The use of factor analysis as a method for predicting productivity at Wildhorse Field, Weld County, Colorado

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The use of factor analysis as a method for predicting productivity at Wildhorse Field, Weld County, Colorado
Buddy, Mark Steven
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xi, 158 leaves : illustrations, maps (including 3 folded in pocket), photographs ; 29 cm


Subjects / Keywords:
Petroleum -- Geology -- Colorado -- Weld County ( lcsh )
Oil fields -- Colorado -- Weld County ( lcsh )
Factor analysis ( lcsh )
Factor analysis ( fast )
Oil fields ( fast )
Petroleum -- Geology ( fast )
Colorado -- Weld County ( fast )
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )


Includes bibliographical references (leaves 79-82).
General Note:
Submitted in partial fulfillment of the requirements for the degree, Master of Basic Science, Department of Geology
Statement of Responsibility:
by Mark Steven Buddy.

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Source Institution:
University of Colorado Denver
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Auraria Library
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
22947523 ( OCLC )
LD1190.L44 1989m .B82 ( lcc )

Full Text
Mark Steven Buddy
B.S., Western Michigan University, 1978
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Master of Basic Sciences
Department of Geology

This thesis for the Master of Basic Sciences degree
Mark Steven Buddy
has been approved for the
Department of Geology
Date 11-20-89

Buddy, Mark Steven (M.B.S., Geology)
The Use of Factor Analysis as a Method for Predicting
Productivity at Wildhorse Field, Weld County,
Thesis directed by Professor Martin G. Lockley
Wildhorse field is productive from the D
sandstone member of the Cretaceous Dakota group. The
reservoir is a fine grained sandstone which is often
tight and produces hydrocarbons in relatively low
volumes. Evaluating the productive potential of the
formation has been a recurring problem in the development
of this field. Traditional methods of formation
evaluation such as drill stem tests, and water saturation
calculations often yield unreliable results because of
the tight nature of the formation, and the high
interstitial water content of the fine grained sands.
In this study factor analysis is used to identify
parameters which are most important in determining a
well's producibility. Thirty-nine wells from the field
were digitized over the D sand interval. Eight
variables, deep induction, medium induction, shallow
induction, spontaneous potential, gamma ray, bulk
density, porosity, and caliper were sampled at two foot
intervals. It was found that four factor end members can

be used to reliably describe the data. These are
resistivity, lithology, porosity, and hole conditions.
In particular the results of the analysis confirm that
factor derived lithology and porosity are far better
indicators of productivity than traditional variables.
When these two factors are combined they may provide an
empirical estimate of permeability that correlates
strongly with the observed productivity at Wildhorse
The form and content of this abstract are approved. I
recommend its publica*"*

to my family

I would like to thank all the people and
organizations that gave their assistance to this project.
Thank you to Diversified Operating Company for supplying
core and production data, and Petroleum Information for
supplying well logs. Thank you to Japex (U.S.) Corp. for
the use of materials and eguipment and to Sammie Jahnkie
for her help with the drafting.I also need to thank
Dakota the dog for his unfailing loyalty during this
project. His wet nose induced study breaks, which kept
burnout at bay. I wish to thank my parents for their pep
talks, motivational speeches and most of all their belief
in me. Special thanks go to Dr. Jeffery Yarus for his
patience, understanding, dedication, instruction, and
repeated explanations. He provided a challenge that I
never would have sought by myself. Without his help,
this project could never have been started or completed.
And lastly, I would like to thank my loving wife,
Colleen. Her love and unwavering support has buoyed me
through the down times of this project and kept
discouragement from setting in. Now, I can finally clean
the den.

I. INTRODUCTION.................................... 1
Factor Analysis.............................. 3
Study Area................................... 6
II. GEOLOGIC HISTORY................................ 8
Geology of Wildhorse Field.................. 16
III. METHODOLOGY.................................... 28
Correlation Matrix..................... 3 0
Factor Extraction........................ 36
Factor Matrix............................ 38
Reproduced Correlation Matrix............ 39
Factor Rotation.......................... 42
Factor Scores............................ 45
Overlay Plots............................ 47
IV. RESULTS...................................... 4 9
Discussion.................................. 52
Conclusions................................. 76
Summary..................................... 77
BIBLIOGRAPHY......................................... 79
APPENDIX............................................. 8 3
D SAND IN WELL D8-6............................ 84

IN LOTUS 123 FORMAT.......................... 89
ANALYSIS ROUTINE.............................. 126
FROM WELL LOGS................................ 128

1. Correlation matrix for factor analysis of
S1A-5R......................................... 32
2. Anti-Image correlation matrix for factor analysis
of S1A5R....................................... 34
3. Results of factor extraction for factor analysis
of S1A-5R........................................ 37
4. Unrotated factor matrix for factor analysis of
S1A-5R........................................... 40
5. Reproduced correlation matrix for factor analysis
of S1A-5R........................................ 41
6. Rotated factor matrix for factor analysis of
S1A-5R........................................... 44
7. Factor score matrix for factor analysis of
S1A-5R........................................... 46
8. Comparison of rotated factor matrices of S1A-5R
and S3-5......................................... 50
9. Table showing the maximum factor score values,
initial production rates, and well treatment for
the wells in the data set........................ 53
10. Comparison of rotated factor matrices of S1A-5R,
D2-6 and EMD1-7................................ 63
11. Cash flow projections for economic analysis
(appendix 5).................................... 134

1. Regional map of the Denver Basin showing the
basin configuration and bounding features...... 2
2. Location map showing the relative location
of Wildhorse field............................. 7
3. Stratigraphic column of Eastern Colorado....... 9
4. Stratigraphic column for the Cretaceous of
eastern Colorado................................. 12
5. Detailed stratigraphic column for Wildhorse
field............................................ 18
6. Standard well log showing the three D sand
members.......................................... 20
7. Net sand isopach of the D1 sandstone............ 23
8. Net sand isopach of the D2 sandstone............ 24
9. Net porosity of the D1 sandstone................ 26
10. Net porosity of the D2 sandstone................ 27
11. Example of standard well log showing the
digitized zone and correlation points............ 29
12. Flow chart outlining the steps involved in
factor analysis.................................. 31
13. Interpreted factor score plot for S1A-5R....... 48
14. Comparison of standard well logs with
the factor score plots for S1A-5R (well A),
and DIO-31 (well B).............................. 55
15. Comparison of standard well logs with
the factor score plots for S1A-5R (well A),
and S4-5R (well C)............................... 57

16. Comparison of standard well logs with
the factor score plots for S1A-5R (well A),
and SD2-5H (well D)............................. 61
17. Comparison of "normal" factor score plot and
anomolous factor score plots for well S1A-5R,
D2-6, and EMD1-7................................. 65
18. Map showing the areal distribution of the
anomolous wells.................................. 67
19. Map showing the areal distribution of the
economic wells................................... 69
20. Plot showing the combined factor scores of
lithology and porosity versus initial
production rates............................. 72
21. Plot showing the resistivity factor score
values versus initial production rates........... 75

I. Interval isopach between the X-Bentonite and the
base of the D sandstone
II. Net D sand isopach
III. Structure top of the D sand

The Denver Basin is a Rocky Mountain foreland
basin formed during the Laramide Orogeny. It is one of
the largest structural basins in the Rocky Mountain
region (figure 1). Oil and gas production from
Creataceous reservoirs in the basin has long been an
important source of revenue to the region. Since the
discovery of Wellington field in 1923 along the western
flank of the basin, it has produced more than 300 million
barrels of oil. The majority of this oil has come from
the D and J sandstones of the Cretaceous Dakota group.
However, as in other petroleum producing regions,
decision making criteria for completing potentially
economic wells are sometimes vague and often unreliable.
The D sandstone is commonly interpreted as being
a channel sand. Typically D sand hydrocarbon
accumulations occur as channels draped over structurally
positive areas. However, as exploration for the more
subtle trap becomes increasingly important, the
distribution of more subtle permeable zones within
channels becomes difficult to predict, and the overall
tight nature of the D sand in some areas can render

Figure 1: Outline of the Denver basin showing the bounding features.
Structure contours on the Precambrian basement (modified
from Kennedy, 1983).

