discontinuities. 
The size, shape, and orientation of table 1 because it is assumed that such 

each discontinuity on the base map large discontinuities would have been 

(fig. 4) are measured, and the results located during exploratory drilling. 

are compiled (table 1). Discontinuities This assumption is demonstrated to be 

with a-axis lengths greater than valid in a later section of this report. 

10,000 feet have been omitted from 

TABLE 1. - Characteristics of coalbed discontinuities in study area of Beckley 

Coalbed and results of hypothetical vertical drilling program 

Mean.. ....... 1 2.377 

Discontinuity 

reference 

number 

NAp Not appli~~ble. 

A-axis 

length, 

ft 

B-axis 

length, 

f t 

525 

550 

310 

170 

400 

515 

320 

2,050 

1,100 

1,675 

2,250 

450 

1,525 

1,760 

500 

300 

785 

1,185 

1,650 

948 

I 

Shape (:I::: :) 

0.60 

039 

.52 

.3 1 

055 

.67 

053 

034 

.29 

.25 

.69 

039 

033 

.63 

045 

.38 

021 

.41 

.60 

045 

Orientation 

(deg clockwise from 

north, except where 

otherwise 

indicated) 

132 

65 

15 

Borehole spacin 

necessary to 

achieve 100 pct 

probability of 

encountering 

discontinuity1 

' Located by 

hypothetical 

drilling 

program 

No 

Yes 

Yes 

Yes 

Yes 

Yes 

Yes 

Yes 

No 

Yes 

'calculated from published probability tables (9). - 
PROBABILITY OF ENCOUNTERING DISCONTINUITIES DURING VERTICAL DRILLING 

Vertical drilling is the most commonly used method of obtaining geologic 

data during coal exploration and development and is also widely used for 

coalbed methane drainage. In each of 

these applications, it is important to 

quantitatively evaluate the probability 

of encountering coalbed discontinuities 

during drilling. During exploratory 

and/or developmental drilling, it is generally advantageous to encounter any discontinuities present on a property so 

that accurate reserve estimates can be 

made and so that potential mining problems can be anticipated and minimized 

during mine planning. In contrast, it is 

detrimental to encounter discontinuities 

during methane drainage drilling because 

discontinuities can obstruct methane 

drainage boreholes and block anticipated 

gas migration paths to the boreholes. 

The following discussion outlines how 

probabilities of encountering discontinuities during vertical drilling are estimated. Also discussed is the importance 

of these estimates to both methane drainage and exploratory and/or developmental 

drilling programs. 

Probability Analysis 

Assumptions and Variables 

After the size, shape, and orientation data have been compiled, estimating 

the probability of encountering coalbed 

discontinuities during vertical drilling 

is simply an exercise in statistics. The 

size, shape, and orientation data are 

collected from mined-out areas as previously described. Then, the assumption is 

made that similar discontinuities exist 

in unmined areas of the coalbed. Probabilities are calculated from the minedout area and then applied to the unmined 

area. 

Before these probability tables can be 

used, the following questions must be 

considered : 

1. Will a square, rectangular, 

or hexagonal drilling grid pattern 

be used? 

2. Are the targets (discontinuities) preferentially distributed within 

the area? 

3. Are the discontinuities preferentially oriented? 

4. What are the shapes of the 

discontinuities? 

5. What discontinuity sizes may be 

expected and, more importantly, what is 

the smallest discontinuity that those 

carrying out the drilling program must be 

aware of in order to accomplish the 

objectives of the drilling program (or, 

conversely, what is the largest discontinuity the drillers can afford not 

to know about, considering the drilling 

objectives)? 

6. What spacing will (or must) be 

used between adjacent boreholes? 

Each of these variables is considered in the following discussion, 

which demonstrates how probabilities of 

encountering discontinuities are determined for the Beckley Coalbed within the 

study area shown in figures 2-4. The 

effects of these variables on probability 

estimation have been discussed by 

others (4, - - 9). 

