Method and system for determining formation porosity

BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention concerns generally a method and/or system for use in rotary-type well-drilling operations. More specifically, it concerns a method for determining porosity of a formation from drilling response.
2. Description of the Prior Art
In the past, there have been some suggestions for obtaining data as a well is drilled and making a record thereof. Such suggestions purport to obtain such data in various ways. For example, there is an article titled "The Drilling Porosity Log (DPL)" by William A. Zoeller, which was the subject of a Society of Petroleum Engineers of AIME paper number SPE-3066. However, such past efforts have not proved practical in producing useful results.
On the other hand, a U.S. Pat. No. 3,916,684 issued Nov. 4, 1975 has disclosed a practical invention for developing a surface drilling log which indicates a formation parameter as described therein. By adding to that invention a torque measurement and by applying the concepts of this invention, a porosity logging method according to this invention may be defined.
SUMMARY OF THE INVENTION
Briefly, the invention concerns a method for determining porosity of a formation from drilling response, wherein a bit is attached to the lower end of a drill string that is rotated while the downward force on said bit is controlled. It comprises the steps of measuring the revolutions of said bit, and measuring the depth of said bit in the borehole. It also comprises measuring the weight on said bit, and determining the tooth dullness of said bit. In addition, it comprises measuring the torque applied to said drill string, and determining a reference torque empirically as well as determining said porosity by combining said measurements and determinations.
Again briefly, the invention concerns a system for determining porosity of a formation from drilling response. In the system, a bit is attached to the lower end of a drill string that is rotated while the downward force on said bit is controlled, and the torque applied to rotate said drill string is measured. The system comprises in combination means for measuring the revolutions of said bit including a tachometer, and means for measuring the depth of said bit in the borehole. The system also comprises means for determining the tooth dullness of said bit, and means for correlating said measurements and determination in accordance with the equation: ##EQU1## wherein: .mu. = ratio of total porosity to the porosity effecting the atmospheric compressive strength
ln = natural logarithm of
N = rotational speed of bit
T = torque
P.sub.e = effective confining pressure
D = bit diameter
R = penetration rate
W = weight on bit
.sigma.ca max = atmospheric compressive strength extrapolated back to zero porosity,
in order to represent a porosity parameter of the formation. The system also comprises means for recording said porosity parameter on a record medium as it is advanced, and means for advancing said record medium in accordance with the depth of said bit.

BRIEF DESCRIPTION OF THE DRAWINGS
The foregoing and other objects and benefits of the invention will be more fully set forth below in connection with the best mode contemplated by the inventors of carrying out the invention, and in connection with which there are illustrations provided in the drawings, wherein:
FIG. 1 is a schematic perspective with blockdiagram showings, which illustrates a rotary-type drilling rig with elements for carrying out the invention;
FIG. 2 is a schematic indication of a weight sensor which measures hook load;
FIG. 3 is a schematic diagram including a blockdiagram circuit showing, that illustrates in greater detail the element in FIG. 1 which develops signal C thereof;
FIG. 4 is a block diagram indicating the flow of data involved in the multiplexing of the weight and torque signals, and indicating the parallel computer inputs for revolutions and depth signals B and C to the system indicated by FIG. 5, and
FIG. 5 is a schematic block diagram indicating the elements involved in correlating the four input signals developed by the system according to FIG. 1, so as to produce a record of the porosity.

DETAILED DESCRIPTION
It has been discovered that by making use of the signals developed from determining the dimensionless ratio T/WD which was described in a U.S. Pat. No. 3,782,190, along with a drilling parameter according to the above mentioned U.S. Pat. No. 3,916,684, an output that is in accordance with the porosity of the formation being drilled may be developed.
An analytical relationship between rock porosity and compressive strength has been determined by laboratory drilling work with roller cone rock bits, to be in accordance with the following relationship: ##EQU2## where ".phi." stands for porosity; ".mu." stands for the ratio of total porosity to the porosity effecting the atmospheric compressive strength; "ln" stands for "natural logarithm of"; and ".sigma.ca" stands for atmospheric compressive strength.
