U.S. patent number 3,761,701 [Application Number 05/162,693] was granted by the patent office on 1973-09-25 for drilling cost indicator.
Invention is credited to Meta Luella Vincent, administratrix, Renic P. Vincent, deceased, Lawrence B. Wilder.
United States Patent |
3,761,701 |
Wilder , et al. |
September 25, 1973 |
DRILLING COST INDICATOR
Abstract
In drilling oil and gas wells, particularly by the rotary
drilling technique, it is necessary periodically to pull the drill
string from the well in order to replace a worn bit. The most
economic drilling is that in which the type of bit and the drill
rig operating conditions are matched to the characteristics of the
rock being drilled so that the cost of drilling, between bit
changes works out to the lowest possible value per foot. This
invention concerns a rig floor drilling cost indicator which is
basically an analog computer which graphically shows the fractional
wear on the bit, the average cost of drilling per foot, and the
incremental cost of drilling a foot of hole. These indications
permit the driller or the tool pusher to determine with
considerable accuracy both the arrangement for minimal cost
drilling, and when to change the bit. Most of the equations solved
by this computer are novel.
Inventors: |
Wilder; Lawrence B. (Tulsa,
OK), Vincent, deceased; Renic P. (LATE OF Tulsa, OK),
Vincent, administratrix; Meta Luella (Tulsa, OK) |
Family
ID: |
22586734 |
Appl.
No.: |
05/162,693 |
Filed: |
July 14, 1971 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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874562 |
Nov 6, 1969 |
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Current U.S.
Class: |
702/9; 73/152.45;
73/152.49; 705/400 |
Current CPC
Class: |
G06G
7/64 (20130101); E21B 44/00 (20130101); G06Q
30/0283 (20130101) |
Current International
Class: |
G06G
7/00 (20060101); E21B 44/00 (20060101); G06G
7/64 (20060101); G06g 007/00 (); G06g 007/48 () |
Field of
Search: |
;235/193,184,194,197
;346/30 ;73/151,151.5 ;175/39 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Alterman Engineered Bit Logs Cut Drilling Cost, World Oil, March
1969, p. 38/43..
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Primary Examiner: Gruber; Felix D.
Claims
We claim:
1. Apparatus for the analog computation of drilling variables
associated with a rotary drill rig comprising
means (a) for generating a voltage in a circuit directly
proportional to R.sup..alpha. , where R is the rate of rotation of
the rotary table of said rig and .alpha. is an exponent relating
drill bit life with rate of rotation of said bit,
means (b) for generating from said voltage a second voltage varying
directly as W.sup..beta. , where W is the weight on the drill bit
of said drill rig and .beta. is an exponent relating drill bit life
with weight on said bit,
means (c) for generating from said second voltage a third voltage
varying directly with the time t required to drill with said bit
and said drill rig a unit distance in the ground, and
an impedance (d) large compared with that of said means (c)
connected in a closed circuit in series with the output of said
means (c), in such a fashion that the total impedance in said
circuit is substantially that of said impedance (d), whereby the
current in said circuit varies as R.sup..alpha. W.sup..beta. t.
2. Apparatus for the analog computation of drilling variables
associated with a rotary drill rig comprising
means (a) for generating a voltage in a circuit directly
proportional to R.sup..alpha. , where R is the rate of rotation of
the rotary table of said rig and .alpha. is an exponent relating
drill bit life with rate of rotation of said bit,
means (b) for generating from said voltage a second voltage varying
directly as W.sup..beta. , where W is the weight on the drill bit
of said drill rig and .beta. is an exponent relating drill bit life
with weight on said bit,
means (c) for generating from said second voltage a third voltage
varying directly with the time t required to drill with said bit
and said drill rig a unit distance in the ground, and
a high impedance recording voltmeter, the impedance of which is
large compared to that measured across the output of means (c) in
the absence of said voltmeter, said recording voltmeter including a
strip record and means for printing an indication of the voltage
generated by means (c) on said strip record as drilling
progresses.
3. Means for computing and recording drilling variables associated
with a rotary drill rig comprising
means (a) for successively generating a voltage directly
proportional to R.sup..alpha. W.sup..beta. t where R is the rate of
rotation of the rotary table of said rig, .alpha. is an exponent
relating drill bit life with rate of rotation of said bit, W is the
weight on the drill bit of said drill rig, .beta. is an exponent
relating drill bit life with weight on said bit, and t is the time
to drill with said bit and said rig a uniform distance in the
ground, for a succession of such uniform distances,
means (b) responsive to said means (a) for generating a second
potential directly proportional to the successive sum of a
plurality of said voltages from means (a),
an adjustable impedance (c) large compared with that of said means
(b) connected in series with the output from said means (b),
and
a recording current meter connected in series with said impedance
(c) and the output of said means (b) to complete a series circuit,
said meter being adapted to record on a moving strip record
separately the value of the current in said circuit for each of a
plurality of times corresponding to each said successive sum.