Determination of Probabilities for 

the Beckley Coalbed 

Drilling Grid Pattern 

Other investigators have provided Coalbed drilling for purposes of 

the mathematical proof and probability methane drainage, exploration, and/or 

tables necessary to determine the proba- development is rarely carried out on the 

bility of encountering any elliptical basis of a regular geometric borehole 

target using drilling grid patterns with pattern for a variety of strategic, 

various spacings between boreholes (9). - economic, and logistic reasons. In most 
cases, however, existing borehole pat- that the Beckley's discontinuities are 

terns approximately fit some regular randomly distributed and oriented. 

geometric pattern so that probability 

analysis can be performed with some Discontinuity Shape 

degree of confidence. In order to maintain simplicity and because the probabil- Because shape is a major variable in 

ity tables (9) - used in this analysis are the probability tables (9) used in this 

calculated on the basis of regular analysis, discontinuity sFapes within the 

geometric drilling patterns, a square study area are analyzed first. Figure 8 

drilling grid pattern is used throughout is a plot of shape (b-axisla-axis) versus 

this analysis. long axis (a-axis) length for the 19 discontinuities listed in table 1. Shape 

Discontinuity Distribution and ranges from approximately 0.20 to approxOrientation imately 0.70 overall, but there appears 

to be a significant relationship between 

Examination of the Beckley Coalbed shape and size: Discontinuities with adiscontinuity map (fig. 4) and the dis- axis lengths greater than 3,300 feet discontinuity orientation plot (fig. 7) sug- play little variability in shape, with 

gests that the discontinuities are values ranging from approximately 0.20 to 

neither preferentially distributed nor approximately 0.35; whereas smaller dispreferentially oriented. Therefore, the continuities display much variability 

analysis may proceed under the assumption in shape, with values ranging from 

. 1 I 1. I I I 

- . - 

. 

- . - 

. . 

- - 

.. 

- - 

. 

- 

a Measured discontinuities 

- 

I I I I I I 

0 1 2 3 4 5 6 7 

DISCONTINUITY LENGTH (A-AXIS), I o3 ft 

FIGURE 8. - Size versus shape of Beckley Coalbed discontinuities. 
approximately 0.30 to approximately 0.70. 

This size-shape relationship may have 

genetic significance, but this cannot be 

confirmed because detailed geologic 

information on the area in the vicinity 

of these discontinuities is not available. This relationship must be taken 

into account, however, when estimating 

probabilities of encountering discontinuities using the previously cited probability tables. 

Discontinuity Size and Borehole Spacing 

Discontinuity size and borehole 

spacing can be considered simultaneously 

because they are closely related in the 

probability tables (9) and because one is 

often a known (or assumed) quantity while 

the other is an unknown quantity. For 

example, by assuming the size of discontinuities in an area, the borehole spacing required to locate discontinuities 

during exploratory drilling in that 

area can be determined. This can be 

illustrated by examining a probability 

table that has been modified from the 

probability tables in reference 9 to be 

directly applicable to the Beckley 

discontinuity problem. This modified 

probability table, table 2, summarizes 

the probabilities of encountering discontinuities of various sizes using various 

borehole spacings for discontinuities of 

shapes 0.30, 0.50, and 0.70. 

The first set of probability values 

in table 2 (under the heading 

"SHAPE 0.30") can be directly applied in 

estimating the probabilities of encountering discontinuities with a-axis 

lengths greater than 3,300 feet in the 

Beckley Coalbed using various borehole 

spacings. This is because discontinuities of the Beckley Coalbed that are 

longer than 3,300 feet in a-axis length 

have shapes of approximately 0.30, as 

previously shown in figure 8. Table 2 

shows, for example, that where a 

4,000-f oot (a-axi.s) discontinuity of 

shape 0.30 is present, boreholes spaced 

5,000 feet apart in a square grid pattern 

would each have a 55.4 percentaprobability of encountering the discontinuity. 

ft can also be seen from table 2 that for 

a discontinuity of this same size and 

shape (4,000 feet long, shape 0.30), the 

probability of encountering the discontinuity increases as the distance between 

boreholes decreases, as follows: the 

probability is 75.8 percent for boreholes 

spaced 4,000 feet apart, 84.3 percent for 

boreholes 3,500 feet apart, 94.3 percent 

for boreholes 3,000 feet apart, 99,4 percent for boreholes 2,500 feet apart; and 

for any smaller spacings between boreholes the probability of encountering a 

discontinuity is 100 percent, As 

illustrated by this example, table 2 can 

be used to estimate the probabilities of 

encountering various-size discontinuities 

of shape 0.30 using any borehole spacing 

(and assuming a square grid pattern). 