This mechanical porosity can be written as: ##EQU3## which brings in the effect of the rock failure mode as described by the dimensionless ratio (4T/WD) as mentioned above, and the effective confining pressure P.sub.e. The other terms of the equation (2) stand for the following:
K = The intercept of torque vs. weight on bit
N = rotational speed of bit
W = weight on bit
.alpha. = slope of torque vs. weight on bit
D = bit diameter
R = penetration rate
T = torque
.sigma.ca max = atmospheric compressive strength extrapolated back to zero porosity.
But, since "bit to surface" signals are not available as a practical matter, the surface measurement of torque and weight at prescribed conditions must be made on a footage interval basis. This would consist of first "weighing" the drill string and rotating, to determine viscous drill string torque, and second of making a series of short duration weight vs. torque checks at a fixed (low) rotary speed to determine K and .alpha. in equation (2). Under such procedure, the equation (2) can be rewritten as follows: ##EQU4## This equation can be evaluated by two measurements of torque, one at zero weight and one at a reasonable drilling weight, with both measurements made at a fixed, low rotary speed. The porosity indication so obtained is an incremental measurement. Two terms the equation will require estimation, and these are the ".sigma.ca max" and the "P.sub.e ". However, they may be determined on the basis of offset well data and experience.
Referring now to FIG. 1, there is shown a drilling rig which includes a platform 11 upon which stands a derrick 12 and a draw works 13, as well as an anchor 14 for the free end or deadline of a cable or drilling line 15 that is threaded over the sheaves of a crown block 18 and a travelling block 19. The travelling block, of course has attached thereto the usual hook 22 for supporting the drill string (not shown) that is attached beneath a kelly 23. The drill string is rotated in a standard manner by a rotary drive employing an input shaft 24 that is being driven by an engine 25. There is also a tachometer 26 that provides an AC signal having a substantial number of cycles per revolution of the rotary drive shaft 24. While such tachometer signal may be developed in various ways, it may be developed by part of the apparatus which takes the form shown and described in a U.S. Pat. No. 3,295,367. Thus, it is an AC signal generator that develops thirty electrical cycles per revolution of the rotary drive shaft 24, and in a typical case, there would be a gear ratio such that there are five revolutions of the drive shaft for each revolution of the rotary table. Consequently, there is an AC signal generated which has one hundred and fifty electrical cycles per revolution of the rotary table. Of course, these numbers would vary somewhat depending upon the dimensions of the elements involved.
In addition, there is a torque meter 27 which might take various forms but is preferably like one shown and described in the above noted U.S. Pat. No. 3,295,367 issued Jan. 3, 1967. This basically develops a pair of AC signals which have a relative phase angle that is proportional to the torque being measured. Such phase angle is measured in terms of a D.C. analog signal which will be developed at a circuit connection 66, and is identified as the signal D.
In the foregoing manner, the rotation of the drill string and the bit attached to the lower end thereof may be measured by increments of the revolutions. This is so since the signal developed by the tachometer 26 provides an AC signal having a predetermined number of cycles for each revolution. This aspect is described in more detail in U.S. Pat. No. 3,774,445 issued Nov. 27, 1973. However, since use in made of the number of turns, there is a single pulse per revolution also developed.
In order to measure the weight being applied to the bit, the anchor 14 has a hook-load weight indicator which acts in the manner described in the aforementioned U.S. Pat. No. 3,774,445. Thus, as indicated in FIG. 2, there is a hydraulic tubing 75 that is indicated in dashed lines in FIG. 2. Hydraulic fluid in the tubing 75 applies fluid pressure to a Bourdon tube 76 that actuates a potentiometer sliding contactor 77 to produce a variable DC output. Thus, the hook-load weight measurement determines the amount of hydraulic pressure in the tubing 75 and sets the slider 77 of the potentiometer. This produces the indicated DC signal on a circuit line 72, which is indicated in the drawings by a capital letter A.