4. Apparatus for the analog computation of drilling variables
associated with a rotary drill rig comprising
means (a) for generating a voltage in a circuit directly
proportional to R.sup..alpha. , where R is the rate of rotation of
the rotary table of said rig and .alpha. is an exponent relating
drill bit life with rate of rotation of said bit,
means (b) for generating from said voltage at the output from said
means (a) a second voltage varying directly as W.sup..beta. , where
W is the weight on the drill bit of said drill rig and .beta. is an
exponent relating drill bit life with weight on said bit,
means (c) connected to the output from means (b) for generating
from said second voltage a third voltage varying directly with the
time t required to drill with said rotary drill rig a unit distance
in the ground,
means (d) connected to the output of means (c) for generating from
said third voltage a fourth voltage varying directly as the sum of
the cost of said bit and the cost to place said bit at the bottom
of the well being drilled by said rig,
an adjustable impedance (e) in series with the output from said
means (d) and large compared with the output impedance of said
means (d),
a first amplifier (f) closing a circuit with the output of said
means (d) and said impedance (e), for producing an output voltage
directly proportional to the current in said circuit,
means (g) for producing a fifth voltage directly proportional to
the product of rig cost per unit time interval times the time
required to drill with said bit and said drill rig said unit
distance in the ground,
a second amplifier (h) of substantially the same gain as that of
said first amplifier (f), the input to which is connected to the
output of said means (g) and the output of which is connected
additively in series with that of said first amplifier (f), and
a recording voltmeter connected in series with the outputs of said
first amplifier (f) and said second amplifer (h), said voltmeter
being adapted to record on a moving strip record the sum of the
output voltage of said first amplifer (f) and said second amplifier
(h) at a plurality of times corresponding to the successive driling
of each of a plurality of integral multiples of said unit distance.
Description
BACKGROUND OF THE INVENTION
1. Field
This invention pertains to an analog computer responsive to
movement of the traveling block of a rotary drill rig. With this
single connection, it presents the driller in graphical form the
fraction of the bit life used up in any particular time. He is also
shown the incremental cost of drilling the last foot, and the total
average cost per foot of drilling the current bit.
The driller "sets into" the computer the average weight on the bit
and the rpm at which the rotary table is revolving, as well as the
anticipated bit life, the hourly cost of operating the drill rig,
the purchase cost (or rental cost) of the bit, and the time
required to make a round trip of the drill string to replace the
bit. Preferably the entire computer is energized with alternating
current at commercial frequency, for example, 60 hertz.
2. Description of the Prior Art
Factors affecting the speed at which a well can be drilled and the
economics of this drilling have been very widely discussed in the
petroleum industry press. Factors that affect cost per foot, which
is the usual measure of over-all effectiveness in drilling can be
divided into two broad categories: (1) Those out of control of the
operator; and (2) those under his control. The former includes
formation characteristics, formation fluid content, formation fluid
pressure, depth, location, etc. The latter category includes pipe
and hole sizes, types of bit, weight on the bit, rotary speed, type
of mud, hydraulics, and sometimes even rig selection. When it comes
down to drilling any particular hole size required by a particular
casing, the driller has under his control three main variables: Bit
type, weight on bit, and rotary speed.
It is known that each formation usually can be drilled best by one
of four types of drilling action, such as scraping, as with drag
bits, chipping, as with rolling cutter rock bits, crushing, as with
tungsten carbide insert rock bits, and abrading, as with diamond
bits. Except in very thick, uniform formations, the type of rock
being drilled may change several times within the depth drillable
by a single bit. Accordingly, the driller, or someone in
supervision over him, selects the bit that experience indicates as
most effective under the conditions expected.
Once the bit has been selected and a trip has been made to place it
on bottom, the major variables under the driller's control are the
weight on the bit and the revolutions per minute at which the bit
is rotated. Bit tooth wear increases more rapidly for each
increment in weight on the bit until the bit can fail due to
compressional tooth failure. If the bit is toothed, there is little
reason to apply weight beyond the point where the teeth penetrate
their entire height into the formation. At the other end of the
scale, there is a minimum weight below which a bit will not drill
because the unit stress on the rock has not reached rock failure
strength. Most investigators state that drilling rate is directly
proportional to the bit weight multiplied by a constant that is a
fucntion of the formation, of the type of bit, and the drilling
fluid. (See "Engineering Design of Drilling Operations," Jack H.
Edwards, Drilling and Production Practice, AIME 1964, page 40;
"Analytical Determination of Optimum Bit Weight and Rotary Speed
Combinations," J. W. Graham and N. L. Muench, Society of Petroleum
Engineers, Preprint Paper 1349-G, page 4.)
In 1958 the American Association of Oilwell Drilling Contractors
sponsored a series of field tests to determine the effects of
weight and speed on drilling rate. The results were published in
the Petroleum Engineer for Jan. 1958, pages B40 to B52. In this
reference on page B43 E. M. Galle and H. B. Woods show drilling
rate proportional to weight on bit raised to the 1.2 power.
Galle and Woods in a later article, "Best Constant Weight and
Rotary Speed for Rotary Rock Bits," 1963 AIME Drilling and
Production Practice, pages 48-55, showed that the rotary
speed-drilling rate relationship was different from soft and from
hard formations. They used an exponent of one when the average or
hard formation was being drilled, and six-tenths for very soft
formations. Other authors have given various values for the
exponent, generally less than one, or at maximum not greater than
1.1.
A number of patents have considered the matter of drilling
parameters and their effects on drilling economics. The single
reference that appears closest to the work disclosed herein is the
Dellinger et al. U.S. Pat. No. 3,364,494 in which the footage
drilled by the bit is automatically plotted against the drilling
time on a mechanical graph-drawing machine, there being a suitable
offset for the trip time and an equivalent time (in terms of rig
costs) for the bit cost. The plot is drawn on graph paper bearing a
special set of lines in terms of costs per foot. The driller can,
by looking at the graph, determine the condition under which most
economic average drilling is obtained.
Arps in U.S. Pat. No. 3,345,867, teaches the measure of wear on
roller type rock bits by determining the relative rotational speed
of the drilling string to that of the rotating cones. The rotating
cone speed is determined from the vibration of the drill string as
the teeth on the roller impact the formation. Other more crude
types of drilling rate indicators are shown in earlier patents,
such as Nichols U.S. Pat. No. 2,287,819, using a rotary chart on
which the feet drilled are marked off against the time of drilling;
the Mizell Reissue U.S. Pat. No. 21,297, which shows production of
a somewhat similar chart, and the Pearson U.S. Pat. No. 2,935,871,
concerning a drilling rate plotter.
