Application of true vertical depth, true statigraphic thickness and true vertical thickness log diplays


Bateman, R.M.; Hepp, V.R.

Transactions of the SPWLA Annual Logging Symposium 23-26 June 1981, Mexico City, Mexico: 1-15

1981


In matters of well-to-well correlation and reservoir volume calculation, logs are necessary instruments. In the simple case where the wells are vertical and the bedding is horizontal, correlations can be made directly between logs of neighboring wells, and reservoir volume is calculated by multiplying reservoir thickness, directly derived from the logs, by reservoir area, delimited by other means.

SPWLA
TWENTY-SECOND
ANNUAL
LOGGING
SYMPOSIUM,
JUNE
23-26,
1981
Application
of
True
Vertical
Depth,
True
Stratigraphic
Thickness
and
True
Vertical
Thickness
Log
Diplays
by
R.
M.
Bateman
(*)
and
V.
R.
Hepp
(**)
Introduction
In
matters
of
well-to-well
correlation
and
reservoir
volume
calculation,
logs
are
necessary
instruments.
In
the
simple
case
where
the
wells
are
vertical
and
the
bedding
is
horizontal,
correlations
can
be
made
directly
between
logs
of
neighboring
wells,
and
reservoir
volume
is
calculated
by
multiplying
reservoir
thickness,
directly
derived
from
the
logs,
by
reservoir
area,
delimited
by
other
means.
However,
this
simple
case
is
exceptional.
For
one
thing,
most
reservoirs
exist
as
the
result
of
some
structural
event
or
accident,
implying
some
formation
dip
at
least
at
the
reservoir
periphery.
For
another,
most
wells
deviate
to
some
extent
from
vertical,
intentionally
or
not.
As
long
as
dips
and
deviations
do
not
exceed
a
few
degrees,
the
simple
vertical-horizontal
case
is
approximated
closely
enough
not
to
need
corrections.
But
when
deviations
and
dips
exceed
about
ten
degrees,
corrections
are
needed
because
apparent
formation
thicknesses
measured
on
logs
are
greater
than
true
stratigraphic
thicknesses
by
different
amounts
in
different
wells.
This
adds
to
the
difficulty
of
well-to-well
log
correlation.
Also,
if
wells
are
deviated
from
vertical,
and
if
formations
have
substantial
dip,
apparent
thicknesses
differ
from
the
vertical
thicknesses
needed
for
reservoir
volume
calculation,
and
must
be
corrected.
To
achieve
these
corrections
in
a
convenient
manner,
modern
data
processing
affords
three
different
computed
log
products:
the
TVD,
TST
and
TVT
plots.
Their
principle,
their
meaning
and
their
interpretation
are
the
object
of
this
paper.
It
will
be
seen
that
proper
interpretation
requires
considerable
caution
and
may
be
quite
difficult.
(*)
Petrophysical
Data
Consultants,
Houston,
Texas.
(**)
Amoco
International
Oil
Co.,
Houston,
Texas.
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1
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SPWLA
TWENTY-SECOND
ANNUAL
LOGGING
SYMPOSIUM,
JUNE
23-26,
1981
Common
Principles
of
TVD,
TST
and
TVT
Plots
Figures
1,
2,
3
and
4
illustrate
the
principles
of
thickness
transformations.
Formation
parameters
recorded
by
logging
tools
are
reproduced
without
alteration,
but
their
depths
are
altered
to
suit
respective
purposes.
Depths
should
be
thought
of
as
summations
of
overlying
formation
thicknesses.
Two
methods
exist
for
computation
of
altered
depths:
-
Common
surface
point,
assuming
a
hole
drilled
from
the
same
surface
point
or
formation
top
with
a
different
course.
Common
subsurface
point,
assuming
a
hole
drilled
either
vertically,
or
normal
to
the
bed
dip,
from
some
point
in
the
actual
well
course,
such
as
a
formation
top,
or
a
point
of
formation
dip
change.
Depths
may
be
reset
arbitrarily
at
the
common
point.
In
this
approach
it
is
set
to
zero,
thus
representing
only
thickness
as
counted
down
from
the
common
point.