standard log analysis and drillstem tests virtually
useless. Because the nature of these producing rocks is
complex and the relationship between those factors
controlling economic production is subtle, statistical
analysis of well log data may help to develop a set of
meaningful parameters that can relate specific reservoir
characteristics to depositional environments and to
ultimate productivity.
Although traditional methodology for solving
these problems would involve structure mapping, facies
mapping, core analysis and well log analysis, these
procedures provide little information regarding ultimate
productivity in complex reservoirs. Factor analysis of
the standard well log data can improve variable
resolution and provide a method of quantifying whether or
not a given well will perform greater than an established
economic minimum prior to implementing expensive
completion procedures.
Factor Analysis
Factor analysis is a multivariate statistical
technique used to identify end members from complex data
sets by removing data redundancy. It was pioneered and
successfully applied in the 1920's and 1930's as
psychologists sought to measure "intellegence" from the
results of dozens of various "intellegence" tests. Any

situation in which it is desirable to remove data
redundancy and identify a reduced number of factors or
which can explain the interrelationships between several
complex variables may lend itself to a factor analytical
Recent geological applications have included the
use of factor analysis to characterize end members in
grain shape studies (Ehrlich et al, 1980). This
technique has been used to determine sediment provenance
and transport history (Yarus, 1978; Mazzullo and Sims,
1983; Kennedy and Ehrlich, 1985). Miesch (1976), and
Klovan and Miesch (1976), use factor analysis to unmix
petrologic assemblages and define geochemical end
members, and Ehrlich et al (1983, 1984), use
factor analysis to reduce and classify the number of
variables generated during petrographic image analysis.
Although factors cannot be observed or measured
directly, they are often intuitive and postulated to
exist in order to explain similarities between actual
measured observations of different variables. Because
they are contained within the data but cannot be directly
measured, they can be considered latent variables
(Cureton and D'Agustino, 1983). A basic assumption of
factor analysis then is relationships or correlations
between variables are the result of shared latent
variables or factors. For example, the density log,

neutron log, and sonic log are all used to estimate
porosity. Yet each was designed to measure different
physical characteristics of the formation. In standard
well log form their analog displays will share a certain
amount of similarity. Factor analysis can present a
variable which carries the information common to all
three of these measured variables thus reducing the
redundancy and the dimension of the data set. By
identifying the factors which are correlative between
several variables we are able to create a minimum number
of new variables (in this case one representing
porosity), which are linear combinations of the old
variables such that the new variables contain the same
amount of information (Joreskog et al, 1976). These new
factor derived variables will be mutually independent or
uncorrelatable and can be considered "end members".
In a strict sense this technique can be called
vector analysis because the new factor variables are
extracted from the data as eigenvectors that describe a
correlation matrix created from the original data
(Ehrlich and Full, 1987). The eigenvectors or new
variables can account for most of the variance seen in
the system. When these vectors are interpreted or
assigned meaning, they might be considered factors, i.e.
it is a factor that underlies the observed relationship
between the density, neutron, and sonic porosity

variables. This type of factor analysis is termed "R-
mode" factor analysis. "R-mode" is used to understand
the inter-relationships amoung variables. "Q-mode" is
used to understand the inter-relationships amoung samples
(Klovan, 1975). "R-mode factor anlaysis was used in
this study.
A more detailed description of factor analysis
can be found in Davis (1986), or Joreskog (1977). Klovan
(1975), also offers a very succinct explanation.
Study Area
The Wildhorse field in eastern Weld County,
Colorado (figure 2) was chosen for this study because in
many ways it typifies the problems that many of the tight
D sand reservoirs experience throughout the basin. Well
log analysis is unreliable, drill stem tests are
inconclusive and the permeability within the field is
difficult to predict without direct measurement. It
appears many of the wells could have avoided costly
completions had the operators had access to a more
reliable measure of productive potential. Also because
Wildhorse has been developed only recently, data is more
readily available and of the same vintage thus providing
a more homogeneous data set.

Figure 2: Location of study area in relation to the surrounding

The Denver-Julesburg basin is both a structural
and stratigraphic basin that encompasses approximately
60,000 square miles in NE Colorado, SE Wyoming, and SW
Nebraska. On the west, it is bound by the Rocky Mountain
front range, on the north by the Hartville uplift, on
the south by the Apishapa uplift and the Las Animas arch,
and on the east by the Chadron arch and the central
Kansas uplift. Tectonically it is an asymmetrical basin
characterized by a steeply dipping western flank and a
gently dipping eastern flank (figure 1).
The axis of the basin lies parallel and adjacent
to the front range uplift with the deepest portion
reaching a depth of approximatly 7000 feet below sea
level at the Colorado-Wyoming border. The main
depocenter lies beneath Denver and contains up to 13,000
feet of sediment (Sonnenberg and Weimer, 1981).
For much of the basin the stratigraphic record
begins in the Pennsylvanian with the Fountain Formation
(figure 3). The Fountain consists of a thick non marine
sequence of conglomerates and arkoses that were deposited
as coelescing alluvial fans along the ancestral front

Figure 3: Stratigraphic column for the Denver Basin,
(from Kennedy, 1983)

range. These arkosic deposits grade laterally into
shales and lacustrine deposits which onlap the Chadron
and Las Animas arches.
Permian sedimentation is represented in northern
Colorado by the aeolian Lyons Formation.
By Triassic time the basin had become an enormous
westward dipping mudflat (Maughan 1980). During Triassic
time the transcontinental arch had become positive,
restricting deposition to the north and south of this
growing feature. Triassic sediments are comprised of
conglomerates and shallow near shore deposits. After a
period of erosion, Jurassic seas advanced from the north
to begin a new period of continuous sedimentation. The
Late Jurassic Morrison formation represents very low
relief continental deposition orginating in floodplain,
fluvial channel, and lacustrine environments. The lower
Dakota group interfingers with the Morrison formation
making an exact determination of the Jurassic-Cretaceous
boundary difficult (Haun, 1963). However, Peterson
(1972), suggests that the contact between the Morrison
and basal Cretaceous conglomerate is represented by an
erosional unconformity.
The Cretaceous deposition in eastern Colorado was
dominated by epicontinental seas of the Western Interior
seaway. The Western Interior seaway had its origins in
the Jurassic and is characterized by a series of

transgressions and regressions. Changes in sea level were
controlled by sediment supply, rate of down warp, and
uplift of the highlands to the west (Kauffman 1977).
Throughout the Cretaceous the climate was warm
and humid. Coastal areas were mostly swampy with sandy
shorelines that formed barrier bars and islands. These
barrier island complexes sheltered the extensive esturary
and lagoon complexes that had also formed in this
environment (McGookey,1972).
Initial formation of the Western Interior
Cretaceous seaway began in late Jurassic time with the
beginning of the Sevier Orogeny. The down warping of the
interior was in response to the intense thrusting and
uplifting occurring in the Sevier orogenic belt to the
west. The earliest Cretaceous deposition is represented
by conglomerates that were sourced by the newly formed
western highlands. Conglomeratic deposition did not
occur in eastern Colorado until Aptian time (figure 4).
Prior to this time the entire Neocomian stage in eastern
Colorado is characterized by erosion or nondeposition as
sediments of this age are not present in the Denver Basin
(McGookey, 1972).
The first Cretaceous marine transgression
occurred during Albian time (Reeside and Cobban, 1960).
Called the Skull Creek seaway, its invasion occurred from

Detailed stratigraphic column of the Cretaceous for
the Denver basin (modified from McGookey, 1972)

ancestral Gulf of Mexico with the Arctic Ocean. The
eastern boundary of the Skull Creek Seaway was the
Continental arch, and on the west it was bounded by the
low hills and volcanic centers left by the Sevier Orogeny
in western Utah and central Idaho (McGookey, 1972).
Skull Creek sediments are paludal or shallow marine gray
to black shales and thin coals.
A regressive phase followed the Skull Creek
transgression. This regression was responsible for
deposition of the J sandstone. The J was deposited as a
series of deltas and shoreface deposits that rimmed the
retreating Skull Creek seaway. The J sand is represented
primarily by deposition occurring on the eastern edge of
the basin. Contemporaneously, along the western edge of
the basin, the South Platte formation was being deposited
under similar conditions as the J sand. The east and
west deltas eventually began to coalesce causing a
separation of the seaway into once again an Arctic and a
Gulf component (Haun, 1963). The Mowry and Huntsman
shales were deposited near the end of the Lower
Cretaceous. An Arctic transgression of the Mowry sea
deposited the Mowry shale with the Huntsman being
deposited up to 75 miles south beyond the limit of Mowry
deposition. On the eastern flank of the basin, the
depositional limits are coincident (Haun, 1963). This
began an extremely long period of marine dominated

deposition extending from late Albian to middle
Maestrichian time.
The Greenhorn Seaway would eventually reconnect
the southern and northern segments of the Western
Interior Seaway.
The D sandstone represents a major regression in
this overall transgressive phase. It is considered to be
the last significant contribution to the basin of
continental arch sourced elastics (McGookey, 1972).
While the D sand is not directly represented in outcrop,
the upper parts of the Dakota sandstone type section in
Dakota County of northeast Nebraska can be correlated
with the D sandstone (McGooky, 1972). The sands of the
Dakota type section are predominately fluvial in origin.
Although areas of the D sand can be interpreted as being
deltaic, the overall aspect of the D sand is considered
to be that of a coastal plain environment (Haun, 1963).
It seems the overall deposition of the D sand is very
similar to that of the J sand, however, the argument for
deltaic deposition of the D sandstone is not quite as
convincing. The difference may be due to changes in
sediment supply. That is, the D sand regression does not
represent as large of a eustatic fluctuation as the J
sand regression, thus sediments are finer grained and
deposited in a lower energy environment.
After D sand deposition, the basin once again