In general these arrangements are useful but lack precision. In
many cases they do not even attempt to consider the most valuable
economic factors required to drill a well under optimum conditions.
For example, no one has been able to plot in the past on a strip
chart the fraction representing the bit life lost in drilling, say,
a foot of formation in comparison with the total estimated life of
the bit. Similarly, one has not been able to log directly on such a
strip chart the incremental cost involved in drilling the last
foot. The charts purporting to measure average driling cost, such
as, for example, the Dellinger et al. system, do not, in fact,
directly or linearly record the average drilling cost, but require
extrapolative reading in terms of a series of cost indicator lines.
On the other hand, the computer which we describe herein does
permit graphing these important variables directly on a strip
chart.
The results obtained could perhaps be compared to those which can
be obtained by other means, for example, by digital data
manipulation in a general-purpose programmed computer. Such units
are described in the World Oil of Jan. 1968 on page 88, and World
Oil for Feb. 1, 1968, page 40-1. Such equipment is more delicate
and much more expensive, thus can be justified only in the cases of
very expensive wells.
Finally, it is known that other types of analog computers are
available, for example one described in Drilling for Jan. 1969 on
page 42, which monitors rotary speeds and bit weights, multiplies
these two quantities together and compares it against the optimum
product already set into the machine, then operates a brake control
unit to modify the bit weight and correct it to the desired
condition. Such equipment is again useful, but it will not produce
the important economic parameters available when using our analog
computer.
SUMMARY of the INVENTION
Basically the driller adjusts certain dials which control
potentiometers or equivalent electrical apparatus setting up
electrical signals related to the weight on the bit, the average
bit rpm, the rig cost per unit time, the bit cost, and the like,
and which read out directly in the form of graphs on a strip chart.
The fraction of the bit life expended by drilling up to the
present, the incremental drilling cost for drilling the last unit
length in the well, and the average cost per foot, including
appropriate trip time and bit cost, for the total formation section
that has been drilled by the current bit are then plotted. The only
attachment between the computer and the drill rig is a taut-line
arrangement attached to the traveling block or the swivel and
passing around a cathead or drum at the computer so that it rotates
in direct relation to the downward motion of the drilling bit
through the formations. The graphs are always available to the
driller so that he can make appropriate corrections in rotary speed
or weight on the bit in order to secure further optimization of
drilling costs and to know when it is desirable to change bits.
BRIEF DESCRIPTION OF THE DRAWINGS
The attached drawings form a part of this disclosure and are to be
read in conjunction therewith. In these FIGS.,
FIG. 1 represents in very schematic form a drill rig with
attachment from the swivel or traveling block to the drilling cost
indicator.
FIG. 2 shows the arrangement for sending out periodic electrical
signals showing each time that a stated unit length of drilling has
been accomplished (for example, each foot).
FIG. 3 shows the basic analog computer arrangement for measuring
the fraction of the bit life expended in drilling a single unit
length in the formation.
FIG. 4 shows the apparatus in the computer for summing up and
graphically recording the total fraction of the bit life expended
up to the present.
FIG. 5 shows the equipment involved in plotting the incremental
cost, that is the cost to drill a single additional foot under the
drilling parameters set in the machine.
FIG. 6 shows the equipment used in preparing a chart of the average
cost per foot involved in all drilling with the current bit.
FIG. 7 shows in isometric view one form of the drilling cost
indicator.
FIG. 8 represents one form of chart produced by the drilling cost
indicator .
DESCRIPTION OF THE PREFERRED EMBODIMENT
When drilling rock formations using a rotary drill rig, the
important variables immediately available for control by the
driller are the weight on the bit W and the rotational speed of the
drill bit R. Increase of the weight on the bit increases the
drilling rate, as does increase in the revolutions per minute of
the drill bit. On the other hand, increases in weight or bit rpm
also decrease the sharpness of the bit whether it be any of the
four ordinary types of bit, and thus has a tendency to decrease
drilling rate. The most effective combination of these two
variables produces the greatest over-all effectiveness and least
cost per foot drilled. Generally it has been found difficult to
predict in advance the part of the total bit life which has been
expended by drilling under a particular set of circumstances, and
it has not been possible to determine the most economic conditions
for the drilling to proceed. This is particularly true when
drilling in a region where there has not been much prior drilling,
but is also frequently found true even though many wells have been
drilled in a particular oil or gas field.
We have found it was possible to combine the drilling variables
into a set of equations which can be formulated into the design of
an analog computer enabling the driller to read from strip charts
produced by the drilling cost indicator the fraction of the
anticipated bit life expended in drilling with a particular bit up
the the present, the incremental drilling cost, and the current
average drilling cost per foot for the current bit. These strip
charts permit the driller to determine when he can improve drilling
performance by increasing or decreasing the weight on the bit or
the bit rpm, and the point at which it is advisable to change the
bit.
The computer constructed in accordance with these equations is an
analog device which is connected mechanically to the rotary drill
rig only at the rotary swivel, or equivalent, so that the location
of the bit as drilling proceeds is automatically fed into the
computer. The driller adjusts six static parameters which
constitute inputs into the computer. These variables are the cost
of the bit, the cost of the rig per hour, the cost of making the
round trip of the drilling string to replace the bit (or its
equivalent, the time to accomplish the bit change and replace the
new bit at the formation), the bit life factor (explained below),
the rotary speed and the weight on the bit. These last two
parameters may be adjusted or up-dated by the operator at any time
during the life of the bit when the driller changes these
variables.
Another variable input is real time, which is generated by clocks
within the computer. The computer is furnished with electric
current, preferably alternating current of the normal power
frequency, for example, 60 hertz in the United States. This
electric energy actuates the computer to produce the strip chart
outputs. Ordinarily the strip charts are driven past the recording
pens in direct relation to the depth at which drilling is
occurring, but the strip charts may also be driven past the pens at
a constant time rate.
