Geology Reference
In-Depth Information
To find the coordinates of an intermediate point, P, between P
1
and P
2
, let
r
be the
distance along the well from the upper control point to the point P. In a right-handed
xyz
coordinate system (Fig. 2.7) with
z
positive upward, positive
x
= east and positive
y
= north, the point P (
x
,
y
,
z
) between P
1
(
x
1
,
y
1
,
z
1
) and P
2
(
x
2
,
y
2
,
z
2
) at a location given
by the ratio
r
/
s
(where
r
+
s
=
L
), has the coordinates (Eves 1984)
x
=(
rx
2
+
sx
1
)/(
r
+
s
) ,
(2.3a)
y
=(
ry
2
+
sy
1
)/(
r
+
s
) ,
(2.3b)
z
=(
rz
2
+
sz
1
)/(
r
+
s
) .
(2.3c)
L
is found from the Pythagorean theorem:
L
=[(
x
2
-
x
1
)
2
+(
y
2
-
y
1
)
2
+(
z
2
-
z
1
)
2
]
1/2
.
(2.4)
Substitute
s
=
L
-
r
into Eq. 2.3 to obtain
x
=(
rx
2
-
rx
1
+
Lx
1
)/
L
,
(2.5a)
y
=(
ry
2
-
ry
1
+
Ly
1
)/
L
,
(2.5b)
z
=(
rz
2
-
rz
1
+
Lz
1
)/
L
.
(2.5c)
If the well is straight between the upper and lower points,
L
will be equal to the log
distance. If
L
is not equal to the log distance, then the well is not straight and the calcu-
lated value of
L
will give the more internally consistent answer. More precise location of
the point will require definition of the curvature of the well between the control points.
It may be required to locate a contact below the last control point given by the de-
viation survey (Fig. 2.7b). A simple linear extrapolation can be used, based on the
assumption that the well continues in a straight line below the last control point with the
same orientation it had between the last two control points. The subscripts “1” and “2”
again represent the upper and lower control points. Let
∆
x
=(
x
2
-
x
1
),
∆
y
=(
y
2
-
y
1
),
and
∆
z
=(
z
2
-
z
1
), then
x
=
x
2
+
r
x
/
L
,
(2.6a)
∆
y
=
y
2
+
r
∆
y
/
L
,
(2.6b)
z
=
z
2
+
r
∆
z
/
L
,
(2.6c)
where
x
,
y
, and
z
= the coordinates of a point at a well-log distance
r
below the last
control point, P
2
, having the coordinates (
x
2
,
y
2
,
z
2
), and
L
(Eq. 2.4) = the straight-line
distance between the last two control points.
As an example of the location of points in a deviated well, consider the following
information from a well (KB at 660 ft) on which the formation boundary of interest is at