Using the second and third sets of probability values in table 2, the probabilities of encountering various-size discontinuities of shapes 0.50 and 0.70 can 

be similarly estimated. 

A comparison of the probability 

values for shapes 0.30, 0.50, and 0.70 in 

table 2 reveals that as discontinuity 

shape values increase (or as shape 

becomes more equant), there is a greater 

likelihood that discontinuities will be 

encountered. This means that for discontinuities of equal a-axis length, it 

takes a smaller borehole spacing (that 

is, more boreholes) to encounter an 

elongate discontinuity than to encounter 

a more nearly equant discontinuity, For 

example, in order to be sure (or to have 

a 100 percent probability) that a drilling program will encounter all discontinuities that are 2,000 feet long, table 2 

shows that the maxim borehole spacing 

must be 1,000 feet for discontinuities of 

shape 0.30, 1,500 feet for discontinuities of shape 0.50, and 2,000 feet for 

discontinuities of shape 0.70. 
TABLE 2 . . Probabilities of encountering discontinuities of various 

shapes during vertical drilling1 

Discontinuity 

length (a.axis). ft 

SHAPE 0.50 

Borehole spacing. ft 

5. 000 14. 000 1 3. 500 13. 000 12. 500 1 2. 000 11. 500 1 1. 000 1 500 

SHAPE 0.30 

SHAPE 0.70 

500 ............... NZ NZ NZ NZ NZ 0.137 

1.000 ............... NZ 0.137 0.198 0.269 0.353 -550 

1.500 ............... 0.198 -352 . 445 -550 . 760 -980 

2.000 ............... . 352 -550 . 658 . 854 -996 1.000 

2.500 ............... . 550 . 760 . 932 1.000 1.000 1.000 

3.000 ............... . 760 -980 1.000 1.000 1.000 1.000 

3.500 ............... . 932 1.000 1.000 1.000 1.000 1.000 

4.000 ............... . 996 1.000 1.000 1.000 1.000 1.000 

5. 000 ................ 1.000 . 1.000. 1.000 rn 1.000 a 1.000 . 1.000 

NZ Near zero . l1.000 = 100 percent probability . 

0.236 

-758 

. 982 

1.000 

1.000 

1.000 

1 . 000 

1 . 000 

1.000 

1.000 

1.000 

1.000 

1.000 

0.115 

. 388 

. 758 

. 943 

1.000 

1.000 

1 . 000 

1 . 000 

1.000 

1.000 

1.000 

1.000 

1.000 

I NZ ' NZ 

0.085 

-151 

. 236 

-335 

-443 

. 554 

. 758 

. 906 

. 965 

0994 

1.000 

0.758 

1.000 

1.000 

1.000 

1.000 

1.000 

1 . 000 

1.000 

1.000 

1.000 

1.000 

1.000 

1.000 

NZ 

NZ 

0.115 

. 236 

. 335 

. 499 

. 608 

. 758 

-906 

. 982 

1.000 

1.000 

1.000 

NZ 

0.085 

. 191 

. 284 

. 443 

-608 

-758 

-843 

. 965 

1.000 

1.000 

1.000 

1.000 

NZ 

0.115 

-236 

. 388 

-608 

. 758 

-906 

-943 

1.000 

1.000 

1.000 

1.000 

1.000 

NZ 

0.151 

. 335 

. 554 

. 758 

. 906 

. 965 

. 994 

1.000 

1.000 

1.000 

1.OGO 

1.000 

NZ 

0.236 

. 499 

. 758 

-906 

. 982 

1 . 000 

1 . 000 

1.000 

1.000 

1.000 

1.000 

1.000 
Application of Probabilities: 

Hypothetical Drilling Program 

for Vertical Boreholes 

Description of Hypothetical Program 

For study purposes, a vertical borehole drilling program was hypothesized 

for the Beckley Coalbed study area and 

then analyzed. Considering the size and 

shape of the Beckley's discontinuities (table l), it was decided that a 

2,500-foot borehole spacing would provide 

a good compromise between the number of 

boreholes drilled (a consideration 

related to cost) and the size of discontinuities that would be detected (a consideration related to risk) in a 

hypothetical program. The hypothetical 

drilling program is illustrated in 

figure 9. 