returned to marine conditons with the deposition of the
Graneros shale. The Graneros is a neritic, organic rich
black shale that was deposited during the rapid marine
transgression that followed D sand deposition. The base
of the Graneros is recognized by the top of the D
sandstone, and the top of the Graneros is the X-Bentonite
(Sonnenberg, 1987). The X Bentonite is 1 to 6 feet thick
and provides a reliable time marker to correlate
throughout the region.
The Greenhorn cycle continued through mid-
Turonian (figure 4) time with the deposition of numerous
shales and limestones. The Greenhorn Limestone
represents the maximum incursion of the sea during this
transgressive cycle. Subsequent deposition of the
Carlile shale marked the beginning of a regressive phase
which peaked with the deposition of the Codell sandstone,
a fined grained, clay rich, nearshore, sandstone thought
to be the result of sediment redistribution from the
Frontier Formation delta systems to the west (Kennedy,
1983) The top of the Codell is marked by a
disconformity that represents a period of erosion marking
the end of the Greenhorn cycle and the beginning of the
Niobrara Cycle (Kauffman, 1969).
The Niobrara cycle was dominated by carbonate
deposition in the form of shaly carbonates as chalks of

the Fort Hayes Limestone and the Smokey Hill Limestone.
The end of this cycle coincides with major uplifting in
western Utah and eastern Idaho. The Niobrara tends to be
thin in the northern Denver basin due to recurrent
movement along the transcontinental arch.
The Claggett transgression is represented by a
change from the chalks and shales of the Niobrara
Formation to the dark marine shales of the Pierre Shale
(McCubbin, 1972). The Denver basin was dominated by
Pierre Shale deposition until late Maestrichtian time
when the gradual regression of the Pierre seaway gave way
to continental and fluvial sediments of the Laramie
Formation to close out Cretaceous deposition in the basin
(McGookey, 1972).
Geology of Wildhorse Field
The Wildhorse field is located primarily in
sections 5, 6, 7, and 8, T7N, R58W, central Weld County,
Colorado (figure 2). It is approximately 2 miles west of
the town of New Raymer.
Geographically the area can be classified as
rolling grasslands with gently incised drainages. Dry
land farming and ranching are the predominant forms of
land utilization.

The Wildhorse field was discovered in the mid
1950's by the Houser Turner No.2 well. This well produced
minor amounts of oil and gas from the D sand member of
the Upper Cretaceous Dakota group. Subsequent
development attempts proved fruitless because of the
tight nature of the D sand in this area. Oil prices at
this time were such that reservoirs of this type were
noneconomical and completion attempts were not routinely
made. It wasn't until the early 1980's that prices had
increased to the point where companies could explore for
low volume tight reservoirs. In 1981 Sundance Oil
completed the Nickerson 1-8 in the NE1/4 of section 8,
T7N, R58W, for 1197 MCFGPD and 24 BC. This began a
flurry of activity in which several companies vied for
acreage positions and began field development. At this
writing there are 37 producing wells in the field with
additional locations planned. Some of the producing
wells are reentries or twins of wells that were plugged
and abandoned during the 1950's. Cumulative production
has reached over 2.3 BCF gas, and 395000 BO as of
September 1987.
The primary productive zone at Wildhorse field is
the D sandstone member of the Cretaceous Dakota group
(figure 5). The D sand was deposited during a regression
of the Greenhorn seaway. In general D sand deposits

"D" Ss
o Huntsman

o a a Platte
0 J' Ss
W o CO Fm.
o (0 Skull Creek
* a
W -1
Lytle Fm.
Figure 5:
Detailed stratigraphic column for the lower Cretaceous
Dakota group (modified from Kennedy, 1983).

represent a prograding coastal plain environment
(Haun,1963). At Wildhorse, three sandstone members can
be identified that are suggestive of a lower delta
plain environment. The lowest of these (D3) is a
coarsening upward sequence seen on the electric logs
(figure 6). This sequence is interpreted to represent
the initial retreat of the Greenhorn seaway and the
progradation of the new coastal zone. In some wells the
sequence culminates with a well developed sand which is
usually followed by a thin shale likely representing a
minor hiatus in the regression of the seaway. Overlaying
this thin marine shale is the D2 sand. The D2 is the
primary reservoir at Wildhorse field. This sand, which
attains a thickness of up to 15 feet, appears to be
deposited as a minor channel during the progradation of
the D delta complex. Core taken from well D8-6 (appendix
1), shows a fine grained moderately to well sorted
sandstone. The lower portion of the D2 contains low
angle crossbeds and trace fossils are sparse. Toward the
top of the D2 interval, trace fossils are more abundant
and bedding becomes horizontal. Also several shale
laminae are seen. Geyer and Pritchett (1978) place the D
sand, at Davis Joyce field to the north, in a "riverine
- dominated" delta system not unlike the depositional
environment seen in present day south Louisiana. Plate I
is an isopach map of the interval between the X-

Figure 6: Standard well log SD1-5H showing the three "D"
members and the surrounding formations.

bentonite, and the base of the D sand. The X-Bentonite
(figure 6) is a time stratigraphic marker that is
recognized throughout most of the northern Denver basin.
This interval isopach map was constructed to determine
the paleotopographic surface upon which the D sand was
deposited. Thick intervals that correspond to thick sand
accumulations suggest that scouring has occurred. A
comparison of plate I and plate II (D sand isopach) shows
that the isopach thicks do correspond to thicker sand
intervals corroborating the presence of scouring during
D2 deposition. This would support Geyer and Pritchett's
(1978) interpretation that fluvial channels were
deposited on a tidal or mudflat surface. Examination of
plate I indicates that this surface had very low relief.
Core taken from well D8-6 (appendix 1), shows that the D2
sand fines upward into a silty zone that displays
moderate to intense bioturbation. The bioturbation
itself is also gradational from a relatively clean sand
that contains sparse to moderate Arenicolites and
Skolithos type burrows to a heavily mottled zone which
appears to contain abundant root casts. The Skolithos
and Arenicolites burrows are interpreted as being
indicative of a near shore or higher energy environments
(Frey and Howard, 1982). As the sands become more silty,
they grade into dark gray to black siltstone with
scattered pyrite and plant fragments. The D2 channel

deposition appears to give way to a lower energy
environment, perhaps a salt marsh, which subsequently
became more restricted and allowed the accumulation of
organic material. This zone looks very much like the
abandoned channel facies described by Land and Weimer
(1978), however the abundance of trace fossils suggests
to this writer that the system was more open and
influenced by the nearshore marine environment.
The thin organic siltstone is overlayed by the D1
sandstone. At Wildhorse the D1 is thin (up to 6 feet
thick) and its distribution is areally less extensive
than the D2. Figures 7 and 8 show the thickness
relationship between the D1 and D2 sands. The D1 was
deposited in the main channel but in areas between D2
thick zones. D1 sands may have been deposited as splay
or overbank deposits but may also represent a marine
reworking of the D2 sand as the Graneros sea inundated
the area. The moderate to extensive bioturbation along
with scattered woody material suggests that the D1 may be
the first evidence of the rapid Graneros transgression.
Geyer and Pritchett (1978) suggest that this rapid
transgression may be responsible for not only preserving
the D channels, but also for winnowing out some of the
interstial clay material thus making the D1 a slightly
cleaner component of the overall sand package.
Porosity distribution in both the D1 and D2 sands

Figure 7: Net sand isopach for the "Dl" sand member at the
Wildhorse field.

Figure 8: Net sand isopach for the "D2" sand member at
Wildhorse field.

does not appear to be completely controlled by depositon.
The more well developed porosity is not always located in
the thickest parts of the channels or sand bodies
(figures 9 and 10). This suggests that thickness alone
(along with its inference of higher energy conditions)
is not sufficient to predict porosity development at this
field. A most notable example of this occurs in section
8 wherein well EMS 2-8 the D2 sand is 15 feet thick but
exhibits no porosity over 10% (fig 10).
Despite its very thin nature, the D1 sand appears
to play a key role in economic production at Wildhorse
field. Most of the wells that were completed in the D1
sand were also completed in the D2. Of the 12 economic
completions in the field, 7 of them had contributions
from the Dl.
The cleaner nature of the Dl sand probably has a
great deal to do with its economic contribution to the
well, but this phenomenon could also be simply due to the
fact that when both the Dl and D2 sands are completed
there is more surface area of the formation exposed to
the wellbore and thus more formation is available for
The field itself is located on a very subtle
structural feature (plate III), but internally structure
does not appear to significantly influence productivity.

Figure 9: Net porosity of the "Dl" sand member at Wildhorse field.

Figure 10: Net porosity of "D2" sand member at Wildhorse field.

Well logs were collected throughout Wildhorse-
Turner field. A total of 43 wells were analyzed and 4
wells were not used due to incomplete data sets, leaving
a total of 39 wells included in the study.
Prior to digitizing, the well logs were
correlated on a stratigraphic marker located
approximately 10 feet above the D sand. This marker was
to be the starting point for digitization (figure 11).
The logs were digitized for an interval of 84 feet
sufficient to penetrate the D sand to a reliable regional
marker in the resistivity log that signals the top of the
J sand unit. Each well was sampled at two foot
intervals. A total of 8 curves were digitized for each
well; the Deep Induction log (ILD), Medium Induction log
(ILM), Spherically Focused log (SFL), Spontaneous
Potential log (SP), Gamma Ray log (GR), Bulk Density log
(DEN), Porosity log (POR), and the Caliper log (CAL),
plus depth made up the variables used in the study.
Digitizing was carried out using a Summagraphics
Inc. Summasketch digitizing tablet coupled with a Compac
PC AT. E Z Dij. digitizing software by Geocomp Inc.