The first equation involved is the fraction n.sub.k of the
anticipated bit life N which is expended in drilling a unit
distance in the ground, for example, one foot. Here we use the
formula
n.sub.k = R.sup..alpha. W.sup..beta. (t.sub.k - t.sub.k.sub.-1)
(1)
where R is the rotary speed, i.e., revolutions per unit time at
which the bit is rotated, .alpha. is an empirical constant set into
the computer, W is the weight on the bit, .beta. is a second
empirical constant set into the computer, and t.sub.k -
t.sub.k.sub.-1 is the time expended in drilling the k.sup.th unit
distance (foot).
The anticipated bit life N is defined as the life of the bit from
the time that the bit in its new condition first commences drilling
until it is so dull that it no longer drills economically, and,
accordingly, should be replaced. It follows that ##SPC1##
where K is the total footage drilled with a bit up to the point
where it is completely dull and must be replaced.
The fraction of the anticipated bit life N expended in drilling K
feet of formation, called Z, is given by ##SPC2##
This is one of the variables which is printed out on a strip chart
by the analog computer and thus informs the driller when the bit is
approaching the end of its useful life.
The second useful equation solved by this analog computer is the
incremental drilling cost, that is, the cost of drilling only the
last unit length in the well, for example, the k.sup.th foot. This
quantity, called Y, is given by
Y = (n.sub.k / N) (C.sub.1 + C.sub.3) + C.sub.2 (t.sub.k -
t.sub.k.sub.-1) (4)
where C.sub.1 is equal to the bit cost, C.sub.3 is equal to the
total cost required to replace the bit (and is thus equal to the
product of the rig cost per unit time times the total time involved
in making a round trip of the drill string in replacing the bit),
and C.sub.2 is the rig cost per unit time. From inspection of this
formula (4) it is apparent that Y is dependent upon the fraction of
the anticipated bit life expended in drilling this k.sup.th foot,
and the time required to drill it.
Finally, the third quantity charted by the drilling cost indicator
is the average drilling cost per unit distance in the ground
(ordinarily per foot) for the current accumulated footage drilled
by the bit in use. This quantity X is given by
X = (C.sub.1 + C.sub.2 [ t.sub.t + (t.sub.k - t.sub.o)]/k (5)
where C.sub.2 is the rig cost per unit time, t.sub.t is the total
time required to replace a bit, and t.sub.o is the time that the
current bit commenced drilling.
Several values which have been mentioned above need further
explanation. The exponents .alpha. and .beta. are quantities which
are determined by analysis of drilling records in the region of
interest. .alpha. can be determined by operating a drill rig with a
new bit at constant weight on the bit while varying the rotary
speed and drilling through a homogeneous formation. Values for this
quantity which, of course, vary as the formations change, have been
determined by numerous authors, see for example "Effect of Rotary
Speed on Drilling Rate" by P. L. Moore, Oil & Gas Journal, vol.
58, No. 33, Aug. 15, 1960, p. 170; "How to Calculate Bit Weight and
Rotary Speed for Lowest-Cost Drilling" by E. M. Galle and H. B.
Woods, Oil & Gas Journal, vol. 58, No. 46, Nov. 14, 1960, pp.
167-176; and "A Method of Utilizing Existing Information to
Optimize Drilling Procedures" by J. W. Langston, a paper presented
at the Annual Fall Meeting of the SPE of AIME, Oct. 3-6, 1965,
Denver, Colorado. Published values, plus a recent analysis of bit
records, indicate ranges for .alpha. from about 0.1 to 1.1,
averaging around 0.33. Lacking better information, the value of
.alpha. may be set at this figure of +0.33.
Similarly, the value of .beta. can be determined by drilling with a
fresh bit through a homogeneous formation keeping a constant rpm on
the bit and varying the weight applied to the bit. Values of .beta.
have been found by other investigators to lie between +1 and +2
(for example the Galle and Woods and Langstron references mentioned
above, and "Computerized Drilling Control" by F. S. Young, SPE
Paper 2241, Oct. 29, 1968, Houston, Texas), but our correlations
indicate for modern bits .beta. should lie between the values of
about +0.14 and about +0.74. A value of +0.34 may be employed in
the absence of more complete knowledge on a particular
formation.
The value for the total anticipated bit life N may be determined by
use of the computer itself, drilling through a homogeneous
formation and noting the value of Z while also noting the value of
X. Where the value of X has decreased to a minimum and starts to
increase, the bit is sufficiently dulled so that it is desirable to
change bits. The corresponding value for Z plotted by the computer
at this point is multiplied by the value for N which was set into
the computer during this drilling and becomes the value of N to be
used the next time when drilling through this same formation.
Equations (3) to (5) are, of course, too complicated for use on the
rig floor. Accordingly, this analog computer was developed for
determining and plotting the various quantities desired,
specifically Z, Y, and X as defined above. If desired the driliing
cost indicator may also plot the values of W and R, particularly of
use when these values are changed by the driller while using a
single bit.
The apparatus is enclosed in a "box," one form of which is shown in
FIG. 7. The computer 1 is mounted on the floor of the rig (see FIG.
1) or at least close to the rig framework 2 so that a line 3 may be
attached to the swivel 4 or the traveling block immediately above
it. The line 3 is wrapped about a drum or cathead 5 and is
maintained in taut condition by having the end not connected to the
swivel run over a pulley 6 attached to the rig framework 2 and down
to a weight 7. The drum 5 is spool shaped with the major part of
the spool of a fixed diameter, preferably such that the
circumference is one unit distance, for example, one foot. Thus,
(see FIG. 2) each time that the swivel moves down one foot due to
drilling of one foot by the bit, the drum 5 rotates through one
complete revolution. The shaft of the drum 5 is mounted in the
frame of the computer box (not shown) on bearings 8.