In order to measure the depth of the bit in the hole, there is a pulse generator 41, shown in more detail in FIG. 3. It is driven from a resilient rimmed wheel 42 which is in friction contact with the underside of one of the sheaves of the crown block 18. In order to take account of only the downward movement of the bit, the signals from the pulse generator 41 are directed to a discriminator 45 that provides output signals over a circuit 46 which leads to a single-pole double-throw switch 47. When the pulses that represent the downward direction are being developed, they will be connected to a circuit 50 that leads to one side of a calibrator element 51 from which the circuit continues via a line 52 to a total-depth counter 55. The output of this counter is a depth signal that is carried over a circuit connection 56 which is identified as the signal C. The details of this depth-measuring pulsecounter system, with the exception of the calibrator element 51, are like the system disclosed in a U.S. Pat. No. 3,643,504.
The calibrator element 51 might take various forms, and it acts periodically to add or subtract a pulse so as to correct for slight size errors in the wheel 42. It is preferably a presettable counter that, when filled, will either add a count, i.e., pulse, to the pulses on line 50, or block the next count, i.e., pulse, from passing. The principles are shown and explained in a U.S. Pat. No. 3,947,664.
It will be understood that the depth measurement may be made down on the rig floor without changing the principles involved. This could be done using conventional instrumentalities.
In order to make a measurement of the revolutions of the drill string, there is a counter 60 (see FIG. 1) that has its input connected to the tachometer 26, as is indicated by a dashed line 61. The revolution counter 60 provides an output signal on circuit 64 which is identified as signal B. This is an AC signal having the frequency described above such that there are approximately one hundred and fifty electrical cycles for each revolution of the drill string. It is reduced to one pulse per revolution to be used in correlating the four signals A, B, C and D.
In order to measure the torque that is being applied to the rotary drive shaft 24 and consequently to the drill string at the surface, there is the above noted torque meter 27 which develops a torque signal that is supplied over the circuit connection 66. This is identified as the signal D. It is multiplexed with the signal A for the purposes of the correlation of the four signals, which was indicated above.
FIG. 4 illustrates in block diagram form the electronic circuits involved in handling the torque and weight signals in accordance with the above described equations. It will be understood that a symbol which is designated by reference number 93 is employed to indicate the fact that multiplexing input is used as between the weight signals (on circuit connection 72) and the torque signals (on circuit connection 66). The multiplex timing which is indicated by a block numbered 98 causes switching so as to connect these alternate inputs over a circuit connection 94 to a single analog-to-digital converter 97. The output 94 of this A/D converter 97 goes to both of the circuit elements 104 and 105, shown in the block diagram. These are for handling, respectively, the weight (signal A) and the torque (signal D) that go to the input of the converter 97. It may be noted that the outputs of A/D converter 97 are continuously connected to the various outputs indicated, but that only the appropriate circuits are activated during each portion of a complete cycle. Consequently, the multiplexed weight signals (A') and torque signals (D') will appear alternately on the output circuits 82 and 83 to become inputs to the calculator 91 (FIG. 5) as will be described below. The multiplex timing to accomplish such alternative activation is controlled by multiplex timing circuits which are indicated by an arrow 109 out from the block 98 and the various arrows 110 into the elements connected to the outputs of the A/D converter 97.
FIG. 5 illustrates, in block-diagram form, the way in which the measured quantities are correlated so as to develop a porosity log at the surface, as the well is drilled. The arrangement includes a calculator 91 that may be any of various electronic calculators, e.g., one manufactured by Wang Laboratories, Inc., Tewksbury, Mass., designated Model 700A or 700B. However, in such case there is required an interfacer 92 in order to transform the signals as they are developed in the system and supplied over connections 82, 64, 56 and 83 which are described as signals A', B, C and D', respectively. These signals are transformed from binary coded digital signals to binary sixteen for input to the calculator. Such interfacer 92 may be one (with modifications) like that manufactured by Adams-Smith, Inc., Needham Heights, Mass., designated Model 100 Instrument Interface for feeding electrical measurements to the WANG 700 Series Calculators.