SP Resistivity
Figure 11: Standard well log SD1-5H showing the resistivity markers
that identify the digitized interval.

was used and the data for each individual curve was
stored in separate ASCII files. Lotus 1-2-3 2.0 by Lotus
Development Corp. was used to edit and combine the files
in a format shown in appendix 2. These files were then
compressed to remove all labels and excess spaces between
the columns, and transfered to SPSS PC+ for factor
analysis. SPSS PC+ by SPSS Inc. is an extremely
versatile statisical software package that was originally
developed to analyze data collected by social scientists.
Most commonly used in a mainframe format, it has been
recently made available for the PC. All data analysis
and manipulation was done using an IBM XT compatable.
The commands listed in appendix 3 were used to
run the factor analysis and construct the factor score
plots. After transferring the data files from Lotus 1-2-3
to SPSS, these commands were used to run the analysis.
Correlation Matrix
Factor analysis consists of several steps
outlined in figure 12. The first important step is the
determination of the correlation matrix (table 1), which
measures the degree of interrelationship between each
pair of variables (Klovan, 1975). Perfect correlation
can be observed along the diagonal of the correlation
matrix where each variable is correlated with itself. In
table 1 all of the resistivity variables are strongly

Data is put into matrix form
using Lotus 123.
Data is standardized to
prepare it for factor analysis.
Measures the degree of
correlation amoung variables.
Factors extracted using
principal component analysis.
Loadings indicate relative
relationship between a factor
and a variable.
Varimax rotation maintains
orthogonality but maximizes
varience expressed by factors.
Estimates of contributions
made from each factor
to each sample.
Factor scores are plotted
against depth.
Figure 12: Flow chart showing sequence of steps followed in
factor analysis.

Correlation Matrix:
DEPTH 1.00000
ILD .03183 1.00000
ILM .07309 .98663 1.00000
SFL .01453 .94805 .96031 1.00000
SP .17077 -.84591 -.78680 -.79200 1.00000
GR -.12061 -.76238 -.73427 -.71898 .77217 1.00000
DEN .58671 -.46212 -.42887 -.48864 .64103 . 11080 1.00000
POR -.62455 .46777 .43198 .49326 -.66068 -.13638 -.99548 1.00000
CAL . 22081 -.81087 -.73157 -.73644 .90890 .80542 .48740 -.51463 1.00000
Table 1: Correlation matrix for factor analysis of S1A-5R.

correlated, and there is a high correlation between SP
and GR variables. Intuitively this makes sense because
the resistivity variables are all measuring some aspect
of resistivity, and the SP and GR variables are measuring
different characteristics of lithology. One of the goals
of factor analysis is to identify factors that explain
these correlations or the relationships between the
variables. If there are no intercorrelations between
variables other than with themselves, the correlation
matrix would represent an identity matrix and there would
be no need for a factor solution.
SPSS then runs several tests to determine the
appropriatness of the factor model or rather, to quantify
the amount of relationship between the set of variables.
The first test run is the Kaiser-Meyer-Olkin (KMO)
measure of sampling adequacy. KMO comapares the magnitude
of the observed correlation coefficients with the
magnitude of the partial correlation coefficients.
Partial correlation coefficients are estimates of the
correlation between unique factors. If the variables are
interrelated through common factors then the partial
correlation coefficients should be small because unique
factors are assumed to be uncorrelated with each other
(Norusis, 1986). Small KMO values indicate that factor
analysis would be an inappropriate method of data
analysis. In the example in table 2, the KMO value is

Anti-Image Correlation Matrix:
DEPTH . 35028
ILD .08991 .81497
ILM -.07300 -.94245 .70204
SFL -.21664 .13333 -.41292 .91084
SP .64076 .34400 -.26197 - .21243 .72314
GR -.35516 -.40373 .35826 .21841 - .68146 .71909
DEN .59664 .23293 -.18145 . 08860 .40335 - .17296 . 62167
POR .70357 .26495 -.20360 - . 15417 .55166 - .32244 .97858 .57937
CAL -.31244 .61512 -.58940 .17572 - .23926 - .28329 .02487 -.00265 .79123
Measures of sampling adequacy (MSA) are printed on the diagonal
Kaiser-Meyer-Olkin Measure of Sampling Adequacy = .69847
Bartlett Test of Sphericity = 240.56463, Significance = .00000
There are 0 (0.0%) off-diagonal elements of AIC Matrix >0.09
Determinant of Correlation Matrix = .0000000
Table 2: Anti-Image Correlation matrix for factor analysis of S1A-5R. Also shown
is the Kaiser-Meyer-Olkin measure of sampling adequacy, and the Bartlett
test of sphericity.

.698 indicating that there is a moderate degree of
interrelation between the variables in the example well
and that a factor solution may be considered. Values
less than .5 are generally unacceptable (Kaiser, 1974).
All wells analyzed yielded KMO values in the acceptable
range indicating the appropriateness of using factor
analysis for these data sets.
The second test is the Bartlett test of
sphericity. This test determines if the correlation
matrix is essentially an identity matrix. The Bartlett
sphericity test is "based on a chi-square transformation
of the determinant of the correlation matrix" (Norusis,
1986). When this number is high and the significance is
low, then the correlation matrix can not be considered an
identity matrix. In the example in table 2 the value of
240.5 represents an adequate value with the significance
level of 0 being excellent (Norusis, 1986). Similar
results were found in the other wells in the data set.
The Anti-Image correlation matrix (AICM) is
another means of expressing the degree to which variables
share common factors (table 2). Assuming that the
variables share common factors, the correlation between a
pair of variables should be small when the effects of the
other variables are eliminated (Norusis, 1986). The
residual correlation is called partial correlation and
considered to be an estimate of the correlation between

the unique factors. Unique factors should be unrelated
so that the numbers in the Anti Image correlation matrix
should be small. The example in table 2 shows that
there in not a large proportion of large correlation
coefficients in the (AICM) and that factor analysis is an
appropriate means of data analysis in this case. The
other wells in the data set exhibited similar results.
Factor Extraction
The next step in the analysis is factor
extraction. This is where the similarity or redundancy
is removed from the data. This was done using principal
component analysis. Principal components are the
eigenvectors of a correlation matrix (Davis, 1986). The
eigenvectors can geometrically represent the varience
seen in the matrix and transform the correlated variables
into a set of mutually independant (uncorrelated)
variables. In principal component analysis, linear
combinations of the variables are formed with the first
principal component accounting for the largest amount of
varience, the second principal component accounting for
the next largest amount of varience, etc. (Norusis, 1986)
(table 3). As many principal components can be
determined as there are variables. By calculating fewer
principal components, the minimum number of variables
that carry the maximum amount of information can be

Final Statistics:
Variable Communality * * Factor Eigenvalue Pet of Var Cum Pet
DEPTH .99829 * 1 5.78647 64.3 64.3
ILD .98166 * 2 2.10038 23.3 87.6
ILM .99032 * 3 .61328 6.8 94.4
SFL .96785 * 4 .30522 3.4 97.8
SP .98022 *
GR .95042 *
DEN .99401 *
POR .99640 *
CAL .94619 *
Table 3: Results of factor extraction for factor analysis of S1A-5R. Shown are
the eigenvalues for the 4 factor solution along with the percentage of
variance accounted for by the factors. Also shown are the communalities
of the variables.

determined thus reducing the dimensionality of the
problem. In table 3 it can be seen that 97.8% of the
varience is represented by only 4 principal components.
Additonal principal components did not add significantly
to explaining the variance. This would suggest that a 4
factor solution is appropriate. However care must be
given to closely examine the remaing factors to ensure
that the information they yeild is not critical to the
study. Because a factor may only account for a small
amount of the varience is not to say that it isn't
siginificant. In this study, factors greater than 4 did
not seem pertinent to the problems at hand. Table 3 also
lists the communality for the variables. The
communalities indicate how much of the observed variance
for each of the variables is explained by the common
factors. Additional background information on principal
components can be found in Davis (1986).
Factor Matrix
The factor matrix contains the coefficients for
each factor that relate to each variable. The
coefficients or factor loadings indicate the relative
relationship between a factor and a variable. High
absolute value loadings have strong relationships to the
variables, and factors with lower values have weaker
relationships. The example unrotated factor matrix in

table 4 shows that factor 1 exhibits high loadings for
the SP, GR, DEN, and Cal variables, while all of the
resistivity related variables (ILD, ILM, SFL) are
inversely correlated. High loadings on the first factor
are expected and indicate that the individual variables
carry considerable redundant information. This makes a
great deal of sense particularly with the well log data
all of which is so highly correlated.
The percentage of contribution that a variable
makes to each factor can be calculated simply by squaring
the variable loading for each factor. The sum of the
squares will equal 100% (Davis,1986). The relative
degree to which a variable loads onto a particular factor
is the basis for assigning meaning and differentiating
the factors.
Reproduced Correlation Matrix
The reproduced correlation matrix uses the
previously estimated correlations from the factor matrix
to "re-estimate" the correlation between variables
(Norusis, 1986). These are compared to the original
estimates seen in the correlation matrix. The difference
between the two is the residual. The residuals are
plotted above the diagonal on the reproduced matrix
(table 5). Large residual values indicate the
inappropriateness of the factor model. In table 5 the