As shown in figure 9, a square 

drilling grid with 2,500-foot spacing 

between boreholes was superimposed on the 

Beckley discontinuity map. Because an 

. ....... 

. .Q. 

LEGEND o 

Hypothetical borehole locations o FA 1 2 km 

Discontinuity Scale 

b 

FIGURE 9. - Beckley Coalbed discontinuity map showing locations of hypothetical vertical boreholes. 
assumption was previously made that Beckley discontinuities are randomly distributed and oriented, the drilling grid was 

arbitrarily oriented north-south. The 

grid was offset 2,500 feet from the north 

and west boundaries of the study area 

because boreholes are seldom drilled on 

boundaries of mine properties. Similarly, no hypothetical boreholes were 

"drilled" within 2,500 feet of outcrop 

because coal thickness data can be collected at numerous locations along the 

outcrop line. In all, the hypothetical 

drilling program simulated the drilling 

of 153 boreholes. 

Results 

Figure 9 shows that 45 of the 

153 simulated boreholes would have 

encountered discontinuities. Thus, if 

the study area is representative of 

unexplored and/or undeveloped areas of 

the Beckley Coalbed, there is a 29 percent probability of encountering a discontinuity during vertical drilling in 

untested areas. 

Discussion of Results 

The probability of encountering a 

discontinuity is actually an estimate of 

the following ratio for the study area: 

total area of discontinuities/total area. 

For this reason, a square drilling grid 

pattern that covers the entire study area 

will encounter discontinuities in 29 percent of its boreholes, regardless of the 

spacing between boreholes. A simple 

mathematical proof of this relationship 

is available (2). - 

The hypothetical drilling program 

located most of the discontinuities that 

are large enough to seriously affect 

methane drainage or mining activities, as 

shown in table 1 and in figure 9. Of the 

11 discontinuities not located, all but 

four are less than 1,000 feet long, and 

six are within 500 feet of outcrop. Only 

two of the undetected discontinuities 

would pose serious problems to methane 

drainage and mining efforts. These two 

discontinuities are located just north of 

the center of the study area; one is 

3,740 feet long with a shape of 0.21, and 

the other is 2,910 feet long with a shape 

of 0.41 (reference numbers 17 and 18, 

respectively, in table 1). In order to 

be sure these two discontinuities would 

be detected, the borehole spacing would 

have fo be reduced to 1,800 feet, and the 

result would be a significantly larger 

number of boreholes and a concomitant 

cost increase. 

An exploratory drilling program similar to the one described above should 

precede methane drainage drilling so that 

tentative mine projections can be taken 

into consideration when the locations of 

methane drainage boreholes are planned. 

Assuming that geologic data concerning 

the distribution of coalbed thickness and 

discontinuities have been obtained from 

such an exploratory drilling program, 

methane drainage borehole patterns (commonly square grids with 1,000-foot spacing between boreholes) can be sited with 

little chance of encountering discontinuities during drilling. However, if a 

methane drainage borehole pattern with 

1,000-foot spacing were drilled across 

the entire Beckley Coalbed study area, 

there would be a 29 percent probability 

that a given borehole would encounter a 

discontinuity, and 29 percent of all the 

boreholes drilled could be expected to 

encounter discontinuities. If relatively 

small borehole patterns (for example, 

5 by 5 boreholes with 1,000-foot spacing) 

were drilled with no data input from 

exploratory drilling, the probability of 

encountering discontinuities would range 

from zero to 100 percent depending on the 

location selected, but these probabilities could not be estimated before 

drilling commenced without exploratory 

information. 

The foregoing discussions demonstrate how systematic analysis of discontinuity characteristics, together with 

application of the probability tables 

from reference 9, can be used to quantitatively estimate the probabilities of 

encountering discontinuities during vertical drilling. This procedure can be 

used in the analysis of cost-risk factors 

involved in designing a drilling program 
and can be directly applied to determina- drainage and exploratory and/or develoption of the borehole spacing and drill- mental drilling. 

ing pattern to be used in methane 

PROBABILITY OF ENCOUNTERING DISCONTINUITIES DURING HORIZONTAL DRILLING 

In recent years, there has been a 

significant increase in the use of horizontal drilling both for coalbed methane 

drainage (1) and for mine development 

work such as locating abandoned mine 

workings. For this reason, it is 

increasingly important to be able to predict probabilities of encountering discontinuities in advance of initiating a 

horizontal drilling program. 

some time, thus allowing methane drainage 

in advance of mining. For developmental 

purposes, drilling locations are determined by the presence of potential problem areas such as abandoned mine 

workings. 