The measured data as represented by signals A', B, C and D' is correlated in accordance with the above noted expression (3) so as to provide an output that may be applied to a strip chart recorder 95 which is advanced by a stepping motor 96. In this manner, the record shows the recorded porosity in accordance with the depth of the bit and irrespective of the time element.
A specific example of a program of providing a porosity drilling log in accordance with the invention is set forth below.
This program is applicable to a Wange electronic calculator Model 700 such as indicated above. It should be noted that the carrying out of trigonometric calculations is processed within steps 0007 through 0168. Also, input data is processed for use in the equation in accordance with the comments shown.
The program codes for a 700 series Wang calculator are as follows:
__________________________________________________________________________700 SERIES PROGRAM CODESCode Key Code Key__________________________________________________________________________0400 + DIRECT 0601 -0401 - DIRECT 0602 .times.0402 .times. DIRECT 0603 .div.0403 .div. DIRECT 0604 .uparw.0404 STORE DIRECT 0605 .dwnarw.0405 RECALL DIRECT 0606 .dwnarw..uparw.0406 .revreaction. DIRECT 0607 .vertline. X .vertline.0407 SEARCH 0608 INTEGER X0408 MARK 0609 .pi.0409 GROUP 1 0610 Log.sub.10 X0410 GROUP 2 0611 Log.sub.e X 0411 WRITE 0612 ##STR1##0412 WRITE ALPHA 0613 10.sup.x0413 END ALPHA 0614 e.sup.x0414 STORE Y* 0615 1/x0415 RECALL Y* 0700 00500 + INDIR 0701 10501 - INDIR 0702 20502 .times. INDIR 0703 30503 .div. INDIR 0704 40504 STORE INDIR 0705 50505 RECALL INDIR 0706 60506 .revreaction. INDIR 0707 70507 SKIP if Y.gtoreq.X 0708 80508 SKIP if Y<X 0709 90509 SKIP if Y=X 0710 SET EXP0510 SKIP if ERROR 0711 CHANGE SIGN0511 RETURN 0712 DECIMAL POINT0512 END PROG 0713 X.sup.20513 LOAD PROG 0174 RECALL RESIDUE0514 GO 0715 CLEAR X0515 STOP *ENTERED BY TOGGLE0600 + SWITCH SETTING__________________________________________________________________________FOR MODEL 720 ONLY*Code Operation *Code Operation__________________________________________________________________________1200 + DIRECT (+100) 1205 RECALL DIRECT(+100)1201 - DIRECT (+100) 1206 .revreaction. DIRECT(+100)1202 .times. DIRECT (+100) 1214 STORE Y (+100)1203 .div. DIRECT (+100) 1215 RECALL Y (+100)1204 STORE DIRECT (+100)__________________________________________________________________________ Any of these codes automatically adds 100 to the Storage Register number. *These codes are generated by toggle switches and special operation keys.