TVD
-
True
Vertical
Depth
Plot
(Figures
1
and
5)
This
plot
ignores
formation
dip,
and
corrects
for
well
deviation
only.
It
thus
represents
formations
as
they
would
look
in
a
vertically
drilled
well,
provided
the
formations
had
zero
dip.
It
is
useful
in
areas
of
directional
drilling
where
dip
is
low,
for
well-to-well
correlations
and
for
reservoir
volume
calculations.
It
is
usually
run
only
in
the
common
surface
point
mode.
TST
-
True
Stratigraphic
Thickness
Plot
(Figures
2
and
6)
This
plot
accounts
for
formation
dip,
and
requires
knowledge
of
true
well
course,
whether
vertical
or
not.
It
displays
formations
as
though
the
well
had
been
drilled
perpendicular
to
them.
If
a
change
of
dip
occurs,
an
equal
and
opposite
change
of
deviation
is
assumed
(Figure
6).
-
2
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SPWLA
TWENTY-SECOND
ANNUAL
LOGGING
SYMPOSIUM,
JUNE
23-26,
1981
If
only
one
dip
is
present,
the
plot
represents
the
logs
that
would
have
been
obtained
if
the
well
had
been
drilled
at
the
same
location
perpendicular
to
that
dip.
If
more
than
one
dip
is
present,
the
interpretation
becomes
more
complicated.
At
each
dip
change,
some
stratigraphic
column
must
either
disappear,
or
thin,
or
thicken,
or
even
repeat
itself.
On
Figure
6,
using
the
common
surface
point
method,
point
A
at
the
bottom
of
the
upper
formation
at
8300'
measured
depth
transforms
to
point
A'
at
3000'
on
the
TST
plot,
while
point
C
at
the
top
of
the
lower
formation
at
the
same
measured
depth
transforms
to
C'
at
the
same
TST
depth.
Yet
all
the
thickness
Cie"
of
the
lower
formation,
not
having
been
logged,
is
not
represented.
The
proper
representation
in
this
case
leaves
the
section
C'C"
blank,
and
plots
C
to
bottom
hole
independently.
The
TST
always
shows
formations
under
their
minimum
thicknesses.
TVT
-
True
Vertical
Thickness
Plot
(Figures
3
and
7)
This
plot
is
closely
related
to
the
TST,
and
as
such
accounts
for
both
well
deviation
and
formation
dip.
It
shows
formation
thickness
as
though
the
well
had
been
drilled
vertically
through
the
dipping
beds.
Evidently,
a
TVT
in
a
vertical
hole
would
be
identical
to
the
original
log.
The
TVT
is
meant
to
be
used
for
reservoir
volume
calculations
from
deviated
hole
logs.
Reductions
in
Special
Cases
If
the
well
is
vertical
and
the
formations
are
horizontal,
all
three
transformed
logs
would
be
identical
to
the
original
log,
and
the
processing
would
be
a
waste
of
computer
time.
If
the
well
is
deviated
and
the
formations
are
horizontal,
the
TST
and
the
TVT
are
identical
to
the
TVD,
and
running
the
latter
is
sufficient.
-
3
-
SPWLA
TWENTY-SECOND
ANNUAL
LOGGING
SYMPOSIUM,
JUNE
23-26,
1981
If
the
well
is
vertical
and
the
formations
dip,
the
TVD
and
TVT
plots
would
be
wasted
computer
time,
but
the
TST
may
be
useful
in
well-to-well
correlations.
If
the
well
is
drilled
perpendicular
to
the
formation
dip,
(as
it
often
tends
to
be
in
hard
rocks
in
particular),
the
TST
would
be
a
waste
of
computer
time,
but
the
TVT
is
needed
for
reservoir
calculations,
and
the
TVD
may
be
of
use
if
deviation
is
pronounced.
Selection
of
Dip
Zones
The
TST/TVT
approach
is
based
on
the
concept
of
dip
zones.
A
dipmeter
survey
is
interpreted
as
a
succession
of
"dip
blocks".