A method of probability calculation 

applicable to horizontal borehole drilling is described below. 

Probability Calculation Method of Calculation 

This section describes a method of 

probability calculation that can be used 

in estimating the probabilities of 

encountering coalbed discontinuities during horizontal drilling. For purposes of 

illustration, this method is then used in 

an analysis of a hypothetical drilling 

program for horizontal boreholes. Again, 

the mined-out area of the Beckley Coalbed 

(figs. 2-4) is used as an example; that 

is, data from the Beckley study area are 

used as the basis for the hypothetical 

program. 

Considerations 

In analyzing the probabilities of 

encountering discontinuities during horizontal drilling, two major questions must 

be considered. They are: 

1. How will drilling locations be 

decided upon? 

2. Once the location decisions 

are made, how will the probabili ties of encountering discontinuities be 

calculated? 

In practice, drilling locations are 

determined on the basis of existing and 

projected mine layouts. For the purpose 

of methane drainage, drilling locations 

for horizontal boreholes are chosen so 

that the boreholes will be drilled into 

blocks of coal that will not be mined for 

Probabilities are individually calculated for each proposed drilling site, 

based on data from mined-out coalbed 

areas. In order to analyze the probabilities that horizontal boreholes of various lengths will intercept a discontinuity, circles of 500-, 1,000-, 1,500-, 

2,000-, and 2,500-foot radii are drawn 

around the drilling site to be analyzed, 

as shown in figure 10. These circles 

define the areas that could be intersected by horizontal holes of various 

lengths (that is, the same lengths as the 

radii). Theoretically, a horizontal hole 

could be drilled in any direction from 

the drilling site, so the circle with a 

radius of 500 feet, for example, delineates the area that would be intersected 

by 500-foot holes drilled in all possible 

directions from the site. Actual horizontal drilling directions would be considerably limited if drilling were to be 

done from the entries of an existing mine 

because boreholes would be drilled only 

in the directions of unmined coal. In 

contrast, horizontal drilling directions 

would not be limited at all if drilling 

were to be done from the bottom of a 

newly constructed shaft (2) because 

unmined coal would be present in all 

directions. 

For each of the circles that intersects a discontinuity, radius lines are 

drawn from the drilling site to the 

two points where the circle and the 
.. 

l-. ,' /' 

1. 

I... 

. --- _ 2,500ft ____-- ~-.//' 

FIGURE 10. - Method of calculating probabilities of encountering discontinuities 

with horizontal boreholes of various lengths. 

Hole 

length, 

f t 

500 

1,000 

1,500 

2,000 

2,500 1 

Angle of 

intersection, 

deg 

0 

33 

88 

100 

100 

Probability, pct 

0 

9 

24 

28 

28 

4 
discontinuity intersect, as shown in figure 10. Any horizontal hole of a length 

equal to the radius of a circle that 

intersects a discontinuity, when drilled 

in a direction that lies between these 

two radius lines, will encounter the discontinuity. For each drilling site, the 

angle between the two radius lines (hereafter called the angle of intersection) 

is measured for each circle that intersects a discontinuity. For example, in 

figure 10, the 500-foot radius circle 

(representing boreholes 500 feet long) 

does not intersect a discontinuity, so 

the angle of intersection is zero. The 

1,000- and 1,500-foot circles do intersect a discontinuity, and their respective angles of intersection are 33" and 

88". 

In certain cases, the angle of 

intersection must be measured to allow 

for a "shadow effect." This effect 

involves two possible cases. In the 

first case, a circle may intersect a discontinuity across a smaller angle of 

intersection than a circle of smaller 

radius. For example, the circle of 

2,000-foot radius in figure 10 intersects 

the 2,000-foot circle and the 2,500-foot 

circle in figure 10 is 100". 