A source of electric energy, preferably an alternating current
generator 9 is used with the drilling cost indicator. It may be
incorporated into the indicator itself, but ordinarily one uses a
commercial source of alternating current or the rig generator. In
either case it is assumed that its output voltage, present across
terminals 10, is essentially constant in amplitude. Two other sets
of output terminals 11 and 12 are used in connection with two
switches 20 and 21 to produce useful signals employed in the
drilling cost indicator. These switches 20 and 21 are of a type
frequently called micro switches, that is, a physically small
switch mounted on the frame of the computer box (not shown) and
equipped with insulated mechanical contacts which actuate the
switch upon external motion of a cam or the like. Switch 20 is a
normally open switch, which closes when the mechanical contact is
depressed. Switch 21 is a normally closed switch which opens upon
actuation of the mechanical contact. Thus from the wiring diagram
shown in FIG. 2 it is apparent that there will be electric energy
across terminals 12, except when the contact on switch 21 is
actuated. Across terminals 11 there will be electric energy only
when the contact of switch 20 is actuated.
The micro switches are actuated from a cam wheel 22 containing two
separate but closely spaced actuators or cams. These can be in the
form of steel pegs or equivalent projecting from the cam wheel 22.
As shown in FIG. 2, lowering of the swivel rotates cam wheel 22 in
the direction of the arrow shown on the cam wheel circumference.
Accordingly, the lefthand peg on cam wheel 22 actuates switch 20
once per revolution just slightly ahead of the righthand peg which
actuates switch 21. As the result of this, electric energy is
momentarily applied across terminals 11 once per revolution just
slightly before electric energy is interrupted across contacts
12.
A magnetic clutch 23 connects the shaft from the drum 5 to that of
the cam wheel 22. It is energized from contacts 10 through switch
16. This switch is closed by the driller whenever a new bit has
been placed on the bottom and drilling is to commence. Similarly,
this switch is opened by the driller whenever drilling ceases and a
round trip is to be made to replace the bit. The shaft carrying cam
wheel 22 also carries a small gear 24 which mates with a large gear
25, the gear ratio being preferably 1:30 to 1:50, for example 1:40.
The shaft of gear 25 supported by bearing 8 from the computer box
frame (not shown) drives a variable resistor 26, preferably of the
helically wound potentiometer type, sometimes called a Helipot, or
the like. Thus the resistance between terminals 27 is always
directly proportional to the total rotations of the drum or cathead
5 while drilling is progressing, and, accordingly, is a measure of
the total footage drilled by the current bit.
Equation 1 defined the fraction of the anticipated bit life
expended in drilling a foot of formation (or in general, a unit
distance). The drilling cost indicator makes the computation of
n.sub.k automatically in a fashion shown in FIG. 3. Potentiometer
28 (Preferably of the helically wound type) is wound with wire
which may be of either varying cross section or varying
resistivity, or both, such that the total resistance varies from
the zero position at some constant to the .alpha. power. Such
potentiometers are commercial items widely available for a large
choice of .alpha. and over a range of .alpha. sufficiently wide to
include the range previously discussed, that is from about +0.15 to
about +0.45. Thus when one sets the slider of the potentiometer at
a distance L from the beginning, the resistance R = b L.sup..alpha.
, where b is a constant. This potentiometer 28 is mounted in the
computer with an appropriate dial which can be manually adjusted,
for example to set on the dial of the revolutions per minute (R) of
the drill bit. If the voltage output of the generator 9 is e, the
voltage e.sub.1 is equal to b.sub.1 e R.sup..alpha. , where b.sub.1
is a constant. Accordingly, this potentiometer provides means for
generating a voltage in a circuit directly proportional to
R.sup..alpha. . This voltage is applied across a second
potentiometer 29. The resistance of this potentiometer is chosen in
a like manner to that of 28 to vary according to some constant to
the .beta. power. It is also preferably of the helical
potentiometer type, and is furnished with a dial permitting one to
manually adjust the slider to any desired value. In this case the
numerical value set on the dial is the weight on the bit W.
Accordingly e.sub.2 is directly proportional to the total voltage
across the potentiometer, e.sub.1, .times. W .sup..alpha.. Thus
e.sub.2 is equal to b.sub.2 R.sup..alpha. W.sup..beta. , where
b.sub.2 is a constant. The voltage e.sub.2 is in turn applied
across a third potentiomter 30 which is arranged with a linear
resistance per unit length, and which is preferably again a helical
potentiometer. Unlike potentiometers 28 and 29, potentiometer 30 is
adjusted to be driven by a clock.sub.1, not a manually adjustable
dial. This clock.sub.1 (31) is an electric synchronous motor
energized from terminals 12 and actuates a shaft 32 which is
connected to the shaft of potentiometer 30 through a magnetic
clutch 33, also actuated from terminals 12. Mechanical spring 34,
of sufficient strength to return the shaft to zero position
whenever clock.sub.1 is not driving it, is also connected to the
shaft of potentiometer 30.
This arrangement of clock, clutch, and spring (sometimes called a
resettable relay) acts in the following manner: As soon as
terminals 12 are energized, i.e., at the start of drilling each
foot, clock.sub.1 (31) commences to rotate synchronously in
accordance with the constant power frequency applied and clutch 33
applies the rotation of the clock output shaft 32 to move the
slider of potentiometer 30 linearly in accordance with time during
the time contacts 12 are energized. The maximum position of the
slider of potentiometer 30 is directly proportional to the total
time elapsed in drilling one foot of formation, therefore
proportional to (t.sub.k - t.sub.k.sub.-1). Accordingly, the output
voltage across terminals 13 from the three concatinated
potentiometers 28, 29 and 30 is directly proportional to
R.sup..alpha. W.sup..beta. (t.sub.k - t.sub.k.sub.-1).