Each
such
block
is
fairly
thick,
of
the
order
of
hundreds
of
feet,
and
within
each
block
the
dip
is
regarded
as
constant.The
procedure
consists
of
examining
a
high
density
dipmeter
arrow
plot
in
conjunction
with
a
lithology
log,
and
deciding
on
the
broad
zones
where
dip
appears
to
be
constant.
This
involves
quite
a
bit
of
visual
filtering,
to
eliminate
variations
which
are
insignificant
in
structural
terms,
retaining
only
a
central
tendency
or
"trend".
Once
a
trend
has
been
identified
it
is
extended
upwards
and
downwards
to
points
where
it
evidently
becomes
invalid
and
is
replaced
by
another
trend.
Thus
dip
zone
boundaries
are
defined
where
dip
is
assumed
to
change
abruptly.
Evidently
this
procedure
remains
open
to
many
sorts
of
questioning
(why
should
the
trend
represent
formation
dip
?
What
if
no
trend
can
be
distinguished
?
What
if
the
trend
is
a
smooth
variation
?
etc...),
but
it
is
justified
by
the
fact
that
it
is
practical
and
that
it
works.
Methods
of
carrying
out
this
procedure
automatically
may
be
devised
and
become
available
in
the
future.
Algorithms
The
algorithms
used
for
computing
the
TVD,
TST
and
TVT
have
been
well
covered
in
the
literature.
Examples
in
this
paper
have
used
the
True
Radius
of
Curvature
method
for
computing
the
directional
surveys.
Any
implementation
of
these
algorithms
for
computer
applications
shoud
be
approachedwith
caution.
Many
programming
languages
differ
in
their
treatment
of
trigonometric
functions
for
angles
exceeding
90
degrees.
Another
area
requiring
care
is
in
the
matter
of
-
4
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SPWLA
TWENTY-SECOND
ANNUAL
LOGGING
SYMPOSIUM,
JUNE
23-26,
1981
precision.
When
depth
data
is
processed,
a
repetitive
accumulation
of
depth
increments
is
made.
As
many
as
10
4
or
more
additions
must
be
made
in
a
normal
well.
Thus
the
precision
of
each
increment
must
be
to
at
least
1
part
in
10
6
or
better.
Depending
on
the
computer
used
(16
bit,
32
bit,
etc.)
the
programming
of
these
algorithms
should
demand
appropriate
precision.
Field
Example
Figure
8
shows
a
"plat"
of
the
well
courses
for
this
field
example
and
Figure
9
shows
a
Northwest-Southeast
cross-section
through
the
platform
position.
Note
the
1:2
reduction
in
depths
in
relation
to
horizontal
distance.
Dips
are
thus
shown
at
about
half
their
actual
values.
Well
courses
are
traced
as
projected
on
the
plane
of
this
cross-section.
For
Wells
1,
2
and
5,
the
projection
entails
little
distortion.
Wells
3
and
4
are
further
out
from
the
plane
of
the
section.
On
Figure
9,
formation
tops
are
at
their
originally
interpreted
depths.
It
is
clear
that
the
structure
is
complex:
the
tops
of
some
formations
appear
at
widely
different
depths
in
the
five
wells
represented
,
if
they
appear
at
all.
For
instance,
Formation
12-0
appears
in
Well
#1
and
in
Well
#4,
but
is
not
seen
in
the
other
three
-moreover,
it
is
found
at
a
TVD
of
3564
feet
in
Well#4
and
at
4939
feet
in
Well
#1.
Well
#4
shows
the
most
complete
stratigraphic
sequence,
apparently
uninterrupted
by
faulting.
Major
fault
F
is
responsible
for
a
major
stratigraphic
gap
between
formation
tops
10-0
and
12-2
in
Well
#2,
and
between
formation
tops
12-0
and
14-0
in
Well
#1.
Other
gaps
exist
and
may
be
attributed
to
lesser
faults.
Figures
10
and
11
compare
the
original
logs
of
Wells
2,
4
&
5
with
their
TST
counterparts,
covering
formations
12-2
through
13-1.