Once an angle of intersection has 

been measured for a circle of a given 

radius, it is converted to a probability 

of encountering a discontinuity simply by 

dividing the angle by 360". If a circle 

intersects a single, irregularly shaped 

discontinuity in more than one location 

along the circumference of that circle, 

an angle of intersection is measured for 

each area where the circle intersects the 

discontinuity. Similarly, if more than 

one discontinuity is intersected by a 

circle, an angle of intersection is measured for each discontinuity. In both 

cases, all angles of intersection measured for a circle of given radius are 

summed before dividing by 360". This 

procedure is repeated for each circle of 

each drilling site in order to arrive at 

mean values for the entire study area. 

The mean probability value calculated for 

each circle corresponds to the probability that a discontinuity would be encountered by a borehole the same length as 

the radius of the circle. 

the discontinuity across a smaller angle Application of Probability Calculation 

of intersection than the circle of Method: Hypothetical Drilling Program 

1,500-foot radius. However, any 

2,000-foot-long horizontal borehole that 

is drilled within the angle of intersection of the 1,500-foot circle would 

encounter the discontinuity. This is 

because the maximum length of the discontinuity lies closer to the drilling site 

than the circle of 2,000-foot radius. In 

the second case, a circle may not intersect a discontinuity although a circle of 

smaller radius does. For example, the 

circle of 2,500-foot radius in figure 10 

does not intersect the discontinuity but 

circles of smaller radii do. In this 

case, the angle of intersection for the 

2,500-foot circle must include the entire 

area where horizontal boreholes 

2,500 feet long will encounter the discontinuity. In both of these cases, the 

following rule must be followed: As circles of larger radii are drawn, the measured angles of intersection can 

never become smaller; they can only 

remain constant or become larger. 

Thus, the angle of intersection for both 

for Horizontal Boreholes 

The probability calculation method 

described in the previous section is 

applied in this section to a hypothetical 

horizontal drilling program for the Beckley Coalbed study area. For study purposes, the entire study area is considered to be a single mine property, when 

in fact, the area includes portions of 

five separate mines (as shown in figure 2). For this reason, it is not possible to locate hypothetical horizontal 

drilling locations on the basis of actual 

mine planes. In order to circumvent this 

problem and to analyze the entire study 

area, hypothetical horizontal drilling 

sites are located at each of the hypothetical vertical borehole locations that 

did not intersect a discontinuity. (See 

figure 9.) This provides 108 locations 

that are evenly distributed throughout 

the area of minable coal, so the study 

area is analyzed as if it were being 

developed by a single mine. 
Table 3 summarizes the calculated 

probabilities of encountering discontinuities during horizontal drilling at the 

108 drilling sites in the study area. 

The probabilities presented in table 3 

are mean values based on calculations 

from all 108 hypothetical drilling locations. As the borehole length increases, 

there is a systematic increase in the 

probability of encountering a discontinuity; the mean probability is 4.16 percent 

for a 500-foot hole, 9.44 percent for a 

1,000-foot hole, 13.71 percent for a 

1,500-foot hole, 17.09 percent for a 

2,000-foot hole, and 21.41 percent for a 

2,500-foot hole. A bivariate plot of 

horizontal borehole length versus probability of encountering a discontinuity 

(fig. 11) demonstrates that there is a 

remarkably linear relationship between 

the two variables. This linear relationship provides a meaningful basis for the 

evaluation of cost-risk factors in 

advance of initiating horizontal drilling 

programs in other areas of the Beckley 

Coalbed, assuming that the study area is 

representative of the rest of the 

coalbed. 

TABLE 3. - Horizontal borehole length and probability of 

encountering a discontinuity for hypothetical 

horizontal drilling program 

Horizontal borehole Mean probability, 

length, ft - Pet 

FIGURE 11. - Horizontal borehole length versus 

probability of encountering a discontinuity in the Beckley Coalbed. (The 

vatue r is the correlation coefficient 

and is used to test the statistical 

significance of the relationship between boreho le length and probabi lity of encountering a discontinuity; 

r2 is a measure of the proportion of 

the total variation in these two variables that is accounted for by the 

calcu iated regression l ine.) 

LENGTH OF HORIZONTAL BOREHOLE, 1 O2 ft 
SUMMARY AND CONCLUSIONS 

The probability of encountering 

coalbed discontinuities during vertical 

drilling in a specific coalbed can be 

estimated from statistical analysis of 

discontinuity size, shape, orientation, 

and distribution in mined-out areas of 

that coalbed. Published probability 

tables (9) allow determination of the 

size of discontinuities that will be 

encountered using various spacings 

between vertical boreholes, and conversely, what borehole spacings are 

necessary to assure detection of varioussize discontinuities. In uriexplored 

areas of the Beckley Coalbed, there is a 

29 percent probability that a vertical 

borehole will encounter a discontinuity. 