Thus, there is generated across terminals 13 at the end of drilling
each foot an electric voltage directly proportional to the quantity
n.sub.k. One of the lines 13 is connected in series with an
adjustable impedance, resistor 35, preferably a helical
linear-resistance variable resistor furnished with a dial,
adjustable for manual setting. The value of this resistance is set
proportional to the anticipated bit life N. This circuit is closed
through a recording current meter 36, which may be either a
separate unit or more preferably, one channel of a multi-channel
strip chart recorder. It records the current passing through the
meter when a separate, recording potential is applied across two
terminals. In this case the recording voltage is that applied
across terminals 13, that is, the output voltage generated between
the slider and base of potentiometer 30. Accordingly, the recording
ammeter 36 and the adjustable impedance or resistor 35 make up a
high impedance recording voltmeter for measuring the voltage
generated between base and slider of potentiometer 30. As a result,
the strip chart on recorder 36 records the maximum value of the
voltage across terminals 13 divided by the series impedance of the
recording meter 36, impedance 35, and the resistance looking back
into the concatinated potentiometers. The resistance of each
potentiometer preferably is of the order of 100 ohms, that of the
current meter 36 is ordinarily 10 ohms or less, and the maximum
value of the series impedance 35 is in the range of 100,000 to
10,000 ohms. The adjustable impedance 35 has a magnitude which is
large compared to that of the other impedances in the circuit.
Accordingly, the value of the current through the recording current
meter 36, printed on the chart is i = [ b.sub.4 R.sup..alpha.
W.sup..beta. (t.sub.k - t.sub.k.sub.-1)]/N, where b.sub.4 is a
constant. The recorder uses one of the customary chart drives which
may be energized from the alternating current source 9, but
preferably the chart is driven by a flexible shaft turned by the
shaft of drum 5, just as well log charts are driven at the present
time. Thus the strip chart will be moved in accordance with depth
of the drilling bit, and the periodic recording upon it is the
value of n.sub.k, appropriately plotted at the k.sup.th foot. The
chart may also be driven by a clock so that n.sub.k is plotted as a
function of the elapsed time.
A convenient, but not necessary, arrangement is shown in FIG. 3 for
additionally recording on strip charts as functions of depth both
the rotary speed of the drill rig and the weight on the bit. It was
stated that the value of the rotary speed was manually set into the
drilling cost indicator by adjustment of the dial on potentiometer
28. This dial can be mechanically coupled through well-known
commercial means to drive the slider of a second potentiometer 37
mechanically mounted for simultaneous shaft movement. The dashed
line 38 represents this arrangement. The resistance of
potentiometer 37 is made linear and the voltage across terminals 10
is applied to the potentiometer. Thus the voltage e.sub.3 developed
from one end to the slider of the potentiometer 37 is directly
proportional to the revolutions per minute of the bit, or R. A
recording strip chart voltmeter 39 is then connected to record the
value of the voltage e.sub.3 upon actuation of a recording voltage
to terminals 11 which cause the stylus of this recorder to contact
the strip chart. Preferably this strip chart is mechanically
arranged to be driven from the same source as that of the recorder
36 either with reference to footage drilled or to the elapsed time
(in fact, this is true of all strip charts, so no further mention
will be made of this fact). Similarly, if it is desired to record
the weight on the bit W, the slider of potentiometer 29 is
mechanically connected (dashed line 40) to the slider of a third
potentiometer 41 which again is a helical potentiometer with linear
resistance, the terminals of which are connected to terminals 10. A
recording voltmeter 42 is connected to measure the slider voltage
e.sub.4, which is directly proportional to W.
Equaltion (3) is one of the important drilling variables which is
to be graphically presented in strip chart form on the drilling
cost indicator. The circuits shown in FIGS. 2 and 3 are arranged to
give the individual values of n.sub.k / N. The circuit in FIG. 4
sums up the value of n.sub.k / N to produce a strip chart record of
Z. In fact, this arrangement is so convenient that usually recorder
36 is omitted.
The voltage across terminals 13 (FIG. 4) is applied in opposition
to a voltage derived from a potentiometer 43 across the input to a
servo-amplifier 44 driving an electric servo-motor 45. The total
voltage applied across the outside terminals of the potentiometer
43 (preferably a helically wound potentiometer identical to
potentiometer 30, i.e., with a linear resistance and an equal
number of turns), are derived from terminals 10 by an isolating
transformer 46 with a 1:1 ratio. The servo-motor 45 and its
associated amplifier 44, accordingly, make up a conventionally
known device for producing a voltage e.sub.5 equal to the voltage
across terminals 13, i.e., so that the voltage applied to the input
of servo amplifier 44 is zero. Accordingly, when the voltage across
terminals 13 is zero (i.e., at the start of drilling each foot),
the slider of potentiometer 43 is at the zero position and voltage
e.sub.5 is zero. As the voltage across terminals 13 increases,
there is an equal and opposite growth to voltage e.sub.5.
A second potentiometer 47 is physically identical to potentiometer
43 and is mounted to be driven from the same servo-motor shaft 48
through a magnetic clutch 49. This clutch is actuated from
terminals 12. Potentiometer 47 is energized through isolating
transformer 50 (identical to transformer 46) from terminals 10.
With the arrangement shown in FIGS. 3 and 4, the first time the
servo-system is actuated, the slider on potentiometer 47 will be
actuated during the drilling of the first foot following insertion
of a new bit, and will be moved along simultaneously with the
slider of potentiometer 43 to a peak value representing the voltage
directly proportional to n.sub.1. At this point, clutch 49 is
de-energized while the voltage across terminals 13 goes to zero.