PC Extracted 4 factors.
Factor Matrix:
DEPTH .20446 .83680 .37083 -.34458
ILD -.93940 .25378 .14329 .11942
ILM -.90602 .28580 .22939 .18750
SFL -.91563 .21290 .22674 .18089
SP . 95084 . 00706 .13119 .24263
GR .76045 -.48406 .37006 .02958
DEN .66889 .69301 -.21328 .14441
POR -.68319 -.69984 .15876 -.12109
CAL .89801 -.06580 .35546 .09535
: Unrotated factor matrix for factor analysis of S1A-5R.
Table 4

Reproduced Correlation Matrix:
DEPTH .99829* -.00045 -.00128 .00184 .00541 .00193 -.00111 .00016 -.00670
ILD .03228 .98166* .00773 -.02021 -.00226 .01827 .00367 -.00469 -.01290
ILM .07437 .97890 .99032* -.01604 -.00293 .00262 . 00094 -.00070 .00144
SFL .01270 .96827 .97636 .96785* .00348 -.00889 -.00150 .00261 .00198
SP .16536 -.84365 -.78387 -.79548 .98022* -.00320 -.00692 .00241 -.01426
GR -.12254 -.78065 -.73689 -.71009 .77537 .95042* .01225 -.01078 -.04368
DEN .58782 -.46579 -.42981 -.48715 .64795 .09854 .99401* -.00215 -.00562
POR -.62472 .47247 .43268 .49064 -.66309 -.12559 -.99332 .99640* .00794
CAL .22750 -.79797 -.73300 -.73841 .92316 .84910 .49302 -.52257 .94619*
The lower left triangle contains the reporduced correlation matrix;
the diagonal, communalities; and the upper right triangle, residuals
between the observed correlations and the reporduced correlations.
There are 0 (0.0%) residuals (above diagonal) that are > 0.05.
Table 5: Reproduced correlation matrix for factor analysis of S1A-5R. ^

residual values are very low indicating most of the
variance and the observed correlation between the
variables can be accounted for by shared or common
Factor Rotation
The next phase of the factor analysis is the
rotation phase. The purpose of rotation is to try and
simplify the relationship between factors and variables,
and clarify the meaning of each factor. This is often a
problem when there are fewer factors than there are
variables. One method, Kaiser varimax rotation,
attempts to maintain orthogonal relationships between the
factors but maximizes the variance expressed by each
(Kaiser,1958). While the original factors are selected
to account for the maximum amount of variance found in
the correlation matrix, rotation seeks to simplfy
interpretaion by aligning the factors or vectors so that
the loadings of the original variables have either very
high (absolute value) or very low (absolute value)
correlations with the factors (Davis, 1986). Rotation
will reintroduce a small amount of correlation between
the factors. It places the axes in more meaningful
positions so that they correlate better with some of the
original variables (Klovan, 1975). Only a few variables
should load highly on a given factor. If all the

factors load highly for the same variable, then they
cannot be differentiated. In the example (table 6), the
rotated factor matrix shows different relationships than
those seen in the unrotated matrix (table 4). The
resistivity related variables, ILD, ILM, and SFL, now
load highly on factor 1 demonstrating a strong
relationship. The lithology related variables SP, GR,
and CAL now load highly onto factor 2. The DEN (density)
variable has moved to a high loading on factor 3 along
with a high negative loading for POR suggesting that
factor 3 may represent porosity. The Depth and CAL
variables are now loaded more highly onto Factor 4. This
factor most likely represents the hole conditions. A
comparison of table 4 with table 6 clearly shows the
value of this phase of the analysis. In the rotated
factor matrix the percent contribution that a variable
makes to each factor can also be quantified by squaring
the loadings. For example: the loading of ILD is .82893
on factor 1, -.48205 on factor 2, -.24303 on factor 3,
and .05562 on factor 4 (table 6). When these values are
squared, 69% of ILD is represented on factor 1, 23% on
factor 2, 6% on factor 3, and less than 1% on factor 4.
The total percentage is slightly less than 100% due to
errors in rounding. These relative values or loadings
from the rotated factor matrix are the basis for the
factor interpretation.

Rotated Factor Matrix:
DEPTH .12272 .02780 .43451 .89087
ILD .82893 -.48205 -.24303 .05562
ILM .88986 -.38852 -.20535 .07318
SFL .86785 -.37906 -.26409 .03534
SP -.44538 .73360 .49336 -.01655
GR -.48510 .83707 -.11241 -.04202
DEN -.23529 .11835 .93278 .23359
POR .23073 -.15355 -.91683 -.28106
CAL -.41207 .82105 .28328 .14835
Table 6
Rotated factor matrix for factor analysis of S1A-5R. Varimax rotation
has been used to maximize the variance expressed by each factor.

Factor Scores
Once a factor model has been established, factor
scores can be calculated for the individual samples or
depths. In this analysis a sample consists of all the
factor scores at a given depth. Each sample is assumed
to posess a value or contribution from each factor. This
contribution is called a factor score (Krzanowski, 1988).
Factor scores then, represent estimates of how much a
factor contributes to each individual sample. Table 7
illustrates the factor contribution for each sample or
depth interval. For example Fl= -.499 @6380, F2= 2.151
@6380, F3=-l.956 @6380, and F4=-.813 @6380. This example
shows which factor accounts for the most varience at a
given sample depth. Percentage of contribution can be
determined relative to the other factors by summing the
squares and dividing by the total. In this example
factor 2 contributes almost 50% of the total varience
seen in this sample. Since the factor scores are
computed from autoscaled or standardized data, the scores
themselves are represented by units of standard deviation
(Klovan,1975). The determination of the factor scores
provides us with an index upon which to measure the
factors (Bartholomew, 1987). For example if we have
determined that factor 1 is found to represent
resistivity, the factor scores give us an index from

6308.00 -.49956 2.15115 -1.95613 -.81307
6310.00 -.58963 1.44492 -.99371 -1.02993
6312.00 -.81663 -.57810 .24825 -1.32610
6314.00 -.22372 -.83442 1.43257 -1.70105
6316.00 .01497 -.14995 1.13720 -1.47372
6318.00 -.56472 -.60292 -.22307 -.51121
6320.00 -.91565 -1.79977 -1.31946 .37474
6322.00 -.28242 -1.73968 -1.64708 .71490
6324.00 2.53779 -.50756 -.85068 .01821
6326.00 2.43366 .34133 -.03086 -.04542
6328.00 .32875 -.15033 .57413 .21113
6330.00 .14709 .38181 .61246 .28352
6332.00 .12594 .35703 .68017 .49169
6334.00 -.04439 .28081 .54822 .80215
6336.00 -.45684 .15270 .68286 1.01747
6338.00 -.50889 .77742 .60684 1.36421
6340.00 -.68573 .47557 .49824 1.62249
Table 7: Factor score values for each sample depth for
for S1A-5R.

which we can measure that property throughout the data
set. In this case vertically through depth, just like a
well log.
Overlay Plots
The final step in the factor analysis is the
construction of overlay plots. Overlay plots provide a
means in which to measure the factor contributions
thoughout the data set. The factor scores were plotted
against depth to create a factor score log (figure 13).
This new log offers the reduced dimensionality of the
factor analysis in a format that can be used in a fashion
similar to the original well logs. The above procedure
allows us to begin to graphically observe the
relationship between the factors and their associated
underlying variables, and to interpret the underlying
factors responsible for these observations.

Factor 2 Factor 1
Factor 4 Factor 2 Factor 3
Figure 13 :
Interpreted factor score plot from the factor analysis of well S1A-5R. Actual plot has
been inverted and factor logs have been grouped to resemble actual well logs.

The factor analytical procedure described above
was performed on the 39 well data sets from Wildhorse
field. Each of the 39 analyses generated a reduced set
of variables or factors. A 4 factor solution was chosen.
Each factor was assigned a meaning based on the strength
of the variable loadings from the rotated factor matrix
(table 6). The 4 factors consistantly represented the
same properties resistivity, lithology, porosity, and
hole conditions, respectivly from well to well.
The rotated factor matrix shown in table 6 is
representative of the relationships between factors and
variables. Factor 1 has a strong correlation with
resistivity, factor 2 is highly correlated with
lithology, factor 3 represents porosity, and factor 4
suggests hole conditions. Although the loading structures
are not always the same for each well i.e. resistivity is
not always found on factor 1 etc., it was found that for
every well a fairly clear interpretation of what each
factor represents can be made. For example porosity is
represented by factor 3 in well S1A-5R, but it is
represented by factor 2 in well S3-5 (table 8). When

Rotated Factor Matrix:
DEPTH .12272 . 02780 .43451 .89087
ILD .82893 -.48205 -.24303 .05562
ILM .88986 -.38852 -.20535 .07318
SFL .86785 -.37906 -.26409 .03534
SP -.44538 .73360 .49336 -.01655
GR -.48510 .83707 -.11241 -.04202
DEN -.23529 .11835 .93278 .23359
POR .23073 -.15355 -.91683 -.28106
CAL -.41207 .82105 .28328 .14835
Rotated Factor Matrix:
DEPTH .10613 .89199 -.00525 .41663
ILD .49489 .18239 .84544 -.05887
ILM .39775 .15177 .89673 -.03630
SFL .88015 -.16703 .38331 .09054
SP .87165 .27752 -.34369 -.00177
GR .94756 -.05697 -.22089 .07934
DEN .13085 .97795 .12411 -.06882
POR .07670 -.98187 -.12258 .07526
CAL .77440 .22554 -.35439 .45488
Table 8
Comparison of rotated factor matrices
for S1A-5R and S3-5.