A square grid exploratory drilling pattern with 2,500-foot spacing between 

boreholes assures detection of most discontinuities that are large enough to 

cause serious problems for methane drainage and mining programs in the Beckley 

Coalbed. 

The probability of encountering 

coalbed discontinuities during horizontal 

drilling in a specific coalbed can be 

estimated from systematic analysis of 

hypothetical drilling sites in mined-out 

areas of that coalbed. The radii of 

various-size circles constructed around 

the drilling sites represent horizontal 

boreholes of various lengths. The 

part of a given circle that intersects a 

discontinuity, expressed as a circular 

percentage of all possible horizontal 

drilling directions, represents the probability of encountering a discontinuity 

with a horizontal borehole equal in 

length to the radius of that circle. 

Calculations of the probabilities for 

circles of various radii at drilling 

sites throughout a mined-out area allow 

estimation of mean probabilities for 

boreholes of various lengths. In the 

Beckley Coalbed there is a linear 

increase in the probability of encountering a discontinuity as the length of the 

borehole increases. 

Calculations of the probabilities of 

encountering coalbed discontinuities can 

be used in cost-risk analysis in advance 

of initiating a drilling program, whether 

it be for methane drainage, exploratory, 

or developmental purposes. This procedure does not result in the prediction of 

discontinuity locations and is not 

intended to replace detailed geologic 

investigations. This paper has demonstrated, however, that probability calculations can be used to augment the 

knowledge obtained from detailed geologic 

mapping and depositional environment 

reconstructions; and in this role, the 

probability approach can serve as a valuable tool that can be used to help accomplish the safe and economical exploitation of coal resources. 

REFERENCES 

1. Cervik, J., H. H. Fields, and 

G. N. Aul. Rotary Drilling Holes in 

Coalbeds for Degasification. BuMines 

RI 8097, 1975, 21 pp. 

2. Chayes, F. Petrographic Modal 

Analysis. John Wiley & Sons, Inc., New 

York, 1956, 113 pp. 

3. Fields, H. H., J. H. Perry, and 

M. Deul. Commercial-Quality Gas From a 

Multipurpose Borehole Located in the 

Pittsburgh Coalbed. BuMines RI 8025, 

1975, 14 pp. 

4. Griffiths, J. C., and L. J. Drew. 

Grid Spacing and Success Ratios in 

Exploration for Natural Resources. 

Proc. of the Symp. and Short Course 

on Computers and Operations Res. 

in Miner. Ind., The Pennsylvania State 

University, 1966, pp. 41-424. 

5. Houseknecht, D. W. Comparative 

Anatomy of a Pottsville Lithic 

Arenite and Quartz Arenite of the Pocahontas Basin, Southern West Virginia: 

Petrogenetic, Depositional, and Stratigraphic Implications. J. Sediment. 

Petrology, v. 50, 1980, pp. 3-20. 
6. Houseknecht, D. W., and A. T. 

Iannacchione. Anticipating Coal Mining 

Problems in the Hartshorne Formation, 

East-Central Oklahoma, Using Sedimentary 

Facies Analysis (Abs.). Am. Assoc. 

Petrol. Geol. Bull., v. 64, 1980, 

pp. 724. 

7. Lotz, C. W. Probable Original 

Minable Extent of the Bituminous Coal 

Seams in West Virginia. W. Va. Geol. and 

Econ. Survey Map, 1970. 

*U.S GOVERNMENT PRINTING OFFICE: 1982 - 505 - 0021'42 

8. Popp, J. T., and C. M. McCulloch. 

Geological Factors Affecting Methane in 

the Beckley Coalbed. BuMines RI 8137, 

1976, 35 pp. 

9. Singer, D. A., and F. E. Wickman. 

Probability Tables for Locating Elliptical Targets With Square, Rectangular, and Hexagonal Pointnets. Miner. 

Sci. Exp. Sta. Spec. Pub. 1-69, The 

Pennsylvania State University, 1969, 

100 pp.