Logs
shown
are
a
Gamma
Ray
and
a
Dual
Laterolog-Micro
Spherically
Focussed
Log.
On
the
TST
plots,
measured
depths
are
shown
in
small
figures,
while
bold
figures
show
true
stratigraphic
thickness
as
measured
downward
from
the
latest
dip
zone
top
boundary.
Thus,
in
Well
#4,
dip
is
constant
throughout
at
13
degrees
to
East,
and
thickness
accumulates
uninterrupted
through
the
section.
But
in
Wells
2
&
5,
two
interruptions
of
the
dip
trend
occur,
as
shown
in
Table
A.
-
5
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SPWLA
TWENTY-SECOND
ANNUAL
LOGGING
SYMPOSIUM,
JUNE
23-26,
1981
Table
A
Well
#
2
Well
#
4
Well
#
5
Measured
Measured
Measured
Top
Depth
Dip
Azm
Top
Depth
Dip
Azm
Top
Depth
Dip
Azm
4085
10
040
4130
13
090
4000
13
060
4340
15
030
4460
22
240
4625
8
030
4625
10
045
5688
12
070
5800
13
200
At
those
interruptions,
TST
is
reset
to
zero,
and
the
downward
count
is
started
again.
Some
missing
thickness
must
be
expected
at
those
points,
according
to
the
foregoing
Figure
6.
This
is
confirmed
by
the
greater
TST
from
12-2
to
13-1
in
the
uninterrupted
Well
#4
than
in
Wells
2
and
5.
In
Well
#5
correlation
from
12-3
through
13-1
remains
in
doubt
and
some
faulting
is
clearly
present.
While
the
comparison
of
both
figures
may
not
exhibit
dramatic
differences
between
apparent
and
true
thicknesses,
the
TST
appears
much
more
convenient
to
use
in
correlation
from
well
to
well.
For
one
thing,
it
removes
a
doubt
in
the
mind
of
the
correlator,
which
is
of
great
benefit.
When
using
measured
depth
logs,
the
correlator
is
never
really
sure
whether
the
thicknesses
that
he
correlates
differ
because
of
faulting,
because
of
stratigraphic
variation
or
because
of
well
deviation-dip
interaction.
With
the
TST
the
latter
case
has
been
eliminated
and,
to
a
greater
extent,
he
can
be
sure.
For
another,
by
resetting
the
thickness
to
zero,
the
TST
highlights
the
points
of
dip
change
where
correlation
must
be
interrupted.
Finally,
it
is
somewhat
easier
to
figure
out
thicknesses
by
subtracting
thickness
figures
in
the
hundreds,
rather
than
measured,
or
even
true
vertical,
depth
figures
in
the
thousands
or
tens
of
thousands.
-
6
-
SPWLA
TWENTY-SECOND
ANNUAL
LOGGING
SYMPOSIUM,
JUNE
23-26,
1981
Conclusions
All
three
plots
perform
valuable
functions,
but
all
three
may
be
misleading
if
not
used
with
the
proper
caution,
in
particular
with
respect
to
absolute
depths.
1.
The
TVD
is
incorrect
in
both
formation
thicknesses
and
in
absolute
depths
if
formations
have
appreciable
dip.
2.
The
TST
is
always
correct
in
formation
thicknesses.
It
should
be
run
in
the
common
subsurface
point
mode.
If
changes
of
dips
are
present,
it
should
reset
the
subsurface
point
at
each
change
of
dip
and
make
independent
plots
through
each
dip
zone.
This
resetting
may
be
made
automatically
if
the
program
allows
it,
and
manually
otherwise.
3.
The
TVT
may
produce
apparent
thicknesses
greater
than
measured
thicknesses,
as
Figure
7
shows.
Such
thicknesses
may
be
fictitious,
when
beds
are
truncated
in
their
vertical
extension
by
unconformities
or
faults.
It
should
be
run
in
independent
sections
for
each
change
of
dip,
in
the
common
subsurface
point
mode,
as
for
the
TST.
Acknowledgements
The
authors
are
indebted
to
Amoco
International
Oil
Company
for
making
the
field
data
available
and
authorizing
its
publication.