these differences are found they can be explained by the
fact that each well represents an individual data set
within a parent population (Wildhorse field). Factor
analytical results will vary and of course be controlled
by the individual data sets. As long as the factors can
be identified, we can begin to determine what roles the
factors play in a well's productivity.
After each factor had been identified and
labeled, its factor scores were plotted against depth.
With the y axis representing depth, and the x axis
representing the factor score values in units of standard
deviation. These plots then can be used as factor logs
representing resistivity, porosity, lithology, and hole
conditions plotted against depth (figure 13).
The factor logs correlated well with the standard
logs but exhibited expected differences attributable to
removal of the redundant data. The factor logs
corroborated obvious relationships seen in the standard
logs such as "clean" lithologies and high porosities
coinciding with wells that were economically productive.
Many wells exhibiting "clean" lithologies and high
porosities were marginal or subeconomic in their
production. Factor analysis identified these wells by
exhibiting smaller factor porosity values and smaller
factor lithology values than the economically productive
wells. Additionally, factor analysis identified wells

whose factor score plots were anomolous. These wells are
clustered in a manner to suggest that these anomolous
zones represent subtle localized changes that are either
diagenetic or depositional. These also were not
identified by the standard well logs.
As initially stated, production at Wildhorse
field is controlled by a complex set of parameters whose
relationship to the actual observed production is subtle.
Standard well log analysis is not always effective in
identifying these parameters necessary for economic
productivity. Statistical analysis of the well log data
can help identify the essential criteria necessary for
sucessful well completions at the Wildhorse field.
Key to the productivity at Wildhorse is the
combination of porosity and lithology. The factor score
plots allowed the writer to assign factor score values to
porosity and lithology in units of standard deviation for
the productive zone in each well. These values could
then be compared to the electric log and the actual
production observed for the well. It was found that the
correlation between high factor score values and good
intial production rates was strong (table 9).
A comparison of wells in figures 14-16
illustrates how factor score plots may provide a more

D6-6 -1.86 -1.89 -3.75 2.10 130 50 D2 NO TEST A + SWFR
S3-5R -0.65/-1.69 0.20 1.81 1.62 135 511 Dl/2 NO TEST SWFR
S1A-5R -1.65 -1.79 -3.43 2.53 222 278 D2 NO TEST SWFR
D2-6 -0.63/-1.62 0.63 -2.25 1.17/1.36 148 175 Dl/2 NO TEST A+SGFR
WC3-7 -1.58 -1.36 -2.94 2.73 100 63 D2 NO TEST A
SD1-50 -1.54/-0.35 -1.96/-1.68 -3.50/-2.03 0.91 A.68 66 1388 Dl/2 NO TEST SGFR
SI-5 -1.63/-1.40 -2.73/-2.80 1.40/2.60 223 384 Dl/2 NO TEST SGFR
SD2-5H -1.43 -1.43 -2.86 2.34 33 88 Dl/2 10MD SOFR
P1-32B -1.32 -1.63 -2.94 2.40 12 120 D2 NO TEST SWFR
S1-5N -1.20/-1.28 -2.56/-1.20 -3.76/-2.48 2.72 200 200 Dl/2 NO TEST SWFR
S2-5 -1.28/-.07 -1.92/-0.68 -3.20/-1.36 2.80 205 308 Dl/2 NO TEST SAFR
Dl-6 -1.24 -0.13 -1.36 2.00 32 230 D2 NO TEST A
Dll-31 -1.24/-1.20 0.07/-7.69 -1.30/-2.84 1.49/2.34 20 380 Dl/2 NO TEST SWFR
D15-31 -0.91/-1.23 -2.28/-1.40 -3.18/-2.60 1.49/2.08 301 0 Dl/2 NO TEST A+SWFR
S1-5R -1.20 -1.15 -2.35 2.10 200 200 D2 NO TEST SAFR
P1-32N -1.17/-0.91 -0.07/-0.80 -1.23/-1.71 0.33/2.40 48 % Dl/2 NO TEST SGFR
D16-31 -0.67/-1.12 -1.35/-1.27 -2.02/-2.39 2.25 52 56 D2 NO TEST NATURAL
D14-31 -1.12 -1.32 -2.44 1.65 93 158 D2 NO TEST A+SWFR
SD1-8N -1.02 -1.50 -2.52 ? 24 1197 ? GTS
D3-6 -0.% -2.20 -3.16 1.68 180 175 D2 NO TEST A+SWFR
EMS1-8 -0.83 -0.66 -1.48 1.62 10 230 D2 NO TEST A+FR
S4-5R -0.83 -1.04 -1.86 1.95 3 3 D2 NO TEST SWFR
WC1-7 -0.80/-0.72 -1.76/-1.84 -2.56/-2.S6 2.80 82 82 Dl/2 NO TEST A+SGFR
S3-5 -0.71/-0.52 -1.75/-1.43 -2.46/-1.95 0.98/1.82 48 100 Dl/2 NO TEST SWFR
S2-5R -0.64 -0.56 -1.20 2.56 44 141 D2 NO TEST SWFR
DIO-31 -0.61 -1.38 -1.98 0.94 0 0 Dry NO TEST
APB1-1 -0.60 -0.90 -1.50 2.02 0 0 Dry 40MD
EMS3-8 -0.60/-0.10 -1.40 -130 2.10 4 5 D2 NO TEST A+SWFR
D8-6 -036 -1.6 -2.16 2.00 57 75 Dl/J NO TEST A+SWFR
S1-1B -0.56 -1.33 -1.89 1.04 7 ? D2 NO TEST
SD1-60 -0.56 -1.33 -1.89 2.31 12 40 D2 NO TEST NATURAL
EMS2-8 -0.47 -0.23 -0.69 1.76 5 250 D2 NO TEST A+SWFR
APA2-33 0.30 -1.26 -0.96 1.08 0 0 Dry NO TEST
WD2-7 0.75 -1.65 2.40 3.00 17 71 D2 NO TEST A+SWFR
WA1-7 1.40 -0.35 1.75 1.40 60 64 D2 NO TEST A+SGFR
EMD1-7 1.20 -1.62 2.82 1.20 150 145 D2 NO TEST A+SGFR
WC2-7 -0.30 1.80 2.10 1.68 33 52 D2 NO TEST A+SGFR
WK1-13 1.38 1.93 3.30 1.81 0 0 Dry NO TEST
SD1-5H -2.80 1.02 3.82 2.13 7 7 D2 7 7
Table 9: Maximum factor score values, initial production
rates, test results, and treatments for all
wells in the study.

acurate means of predicting productivity than the
standard well logs, and how factor analysis can be
utilized in making completion decisions. Examination of
the standard well logs for wells "A" and "B" (figure 14)
indicates that well "A" has better reservoir development
than well "B". Factor analysis confirms this observation,
and corroborates the observed relationship between actual
production and log response. It is useful to make this
comparison between wells whose relationship is obvious so
that the standard deviation units of factor logs may be
calibrated to the standard well logs. Once calibrated,
the factor logs allow us to anticipate the quality of the
reservoir or the quantity of production to be expected.
Well 'A" was completed for 222 BO and 278 MCFGPD
and well "B" is a dry hole. Comparison of their
respective standard porosity logs (figure 14) shows that
well "A" has 10 feet of 10% porosity in the D2 sand and
has a maximum value of 17%, while well "B" exhibits
porosity values of only 6% or 7%. The corresponding
factor score plots for porosity express absolute values
of standard devation as 1.65 and .605 units
respectively. Comparison of these values with the
standard well logs lets us generalize that factor logs
exhibiting a standard deviation of 2 are excellent, and
wells that have a standard deviation of 0 are poor.
Lithologically, the two wells compare reasonably well.

WELL B (D10 31)
Figure 14
Comparison of standard well logs with the factor score plots for S1A-5R (well A),
and DIO-31 (well B).

