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in
map view, and a thickness of 100 ft. Since the dip of
the reservoir is zero, the TVT equals the TST (100 ft). If
the same reservoir rotates to an angle of 45 deg, as shown
in the upper portion of the figure, the length of the reservoir
shortens to 354 ft in map view. The cross-sectional
area of the reservoir has not changed, as the TST remains
100 ft. thick. In order to map the reservoir and maintain
a cross-sectional area of 50,000 sq ft, the thickness used
must exceed 100 ft. The TVT of the dipping reservoir
measures 141.25 ft, and so 141.25 ft x 354 ft = 50,002.5
sq ft. From this example, you can see that as a reservoir
of fixed length rotates from the horizontal, the projected
areal extent of the reservoir decreases in map view. Therefore,
in order to maintain the same cross-sectional area or volume
of the reservoir, the shortened length must be multiplied
by the TVT.
For
directionally drilled wells the situation becomes more complex. The
log thickness of a given stratigraphic interval can be thicker,
equal to, or thinner than that seen in a vertical well drilled
through the same stratigraphic section. A correction factor
must be applied to the MLT in most deviated wells to convert
the borehole thickness to TVT. The correction factor consists
of two parts: (1) the correction for wellbore deviation angle
within the interval of interest, and (2) the correction for bed
dip. In the textbook "Applied Subsurface Mapping with Structural
Methods"2nd edition (2002) several sections of the
text address this important subject.
Equation
1 shown here is a 3D equation and is considered the preferred
correction factor equation because this one equation can be used
to calculate the thickness correction factor regardless of the
direction of wellbore deviation, and the true dip of the beds
is used instead of the apparent dip required in two-dimensional
equations. We refer to this equation as Setchell's equation.
TVT
= MLT [cos Ψ -
(sin Ψ cos α tan Φ)] Equation
1
|
TVT
= |
True
Vertical Thickness
|
MLT
= |
Measured
Log Thickness
|
Ψ= |
Wellbore
deviation angle
|
Φ= |
True
bed dip
|
α= |
Δ Azimuth
(acute angle between the wellbore azimuth and
the azimuth
of true bed dip)
|
If
the beds are horizontal, then Setchell?s equation reduces to
the simple correction factor Equation 2 which is equivalent
to correcting for wellbore deviation only, yielding a True
Vertical Depth (TVD) thickness.
TVT
= MLT (cos Ψ ) Equation
2
Let's
now consider two directionally drilled wells shown in Fig.
2 from Tearpock and Bischke 2002). Look first at the well
drilled to the east in a down-dip direction (Fig. 2a). Consider
the interval to be a reservoir filled with gas or oil. The
well drilled in a down-dip direction has a MLT of 476 ft. which
exceeds the TVT. We first apply the correction factor
for wellbore deviation only, using Eq.(2). The MLT reduces
to 357 ft, shown in the figure as the TVD thickness, or the true
vertical depth thickness (TVDT). This thickness
also exceeds the TVT of the interval, because the correction
for only wellbore deviation does not take into account the
dip of the beds. The TVDT is that thickness of an interval
obtained from a true vertical depth (TVD) log, and for dipping
beds, TVDT does not equal TVT. With the final
correction for bed dip, the MLT converts to a TVT of 150 ft,
shown in Fig. 2a at the penetration point of the wellbore in
the top of the reservoir. Note that the TST is 123 ft.
The
TST can be calculated by multiplying the TVT by the cosine
of the angle of bed dip (35 deg in this example). The
TST cannot be used for volumetric calculations for dipping
beds. It will underestimate the volumetric reserves.
The
well in Fig. 2b deviates up-dip, to the west. The MLT
for this well of 127 ft is now less than the TVT. Applying
a correction factor for the well deviation angle alone, which
is equivalent to the correction to TVDT, provides an even smaller
thickness of 82 ft. When Eq.(1), the correction factor
equation for both bed dip and wellbore deviation, is applied,
the MLT converts to a TVT of 150 ft. This is the thickness
needed for net sand and net pay mapping, as well as volumetric
calculations.
Various
computer programs can be used to create TVD, TVT, and TST logs
from measured depth (MD) logs for use in mapping. The
deviated well log data, the directional survey for the well,
and bed dip information are necessary as input data. The
log data are obtained from a logging company tapes or digitized
from the actual log. The directional survey data can be
furnished by the directional company that worked the well. The
bed dip information can be obtained either from completed structure
maps or from a dipmeter log. The output logs can be in
standard presentation or at any scale desired.
We
caution here that TVD logs, which are usually a standard part
of the log suite for a deviated well, are too often used for
purposes that are not applicable. A widespread misunderstanding exists,
that a TVD log prepared from a MD log can be used to (1) correlate
with other well logs, (2) determine the vertical separation
for a fault, and (3) count net reservoir quality rock (e.g.
sand) and prepare net pay isochore maps. Remember,
a TVD log is generated by correcting for wellbore deviation
only, and not bed dip. In areas of flat-lying
beds, a TVD log is equivalent to a TVT log because the only
correction factor is for wellbore deviation (Fig. 3).
However,
if the beds are dipping (particularly over 10 deg), a TVD
log typically does not represent the log thickness required
to aid in correlation work, to determine the vertical separation
for a fault, to count net sand or net pay or to construct
net pay isochore maps. For these purposes, we must correct
a deviated well log so that the log thickness represents
the TVT. Look again at Fig. 2and observe the significant
difference in thickness between the TVD and the TVT values. To
determine net sand and net pay from a deviated well log,
we must use a TVT log or its equivalent. By
the equivalent of the TVT log, we mean calculating and using
correction factors for specific intervals of interest, if
a TVT log is unavailable, which is commonly the case. Therefore,
for each interval on the deviated well log requiring the
conversion of MLT to TVT, determine the appropriate correction
factors and apply them to the MLTs for the intervals of interest.
The impact of
Correction Factors
Over
the past 25 years we have seen significant errors in
reserve calculations as a result of someone using the
wrong thickness value to determine the reservoir quality
sand or to prepare net pay maps for volumetric calculations.
Errors of 20 to 30 percent are not uncommon, but on occasion
errors of up to 700 percent have been documented.
In
one field evaluation, the proved producing and proved reserves
behind pipe were reduced from an overestimated value to 150MM
barrels of oil to 35MM barrels of oil. Most of the overestimation
of oil was the result of using the wrong log thickness to
count net sand, net pay and determine volumetrics. If
we consider an average price for oil of $25 per barrel, this
reduction in reserves results in a future revenue write down
of about $2.7 billion.
From
evaluating fields to buy in a data room to determining whether
or not to participate in a prospect; from calculating the
potential reserves in a new discovery, to conducting a study
on a mature field to identify upside potential the bottom
line is "how much oil or gas can I produce and what is my
return on investment". If the wrong numbers are used
for the reserve calculations because of an error in the pay
thicknesses used for volumetrics, your economic analysis
is worthless. |