-
7
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SPWLA
TWENTY-SECOND
ANNUAL
LOGGING
SYMPOSIUM,
JUNE
23-26,
1981
References
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Walstrom,
J.
E.,
Harvey,
R.
P.
and
Eddy,
H.
D.
:
"A
Comparison
of
Various
Directional
Survey
Methods
and
an
Approach
to
Model
Error
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J.
Pet.
Tech.,
Vol.
XXIV,
pp.
935-943,
August,
1972.
2.
Pennbaker,
P.
E.
:
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Net
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Determination
for
Isopach
Mapping
of
Hydrocarbon
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AAPG.
Bull;
Vol
56
No.
8,
pp.
1520-
1529,
August,
1972.
3.
Hepp,
V.
:
"
Vertical
Net
Sandstone
Determination
for
Isopach
Mapping
of
Hydrocarbon
Reservoirs"
-
Discussion
AAPG
Bulletin,
Vol.
57,
p.
1784
-1787,
1973.
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Holt,
0.
R.,
Schoonovers,
L.
G.
and
Wichmann,
P.
A.
:
"True
Vertical
Depth,
True
Vertical
Thickness,
and
True
Stratigraphic
Thickness
Logs",
SPWLA
Logg.
Symp.
Trans.,
1977.
Paper
Y.
5.
Bateman,
R.
M.,
and
Konen,
C.
E.:
"The
Log
Analyst
and
the
Programmable
Pocket
Calculator
-
Part
III
-
Dipmeter
Computation",
The
Log
Analyst,
Volume
XIX,
No.
1,
January
-
February,
1978.
6.
Bateman,
R.
M.,
and
Konen,
C.
E.:
"The
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Analyst
and
the
Programmable
Pocket
Calculator
-
Part
VI
-
Finding
True
Stratigraphic
Thickness
and
True
Vertical
Thickness
of
Dipping
Beds
Cut
by
Directional
Wells",
The
Log
Analyst,
Volume
XX,
No.
2,
March
-
April,
1979.
7.
Peveraro,
R.:
"Vertical
Depth
Correction
Methods
for
Deviation
Survey
and
Well
Log
Interpretation".
-
8
-
SPWLA
TWENTY-SECOND
ANNUAL
LOGGING
SYMPOSIUM,
JUNE
23-26,
1981
About
the
Authors
Vincent
Hepp
Richard
Bateman
Vincent
Rene
Hepp
is
an
Associate
Engineer
with
Amoco
International
Oil
Company
in
Houston,
Texas.
He
graduated
in
1952
from
the
French
National
School
of
Applied
Geology,
of
Nancy,
whith
a
degree
in
Geological
Engineering,
and
went
on
to
take
a
year
of
Graduate
Geophysics
at
the
Colorado
School
of
Mines,
on
a
U.S.
Government
Scholarship.
He
joined
Schlumberger
in
1953,
and
worked
as
a
Field
Engineer
in
Latin
America,
except
for
a
short
interruption
in
1959
when
he
was
transferred
to
Paris,
France.
Mr.
Hepp
has
worked
in
Venezuela,
Peru,
British
Honduras,
Brazil,
Argentina
and
Colombia
from
1972
until
1980
when
he
was
transferred
to
the
United
States
as
a
Senior
Research
Engineer
investigating
Dipmeter
Interpretation
at
the
Schlumberger
Doll
Research
in
Ridgefield,
Connecticult.
Mr.
Hepp
joined
Amoco
International
in
June,
1980.
He
is
a
member
of
SPWLA,
SPE,
AAPG,
and
IAMG.
Richard
M.
Bateman
is
President
of
Petrophysical
Data
Consultants,
Inc.,
of
Houston,
Texas.
He
received
his
B.A.
and
M.A.
degrees
in
Physics
fron
Oxford
University
in
1962
and
1967
respectively.
He
worked
with
Schlumberger
from
1964-
1975
in
North
and
South
America
both
in
field
and
research
assignments.
He
joined
Amoco
International
in
1975.
In
addition
to
digital
log
processing
responsibilities
with
Amoco,
Mr.