Well "A" has a minimum gamma ray value of 31.3 API units,
while well B reaches 45.8 API units. The factor score
plots that represent lithology have absolute values of
1.78 and 1.37 respectively. Although these values are
slightly different, they are similar enough to suggest
that porosity may be controlled by factors other than
lithology. Given the general similarity seen in both the
standard and factor lithology values, the difference in
porosity values may be explained by secondary development
from fracturing.
Water saturation calculations for these wells
show that well "A reaches 28% while well "B" reaches 94%
in the D1 sand and remains at 100% in the D2 sand
(appendix 2 and 4).
A brief visual inspection or log analysis would
enable a geologist to make a completion decision on
either of these wells without the use of factor analysis.
However, other wells are less obvious in their
comparison. For example when well "A" is compared with
well "C", they appear to be quite similar (figure 15).
The porosity logs compare favorably with well "A"
exhibiting 10 feet of 10% porosity and well "C"
exhibiting 8 feet of 10% porosity. Although the maximum
values for "A" are 16% and the maximum values for "C" are
14%, the overall porosity zones in the D2 sand seem to be
very similar. The actual initial production rates from

WELL C (S4-5R)
-10 +10
Comparison of standard well logs with the factor score plots for S1A-5R
(well A), and S4-5R (well C).
Figure 15:

these wells was 222 BOPD and 278 MCFPD from well "A", and
3 BOPD and 3 MCFPD from well "B". While the standard log
porosity values are very similar, the factor log porosity
values are not. The maximum absolute values for the
porosity factor score plots are 1.65 and .82 respectively
for these wells (figure 15). In this example the factor
logs for porosity are more representative of the actual
observed production rates than the standard porosity
Lithologically there is a difference between the
D2 sand in the two wells that may help account for the
differences in production rates. Well "A" has a gamma ray
minimum of 31.3 API units while well "C" has a minimum of
58 API units. This difference is also reflected in the
lithology factor score plots for the wells. Well "A"
achieves a maximum absolute value of 1.78, whereas well
"C" reaches only 1.04. The difference in lithological
values indicates that the D2 sand in well "A" is probably
a "cleaner", less shaley sandstone than in well "C".
It would be expected that the porosity development for
well "A" is superior to well "C" and factor analysis
confirms this relationship with the factor porosity logs
whereas the standard porosity logs do not.
Sw calculations for the two wells show that well
"A" reaches a saturation of 28%, and well "C" reaches a
saturation of 42% (appendix 2). Although in this case

the difference between Sw values in the two wells is
certainly apparent, and suggests that well "A" would be
superior to well "C", several wells in the field were
economically completed with Sw's of 42% and higher. In
this example the use of factor analysis could have
prevented a subeconomic completion by examining the
factor porosity logs. Sw calculations are not always
reliable indicators of a well's productive potential at
Wildhorse field. The fine grain sands have a high clay
content which can contain large amounts of bound water
within its clay lattice structure. This interstitial
water can give erroneous Sw values. For this reason, Sw
calculations were probably not used to make completion
decisions at Wildhorse because several wells were
completed that calculated over 70% water saturation.
Under the circumstances seen at Wildhorse, factor
analysis may be one of the only ways to evaluate a well's
potential before completing it.
Many examples of unreliable Sw calculations can
be found in appendix 2. Along with the digitized
standard well log data are the Sw calculations and the
initial production rates for each well. Well S2-5 had an
Sw of no better than 45% but was completed for 205 BOPD
and 308 MCFPD. Well S1-5R had an Sw of no better than
48% but was also completed for 200 BOPD and 200 MCFPD.
Well D2-6 had an Sw calculation of 58% but still was

economically completed for 148 BOPD and 175 MCFPD. WC2-7
reached an Sw value as low as 35% but was only completed
for 33 BOPD and 52 MCFPD.
Another excellent example of unreliable Sw
calculations is shown in the comparison in figure 16.
Well "A" and well "D" are very similar in physical
appearence however well "A" was completed for 222 BOPD
and 278 MCFPD, and well "B" was completed for 23 BOPD and
88 MCFPD. Porosity values for well "D" exceed 18%
compared with the 16% of well "A". Well "D" has a
thinner porosity zone in the D2 sand but exhibits higher
maximum porosity values. However this higher porosity is
not expressed in the factor score plots. Well "D" 1 s
maximum absolute value is 1.43 compared to well "A" 1 s
1.65 (figure 16). The difference seen between the
factor porosity logs and the standard porosity logs can
be attributed to the fact that the standard logs
represent variables which are interrelated and overlap
resulting in porosity logs that show the influence of
several variables. However the factor logs represent
uncorrelated end members with the overlap or data
redundancy removed.
Lithologically the wells are very similar with
minimum gamma ray values of 32 and 31 API units
respectively. However, the lithology factor score plots
suggest that in well "A" the D2 sand is "cleaner than in

sr n.r>
*310 SP HD
Figure 16: Comparison of standard well logs with the factor score plots for S1A-5R
(well A), and SD2-5H (well D).

well "D" with absolute values of 1.78 and 1.43
respectively. Here again the standard well logs do not
seem to be revealing any information about lithologic
differences that would allow us to discriminate between
the two wells. The factor logs express the differences
in porosity and lithology between these two wells so that
we may anticipate the differences in the actual observed
Sw calculations for both wells are very similar
with values of 28% for well "A" and 36% for well "B"
(appendix 2). Based on Sw calculations alone both of
these wells should have been completed. However the use
of factor analysis could have prevented the subeconomic
completion of well "D".
This study established a factor loading pattern
for most of the wells that allowed a meaninful
interpretation of the factors. This pattern and the
factor's relationship to the variables is considered
"normal" in the context of this study. However several
wells exhibit patterns which can be considered "abnormal"
or anomolous to the study. These anomolous patterns may
be important as indicators of diagenetic processes that
could be influencing the wells. Table 10 compares the
predominant factor pattern in the study to two wells
which exhibit anomolous factor patterns. In S1A-5R, the
meaning behind the four factors is clearly indicated by

Rotated Factor Matrix:
DEPTH .12272 .02780 .43451 .89087
ILD .82893 -.48205 -.24303 .05562
ILM .88986 -.38852 -.20535 .07318
SFL .86785 -.37906 -.26409 .03534
SP -.44538 .73360 .49336 -.01655
GR -.48510 .83707 -.11241 -.04202
DEN -.23529 .11835 .93278 .23359
FOR .23073 -.15355 -.91683 -.28106
CAL -.41207 .82105 .28328 .14835
Rotated Factor Matrix:
DEPTH .32279 .71895 .55377 -.00780
ILD .74605 .08563 .23718 .53246
ILM .93194 -.18430 -.05711 .13403
SFL .44292 -.10134 -.12184 .86761
SP -.78493 .44330 .25987 -.14761
GR -.92305 -.04346 -.07119 -34052
DEN -.20286 .95482 .18800 -.04237
POR .18601 -.95662 -.18713 .03610
CAL -.08404 .33916 .92460 -.05042
Rotated Factor Matrix:
DEPTH -.07194 -.45999 .87794 -.00733
ILD -.90408 .33291 .16209 .15424
ILM -.92715 .29659 .12037 .15702
SFL -.82552 .20187 -.08670 .49784
SP .95920 -.21227 -.14059 .03288
GR .95231 .15462 .08866 .18924
DEN .12934 -.97260 .17070 -.05804
POR -.13299 .97220 -.17603 .02788
CAL .86246 .17376 .42366 -.16986
Table 10: Comparison between normal factor pattern matrix (S1A-5R), and the anomolous patterns seen in D2-6, and EMD1-7.

the high loadings for resistivity, lithology, porosity,
and depth respectively. Well D2-6 overall, maintains the
same end members, however factors 2 and 3 have reversed
their order, factor 3 is not as clearly defined, and
factor 4 is loaded highly with the SFL variable instead
of depth. The differences seen in the factor structure
matrices is also reflected in the factor score plots.
Comparing the factor score plots for these two wells
(figure 17), it can be seen that the lithology factor is
inversed relative to the 'normal'' well. Factor analysis
is indicating that the controls on productivity in this
well may differ from the other wells. Well D2-6 is an
economic well that had an initial production rate of 148
BOPD, and 175 MCFPD. The key to its productivity may be
found by examining the factor structure matrix and the
factor score plots. In table 10 the porosity end member
is clearly defined on factor 2, but the lithology end
member on factor 3 is not as strongly indicated. This
suggests that porosity may not be controlled by lithology
alone. Fracturing or some other diagenetic process could
be responsible for the productivity seen in this well
rather than primary lithology controlled porosity.
Well EMD 1-7 has a similar situation. In this
case the lithology end member is defined by factor 1,
porosity by factor 2, depth or hole conditions on factor
3, and the resistivity end member is less clearly defined

Figure 17: Comparison of "normal" factor score plot and anomolous
factor score plots for wells S1A-5R, S2-6, and EMD1-7.

on factor 4 (table 10). Again, comparing the factor
score plots of this well to S1A-5R (figure 17), we can
see that although the end members load onto different
factors, the curves are very similar with the exception
of the porosity curve which appears to be inversed. This
well is also an economic producer that had an initial
production rate of 150 BOPD and 145 MCFGPD. Once again
factor analysis has identified a well which differs from
the others. This difference may be in the form of
diagenetic controls on porosity as opposed to porosity
being primary and lithologically controlled, or these
differences could be primary and represent slightly
different depositional facies or compositional
Areally the anomolous wells are clustered
together (figure 18), suggesting that some local
variations in the formation are responsible for the
anomolous factor analyses. Again, these variations could
be attributed to primary or secondary processes. A look
at core taken from D8-6 provides some clues as to what
these processes might be. Well D8-6 exhibits a small
amount of fracturing in the core taken through the D sand
interval (appendix 1). While this well is not an
economic producer (57 BOPD, 75 MCFPD), it does verify the
presence of fracturing and leaves open the possibility
that fracturing may be present in the other wells and

Figure 18: Distribution of wells that had anomolous factor
analyses at Wildhorse field.