The servomotor returns the slider on potentiometer 43 automatically
to zero. As soon as cam wheel 22 has passed the position where its
pegs are in contact with switches 20 and 21, i.e., when drilling on
the second foot has started, voltage will gradually increase on
terminals 13, clutch 49 will be re-engaged, and the slider on
potentiometer 47 will gradually be moved up to a position
representing the sum n.sub.1 + n.sub.2. Thus the voltage output
e.sub.6 of potentiometer 47 represents at the end of each foot of
drilling the summation of the maximum voltage across terminals 13
for all of the feet that have been drilled with the current bit and
is therefore proportional to ##SPC3##
This voltage is applied across a series circuit consisting of a
helically wound adjustable impedance resistor 51 identical to
resistor 35, and a recording current meter 52 equipped with a strip
chart moved in accordance with the drilling going on. Whenever the
recording terminals are actuated from terminals 11, this recorder
52 will chart in a distinctively colored ink the value of Z, since
the impedance of the potentiometer 47 and that of the recorder 52
are deliberately kept quite low compared to that of impedance 51
which has been set to the value N. Accordingly, the current in the
series circuit is the value of Z as set out in equation (3).
It should be added here that if no value is known for the
anticipated bit life N, one simply adjusts impedance 51 to a
convenient value and determines the maximum deflection on the strip
chart from recorder 52. If this at the end of the use of that bit
is not the value 1, but the value Z.sub.1, the driller now knows
the correct value for N is the old value divided by Z.sub.1. Thus,
after a use of a particular bit in a particular formation, the
value of N is known.
The next equation solved by this analog computer is that set out as
(4), i.e., the cost of drilling only the k.sup.th foot. (Exactly
the same arrangement may be employed for indicating the cost of
drilling a different interval than 1 foot, for example, the last 2
feet, 3 feet, etc.) This arrangement is shown in FIG. 5. Here three
identical isolation transformers 53, 54, and 55 energized
respectively from terminals 13, 13 and 10, supply voltage to
identical helical potentiometers 56, 57, and 58, each of which has
a dial for manual adjustment, calibrated in dollars. That for
potentiometer 56 represents bit cost. That for 57 represents trip
cost, i.e., the product of the hourly rig cost multiplied by the
time in hours required to replace a bit at the current drilling
depth. That for potentiometer 58 represents rig cost per hour. When
the values appropriate to the current drilling condition have been
set in by the driller, the voltage e.sub.7 is directly proportional
to bit cost .times. n.sub.k. The voltage e.sub.8 is similarly
directly proportional (with the same constant of proportionality)
to the product of trip cost .times. n.sub.k. The series impedance
(an adjustable resistor, preferably a helical potentiometer) 59 is
identical to impedance 51 and, though not shown in FIGS. 4 and 5,
is mounted for simultaneous revolution of the two potentiometer
shafts, so that when one "dials in" the proper value of N for
impedance 51, it is simultaneously set on impedance 59. The
impedance of 59 is preferably 100 times that of potentiometers 56
and 57, at least. Resistance 60 completes the series circuit and
has a resistance low in comparison with that of impedance 59, for
example, less than one one-hundredth of this impedance.
Accordingly, the input voltage across amplifier.sub.2 (61) is
directly proportional to the current flowing through it which is
therefore directly proportional to n.sub.k / N (C.sub.1 +
C.sub.3).
The setting of the slider on potentiometer 58 was directly
proportional to the rig cost. Therefore, to the same
proportionality as the quantities immediately above, the voltage
e.sub.9 represents rig cost. This voltage is applied both to
terminals 15 (used in conjunction with the circuit of 56), and to
the outside terminals of another helical potentiometer 62 of linear
resistance. The slider of potentiometer 62 is shown in FIG. 5 to be
driven by the resettable relay shown in FIG. 3. These are the
clock.sub.1 (31), the magnetic clutch 33, and the resetting spring
34. Accordingly, the slider of potentiometer 62 moves from its zero
voltage position exactly as did the slider of potentiometer 30 to
produce an indication directly proportional to the incremental
drilling time, that is, the time (t.sub.k - t.sub.k.sub.-1). The
voltage e.sub.10 is directly proportional to the product of rig
cost times incremental drilling time. This voltage is applied to
the input of amplifier.sub.3 (63) which is identical to
amplifier.sub.2 (61). The outputs of these two amplifiers are
connected in series and the sum of the two voltages from these two
amplifiers is fed to a recording strip chart voltmeter 64.
Accordingly, the voltage recorded when terminals 11 of recorder 64
are energized will be directly proportional to the quantity Y of
equation (4) and the strip chart thus records the incremental
drilling cost for each foot or equivalent unit of distance, plotted
against the appropriate location of the current drilling bit.