Bateman
travelled
extensively,
and
authored
many
technical
articles.
Mr
Bateman
founded
Petrophysical
Data
Consultants,
Inc.
in
1980.
He
is
member
of
SPWLA
and
SPE.
-
9
-
SPWLA
TWENTY-SECOND
ANNUAL
LOGGING
SYMPOSIUM,
JUNE
23-26,
1981
Single
Bed
Case
Devieted
Well
love
TVD
Hariaantal
Bed
,
77TVD.
Fig
ure
1:
Principle
of
TVD
8
Vertical
Well
Bare
MT
Dipping
Bed
8/
Figure
2:
Principle
of
TST
0
Deviated
Well
Bore
Dipping
Bed
TVT
Figure
3:
Principle
of
TVT
-
10
-
SPWLA
TWENTY-SECOND
ANNUAL
LOGGING
SYMPOSIUM,
JUNE
23-26,1981
PRINCIPLE
OF
TST
AND
TVT
PLOTS
VERT
8
=
Dip
Angle
8
=
Deviation
Angle
DIP
a
=
Dip-to-
Deviation
Angle
a
2
E
DEVIATION
Top
1
%
TST
TVT
it
0
2
Vertical
Measured
Thickness
=
E
MT
True
Stratigraphic
Thickness
TST
TST
=
E
MT.
cos
a.
I
I
True
Vertical
Thickness
TVT
TVT
=
TST/
cos
e
Figure
4
I
I
I
/
/
250
scP
°
00
C'
C
t.s
°°
TST
r
BH
TVD
0
TV
D
1
TVD
2
SPWLA
TWENTY-SECOND
ANNUAL
LOGGING
SYMPOSIUM,
JUNE
23-26,
1981
Multiple
Bed
Case
Figure
5:
Principle
of
TVD
Figure
6:
Principle
of
TST
TVD--
Figure
7:
Principle
of
TVT
TVD
1
--
TVD
2
--
,,--,TVT
I
-i
-
12
-
SPWLA
TWENTY-SECOND
ANNUAL
LOGGING
SYMPOSIUM,
JUNE
23-26,
1981
-1000
0
SOO
1000
1500
2000
2506'5c°
W-3
2000
1500
w-1
W-2
W-4
Field
Example
Multiple
Well
Platform
Figure
8:
Plat
of
Well
Courses
1000
500
500
W-5
-1000
1500
9
-2500
NW
SE
300
0
300
1000
100
3000
2:03
Il
....i.
IL1211
1
W
-
3
Ittl
;
1
11
W-1
IIII
1000
000C
02
1000
2000
SON
4000
5(03
6000
Figure
9:
NW-SE
Section
Showing
projected
well
courses,
formation
tops
and
apparent
dips
in
plane
of
section.
-
13
-
SPWLA
TWENTY-SECOND
ANNUAL
LOGGING
SYMPOSIUM,
JUNE
23-26,
1981
T
12-2
—4207
T
12-2
T
12-2
—4700
—4300
—4300
—4800
—4400
—4400
--4900
T
12-3
—4500
—4500
—5000
—4600
T
12-3
—41300
5100
--
—4100
-4700
—5200
T
13-1
T
13-1
—4800
—4860
-
—5200
—4900
—4900
—5400
T
13-2
—5000
Well
#4
—5000
5
—5500
Well
15
Well
12
—5109
—5100
T
13-1
Figure
ill
Original
Logs
—5600
_-5200
—von
-
14
-
SPWLA
TWENTY-SECOND
ANNUAL
LOGGING
SYMPOSIUM,
JUNE
23-26,
1981
I
I
DO
T
12-2
10°
@
040
°
200
-
0
15
°
@
030
°
T
12-2
77
T
12-2
13
°
@
060
°
400
13'
@
095
°
T
12-3
22
°
@
240
°
100
200
T
12-3
8
°
.
@
030'
T
13-1
L.
200
100
›•-
100
T
13-1
1100
Well
#
5
200
100
10°
@
045°
Well
#
2
300
Figure
11:
TST
Logs
Well
#
4
T
13-1