play a role in productivity at Wildhorse. The precise
reason for the anomolous variations seen in the factor
analyses for these wells is beyond the scope of this
study. Additional data in the form of thin sections and
core would allow us to map facies, fracturing, or
compositional changes that may be accounting for the
differences seen in the anomolous wells. It is important
to note that regardless of the genetic characteristics
that make these wells different, factor analysis appears
sensitive enough to detect the variations seen in these
wells. Anomolous factor patterns are not always
indicative of economic production, but they could alert
an operator that a well might be located in a slightly
different fracture zone or depositional facies. Armed
with this information, the operator may wish to further
evaluate the well using sidewall cores, RFT, or other
methods that could help him reduce the risk of making a
subeconomic completion.
The relationship between the factor scores,
geology, and initial production rates is compelling.
While the factor scores are able to illustrate which sand
is making the most contribution to a well's productivity,
the distribution of the economic wells is somewhat
ambiguous in that it doesn't necessarily follow a
paleoenvironmental geometry. The economic wells fall
into 2 groups (figure 19). When comparing these groups

Figure 19: Distribution of economic wells at Wildhorse field.
Wells that also had production from the "Dl" sand
are indicated.

with figures 7, 8, 9, and 10, we can see that the D1 sand
has a definite influence on the productivity for wells
D15-31, S1-5N, S2-5, SD1-50, and Sl-5. These wells are
located in the thicker D1 porosity zones and the thicker
intervals of the D1 isopach. However not all of the
wells located in the thicker intervals are economically
productive. This is also true for wells completed in
only the D2 sand. Some wells that appear to be edge
wells are economically productive, while others located
in the thickest isopach intervals are subeconomic. The
most striking example of this is in well SD1-8N. This
well exhibits 8 feet of porosity (figure 10) in 14 feet
of net D2 sand (figure 8), but it was completed for 24
BOPD and 1197 MCFPD which is subeconomic. While we could
normally expect better development of porosity and
permeability in the thicker sand intervals, the maps in
figures 7-10 show that this is not always true at
Wildhorse. This suggests that primary depositional
processes are not the most important component of
reservoir development here. Factor analysis also points
out that simple thickness is not all that's important to
productivity at Wildhorse. Using the fracturing
identified in the core taken from D8-6 (appendix 1), in
conjunction with the anomolous factor analyses, it is
postualated that secondary processes such as fracturing

are controlling productivity at Wildhorse.
It is difficult to quantify the relationship
between the factor scores and the observed production.
The interaction between porosity and lithology is
extremely important but adds another dimension to further
complicate interpretation. By taking dimension reduction
one step further, a more clear relationship between the
factor scores and production can be seen. Summation of
the porosity and lithology factor score values provides a
way to quantify the effects of these two properties.
Although this summation is not the result of direct
permeability measurement, porosity and lithology are
certainly contributing factors to permeability, and their
summation may represent a kind of emperical or relative
permeability value. It should be remembered that the
factor score values are derived from standardized data
and that these values are expressed in units of standard
deviation. Therefore they do not represent actual
permeability values. When these numbers are compared
with the actual observed production, there is rather good
correlation between higher combined values, and higher
production rates (figure 20). Figures such as this allow
the operator to graphically see how his well relates to
the other wells in the field and would allow him to make
more informed completion decision. Factor analysis can
be useful in helping an operator assess a well's

Initial Production Rates va. Combined Factor Scores
015 31
Pt 32N
*C*-r ..S02-5M
CttlS-S H M
eAPAt.SI IaAQI.I a0lQ>l
Figure 20: Plot of combined facto*- scores for lithology and porosity versus initial production
rates. 130 BOPD is the economic threshold for this study.

productive potential by providing factor values which can
be correlated with actual observed production in the
field. This may be especially significant in a field
like Wildhorse where the D sand is generally tight making
it difficult to evaluate the potential of the formation
prior to completing the well. At Wildhorse most of the
the wells were not drill stem tested but were simply
completed and then acidized and fractured. The use of
factor analysis could have prevented several subeconomic
completions. As disussed earlier factor analysis
identifies the wells that have the prerequisite reservoir
development for economic productivity. Factor analysis
reveals that the original quality of the formation is
probably the most important criteria for determining the
productive potential of a well and that subsequent
reservoir stimulation can only enhance preexisting
porosity and permeability, it cannot create it.
When an economic analysis is done for the wells
at Wildhorse, a minimum initial production rate can be
established. That is, any well that has an initial
production rate lower than this minimum rate has a
limited chance of being economically successful. (Based
on the parameters of the analysis). This minimum, or
threshold, IP can then be related to the combined
lithology porosity factor scores to determine what
original formation conditions are required to acheive

this IP. The economic analysis determined that 130 BO/day
would be required for a completion to be economical
(Appendix 5 illustrates how this number was derived).
Figure 20 compares the combined porosity lithology
factor scores with initial production rates at Wildhorse
field. It shows that a combined absolute factor score
value of 3 or greater is necessary for a well to be
economic. The region between 2 and 3 may account for
some marginal wells and anything below 2 probably does
not have reservoir quality sufficient to support an
economic completion. Comparison of these values to
actual observed production allows us to index or
calibrate these values with something tangible. The
combination of the the porosity and lithology factor
scores provides producibility index that can be used to
assess a well's economic potential quickly and
Using the same scheme a comparison was made
between the factor scores for the resistivity factor and
initial production rates (figure 21). Similar
relationships were not apparent in this comparison
however this is not unexpected since the resistivity
responses for tight formations and productive formations
are so similar.
At Wildhorse field factor analysis may be one of
the only means in which to evaluate the productive

Initial Production Rato BOPD
Initial Production Rates vs. Resistivity Factor Score Values
rMDI-r etOI-90
a e 01
oio*ii mt si
101 9H
Resistivity Factor Score Values
Figure 21: Plot of resistivity factor scores versus initial production rates,
economic threshold for this study.
130 BOPD is the

potential of a well. Using this technique an operator
would be able to identify which wells should be
completed, plugged and abandoned, or undergo more
extensive evaluation. Wells requiring additional
evaluation could be sidewall cored or RFT'ed to provide
direct measurments of the well's productivity.
1. Factor analysis reduces the overlap or
redundancy contained in the original variables of a
standard well log suite. It identifies the factors which
are correlative between the original variables and
creates new independent variables which are uncorrelative
with each other, and are considered end members. Four
factors: Resistivity, Porosity, Lithology, and Hole
Conditions, account for over 90% of the variance seen in
the data.
2. Because of the tight nature of the D Sandstone
at Wildhorse field, the traditional methods of formation
evaluation such as drill stem tests and log analysis are
often inadequate in determining the productive potential
of a well. Factor analysis has the ability to identify
subtle relationships which play a role in a well's
productivity. In this study factor analysis was able to
determine that a localized diagenetic process such as
fracturing may control the development of porosity and

permeability and ultimately the economic productivity of
the wells in the field.
3. When factor scores are plotted against depth,
a factor score "log" is produced that enables the user to
compare the end members with the standard well logs.
These new factor logs can then be used to make formation
evaluations and determine the relative contributions of
porosity and lithology to the reservoir quality. A high
contribution from porosity relative to lithology may be
an indication of porosity development from secondary
processes such as fracturing.
4. The combined factor score values of porosity
and lithology may represent an empirical permeability
value. This value has a high correlation with initial
production rates and can be used as a productivity index
to predict a well's productive potential. This
productivity index provides a criteria for making
economic decisions in this field.
Factor analysis has been shown to be a useful
tool for identifying productive zones and approximating
the magnitude of their productivity at Wildhorse field.
It also is useful in identifying which zone or sand
stringer is making the most significant contribution to
the well's productivity. Factor analysis also seems to

be able to discriminate subtle facies changes or
differences in diagenetic effects on the formation.
Additional work needs to be done to determine the precise
nature of these differences. In this study it was able
to descriminate between lithologically derived porosity
and fractured or diagenetically derived porosity. This
type of information is useful to both exploration and
development geologists, or to the reservoir engineer.
The geologists may use this information to aid in their
decision as to whether they should attempt a completion.
The engineer can use this information to help plan field
development or plan secondary and tertiary recovery
strategies. This information is available without
incurring the expense of collecting additional data.
Although factor analysis is not necessarily a new
form of data analysis, it is not commonly employed in
geology and petroleum exploration. Advancing technology
gives us tools that provide better resolution and copious
quantities of data. Factor analysis provides a means to
reduce the dimensionality of this data and recognize the
patterns and subtle differences that it may contain.

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Diversified Operating Company
Nickerson 8-6
Sandstone, light-medium gray, fine to very fine grained,
moderatly sorted. Horizontal bedding disturbed by
bioturbation. Scattered carbonaceous material increasing
with depth. Abundant woody carbonaceous material at top
of washout zone. Several large Ophiomorpha burrows
scattered throughout interval. Interval also contains
numerous dark gray silty interbeds. Entire interval
contains large vertical fracture.
Lost core. Probably carbonaceous zone.
Siltstone, dark gray to black, highly mottled bedding
with scattered pyrite filled burrows. Some burrows
are clay filled, (clay clasts?) Grain size increasing
with depth becoming more sandy. Scattered fracturing
throughout, mostly horizontal to subhorizontal.
Silty sandstone, medium gray, fine to very fine grained,
slight grain size increase with depth. Bedding is
highly mottled due to burrowing and abundant root casts.
Some burrows in this zone display meniscate laminae
(Rhizocorallium?) Bedding disruption could also be
due to slumping.




Photograph of core from well D8-6. Depth interval 6307 6379.2.