The third important quantity charted by the drilling cost indicator
is the average drilling cost per foot over the k feet that have
been drilled. This quantity was given by equation (5). The
relatively simple circuit required is shown in FIG. 6. Three
additional identical isolation transformers 65, 66, and 67 are
respectively supplied from terminals 10, 15 and 15. These
transformers in turn energize linear potentiometers, preferably of
the helical type, 68, 69, and 70. Potentiometers 68 and 69 are
arranged for manual adjustment by the driller. In fact, the shaft
of potentiometer 68 is mechanically connected to the shaft of
potentiometer 56, and, accordingly, is set to the bit cost. The
slider of potentiometer 69 is set manually on an appropriate dial
to the trip time. Accordingly, voltage e.sub.11 represents bit
cost, e.sub.12 represents the product of rig cost times trip time,
or trip cost. Linear potentiometer 70 has the slider actuated by a
resetting relay similar to that shown in FIG. 3. Thus it is
composed of a clock.sub.2 (71), a magnetic clutch 72, and a return
spring 73, acting on shaft 74. Clock.sub.2 (71) and clutch 72 are
energized from terminals 10 through a second independent pole of
switch 16, the other pole of which was shown in FIG. 2. Clock.sub.2
runs as long as the driller has switch 16 closed. He closes this
switch only during drilling, and, accordingly, the slider of
potentiometer 72 moves linearly with respect to time during the
entire period that drilling is going on. The gearing in clock.sub.2
differs from that in clock.sub.1 by a factor which can be
appropriately 30 or 60, so that while the first resetting relay
moves the slider of potentiometer 30 through a distance
proportional to a distance of one foot, the slider for
potentiometer 70 is moved one-thirtieth or one-sixtieth of this
distance. Since the setting of potentiometer 70 is proportional to
the total drilling time, the voltage output e.sub.13 is directly
proportional to the product of rig cost times total drilling time,
i.e., C.sub.4 (t.sub.k - t.sub.o).
The three voltages e.sub.11, e.sub.12, and e.sub.13 are additively
connected in series and applied across a large variable impedance
consisting of potentiometer 26, which was also shown in FIG. 2. As
there described, the resistance between terminals 27 is directly
proportional to the total footage drilled by the current bit. The
circuit is closed through a recording current meter 75 of low
impedance. Since the impedances of the part of the potentiometers
68, 69, and 70 is this circuit are also low compared to that of the
setting of potentiometer 26, the current through the circuit is
essentially proportional to the sum of these three voltages divided
by the impedance set in potentiometer 26. The current in the
circuit is directly proportional to the quantity X set out in
equation (5). This value is appropriately recorded since the
actuating terminals of meter 75 go to terminals 11.
It is to be noted that the slider of potentiometer 47 and that of
potentiometer 26 should be returned to zero at the time the bit is
changed. This can be accomplished very simply by providing the
drilling cost indicator with a simple manual return, such as a
crank 80, with appropriate gear 81 which rotates gear 25 back to
zero position, where a mechanical stop (not shown) on gear 25
indicates that the zero position on potentiometer 26 has been
reached. This same arrangement also returns potentiometer 47 to a
zero setting.
The drilling cost indicator may have a number of forms. One
appropriate one is shown in FIG. 7. Here the case 82 is provided
with a plurality of manual dials and appropriate counters for
measuring the quantities set into the various potentiometers, such
as bit cost, rig cost, trip time, trip cost, and expected bit life.
The controls for setting in weight on the bit and rpm of the
drilling string and bit preferably take a different physical form
to distinguish these which may be changed during the course of
drilling from the other quantities. Switch 16 is arranged
conveniently as is return crank 80 for insuring that the driller
will reset these during the trip. The strip charts themselves may
be of any desired form. In FIG. 7 a multiple strip chart 83 has the
three variables arranged from left to right in the order Z, X, and
Y for plotting the fraction of the total life of the bit expended,
the average cost of drilling, and the incremental cost per foot. A
specimen chart from such an indicator is shown in FIG. 8.
In order to change the values of .alpha. and .beta. it is simply
necessary to obtain appropriate helical potentiometers with
different values of these exponents, remove a section of the side
of the drilling cost indicator, and install the new potentiometer
where the old one was used. As has been mentioned earlier, lacking
better information, potentiometer 28 will be used with an exponent
.alpha. of 0.33, and the one involving .beta. (29) will have the
value of 0.34.
In use it is to be noted that the average cost per foot for the
first few feet of drilling is quite high (theoretically infinity at
the start) and decreases rapidly as more footage is drilled. This
is shown graphically by the middle chart in FIG. 8. At some time
during the life of the bit the average cost will decrease to some
minimum value, and remain about there. Drilling will continue with
no appreciable change in this average if the formation drillable
remains reasonably constant, until the bit wear becomes quite
critical, which will cause the drilling rate to decrease, and
increase the average cost of drilling. The bit can be pulled
whenever this minimum has been reached, even if the bit is not worn
out, without increasing the average cost per foot since the next
bit can be expected to drill a similar interval in the same
formation at the same average cost per foot.
Printout of the equation for the incremental cost Y allows, in
effect, for a continous drill-off test to be run while proceeding
with normal drilling. For example, a driller may choose to increase
both the weight on bit W and the rpm R. The next recorded cost for
the increment may increase, decrease, or remain the same. If
incremental drilling cost Y decreases (and this is more sensitive
than the average drilling cost X), the driller will realize that he
can further increase weight on the bit, or rpm, or both. In fact,
this indication of the trend in the drilling cost is of very
definite importance. Even if the value of N placed in the computer
is quite different from the true value, this drilling cost
indicator will still show when wrong combinations of rpm and weight
on the bit are being employed.
The fraction of bit life expended (Curve Z) furnishes the
additional information as to whether the bit still has considerably
useful life or not. For example, assume that a sandstone formation
is being drilled and there is evidence that the bit is becoming
dulled, as indicated both on the X and Y curves. However, the value
for Z shows the bit life is only half expended. A review of logs of
offset wells shows that, for example, only an additional ten feet
of sandstone remain to be drilled before a shale section is to be
expected. The value for Z shows that drilling can be continued into
the shale without fear of losing a cone from the bit. This would be
more desirable than making a trip, since the new bit might be
dulled to the point where it would not adequately drill the shale.
This avoids an extra trip.
It is realized that many changes could be made in the form of the
computer without varying from the basic arrangement shown. The
concatinated potentiometers could be replaced by variable ratio
transformers, for example. Different arrangements to connect to the
drill rig can be worked out. The example shown, however, is
believed to illustrate the utility and simplicity of this
particular type of drilling cost indicator.
* * * * *