______________________________________SPECIAL COMMANDS WHICH MUST BE PRECEDEDBY WRITE ALPHA(Decimal Point Shifting)______________________________________Code Key Operation______________________________________0401 - DIRECT Divide X by 10.sup.10402 .times. DIRECT Divide X by 10.sup.20403 .div. DIRECT Divide X by 10.sup.30404 STORE DIRECT Divide X by 10.sup.40405 RECALL DIRECT Divide X by 10.sup.50406 .revreaction. DIRECT Divide X by 10.sup.60407 SEARCH Divide X by 10.sup.70408 MARK Divide X by 10.sup.80409 GROUP 1 Divide X by 10.sup.90400 + DIRECT Divide X by 10.sup.100701 1 Multiply X by 10.sup.10702 2 Multiply X by 10.sup.20703 3 Multiply X by 10.sup.30704 4 Multiply X by 10.sup.40705 5 Multiply X by 10.sup.50706 6 Multiply X by 10.sup.60707 7 Multiply X by 10.sup.70708 8 Multiply X by 10.sup.80709 9 Multiply X by 10.sup.90700 0 Multiply X by 10.sup.10______________________________________DECISIONSCode Key Operation0410 GROUP 2 Skip if Y positive0411 WRITE Skip if Y = 00510 SKIP if ERROR Skip if Y negative0511 RETURN Skip if Y .noteq. 00610 Log.sub.10 X Skip if X positive0611 Log.sub.e X Skip if X = O0710 SET EXP Skip if X negative0711 CHANGE SIGN Skip if X .noteq. 0______________________________________Miscellaneous0615 1/X Pause0514 GO 180/.pi.0515 STOP .pi./180______________________________________
the specific program for providing a porosity drilling log which illustrates the invention has 650 steps and is as follows:
__________________________________________________________________________STEP CODE KEY COMMENTS__________________________________________________________________________0000 04 08 MARK (Calculator waiting0001 01 06 0106 for signal of com- peltion of 2 ft.)0002 04 09 GROUP 1 (Wait for interfacer0003 15 00 signal to continue)0004 04 07 SEARCH0005 00 01 00010006 05 14 GO0007 04 08 MARK (Evaluating of Cos .theta.)0008 00 03 00030009 06 04 .uparw.0010 07 03 30011 07 06 60012 07 00 00013 06 03 .div.0014 06 05 .dwnarw.0015 06 08 INTEGER X0016 06 01 -0017 07 04 40018 06 02 X0019 06 05 .dwnarw.0020 06 08 INTEGER X0021 06 01 -0022 04 12 WRITE ALPHA (Cosine test) 0023 06 12 ##STR2## "0024 06 09 .pi.0025 06 02 X0026 07 02 20027 06 03 .div.0028 06 05 .dwnarw.0029 07 13 X.sup.20030 04 04 STORE DIRECT0031 00 03 00030032 07 01 10033 07 06 60034 06 04 .uparw.0035 07 01 10036 04 04 STORE DIRECT0037 00 00 00000038 04 03 MARK0039 15 14 15140040 04 05 RECALL DIRECT0041 00 03 00030042 04 02 X DIRECT0043 00 00 00000044 06 05 .dwnarw.0045 04 03 .div. DIRECT0046 00 00 00000047 07 01 10048 06 01 -0049 06 05 .dwnarw.0050 07 11 CHANGE SIGN0051 04 03 .div. DIRECT0052 00 00 00000053 07 01 10054 06 01 -0055 04 00 + DIRECT0056 00 00 00000057 04 12 WRITE ALPHA SKIP if Z = 00058 04 11 WRITE0059 04 07 SEARCH0060 15 14 15140061 04 15 RECALL Y0062 00 00 00000063 07 12 DECIMAL POINT0064 07 05 50065 07 10 SET EXP0066 07 11 CHANGE SIGN0067 07 01 10068 07 01 10069 06 01 -0070 06 01 -0071 06 050072 04 12 WRITE ALPHA SET SIGN0073 05 12 END PROGRAM0074 04 07 SEARCH0075 15 15 15150076 04 08 MARK EVALUATION OF TAN .theta.0077 00 07 00070078 04 12 WRITE ALPHA ARC TAN 90.degree. TEST0079 07 15 CLEAR X0080 06 04 .uparw.0081 07 12 DECIMAL POINT0082 07 05 50083 05 07 SKIP IF Y .gtoreq. X0084 04 12 WRITE ALPHA ARC TAN 45.degree. TEST0085 07 13 X.sup.20086 07 01 10087 06 00 +0088 04 14 STORE Y0089 00 00 00000090 07 02 20091 06 01 -0092 04 05 RECALL DIRECT0093 00 00 00000094 06 03 .div.0095 06 05 .dwnarw.0096 04 14 STORE Y0097 00 01 00010098 06 02 X0099 04 14 STORE Y0100 00 00 00000101 07 01 10102 04 04 STORE DIRECT0103 00 03 00030104 07 01 10105 07 05 50106 06 04 .uparw.0107 07 08 80108 04 04 STORE DIRECT0109 00 02 00020110 04 08 MARK0111 15 13 15130112 04 05 RECALL DIRECT0113 00 00 00000114 04 02 X DIRECT0115 00 03 00030116 04 05 RECALL DIRECT0117 00 02 00020118 04 02 X DIRECT0119 00 02 00020120 04 06 DIRECT0121 00 02 00020122 04 02 X DIRECT0123 00 03 00030124 06 05 .dwnarw.0125 04 00 + DIRECT0126 00 03 00030127 07 02 20128 06 01 -0129 07 01 10130 04 01 - DIRECT0131 00 02 00020132 04 06 DIRECT0133 00 03 00030134 04 03 .div. DIRECT0135 00 03 00030136 04 05 RECALL DIRECT0137 00 02 00020138 04 12 WRITE ALPHA SKIP if X = 00139 06 11 LOGE.sub.e X0140 04 07 SEARCH0141 15 13 15130142 04 15 RECALL Y0143 00 01 00010144 04 05 RECALL DIRECT0145 00 03 00030146 06 02 X0147 04 12 WRITE ALPHA 180/.pi.0148 05 14 GO0149 06 02 X0150 07 04 40151 07 05 50152 04 12 WRITE ALPHA AVERAGE TANGENT SET0153 06 13 10.sup.X0154 06 05 .dwnarw.0155 04 12 WRITE ALPHA SET SIGN0156 05 12 END PROGRAM0157 04 07 SEARCH0158 05 06 INDIRECT0159 04 08 MARK TRANSFER OF COS .theta. INTO0160 15 15 1515 Y REGISTER0161 12 15 RECALL Y0162 14 08 2480163 04 07 SEARCH0164 00 05 00050165 04 08 MARK TRANSFER OF TAN .theta. INTO0166 05 06 INDIRECT Y REGISTER0167 12 15 RECALL Y0168 14 08 2480169 04 07 SEARCH0170 00 06 00060171 04 08 MARK CHECK IF DEPTH IS CORRECT0172 00 01 00010173 04 09 GROUP 10174 15 01 15010175 06 04 .uparw.0176 04 09 GROUP 10177 15 01 15010178 05 09 SKIP IF Y = X0179 04 07 SEARCH0180 00 01 00010181 04 07 SEARCH0182 02 05 02050183 05 14 GO0184 05 14 "0185 05 14 "0186 05 14 "0187 05 14 "0188 04 08 MARK RETRIEVAL AND STORING OF0189 02 05 0205 DATA INTO WANG0190 04 09 GROUP 10191 15 03 15030192 04 14 STORE Y0193 00 05 00050194 04 04 STORE X0195 02 07 02070196 04 09 GROUP 10197 15 05 15050198 06 04 .uparw.0199 04 09 GROUP 10200 15 07 15070201 04 14 STORE Y0202 02 08 02080203 04 12 WRITE ALPHA0204 07 02 20205 04 04 STORE DIRECT0206 01 06 01060207 04 09 GROUP 10208 14 01 14010209 04 12 WRITE ALPHA0210 07 04 40211 04 04 STORE DIRECT0212 01 07 01070213 04 15 RECALL Y EVALUATE TURNS FOR THIS -0214 02 08 0208 2 FT.0215 04 05 RECALL DIRECT0216 00 09 00090217 06 01 -0213 04 14 STORE Y0219 01 08 01080220 04 05 RECALL DIRECT AVG.NET TORQUE TN/N0221 01 07 01070222 06 060223 06 03 .div.0224 06 05 .dwnarw.0225 04 04 STORE DIRECT0226 04 02 X DIRECT0227 07 00 00228 04 04 STORE DIRECT0229 04 00 + DIRECT0230 05 14 GO0231 05 14 GO0232 04 15 RECALL Y IS BIT ROCK OR INSERT?0233 00 07 00070234 07 09 90235 05 08 SKIP IF Y<X0236 04 07 SEARCH0237 01 09 01090238 04 05 RECALL DIRECT IS TOOTH GRADING LESS0239 02 08 0208 THAN 0.50?0240 06 02 X0241 04 05 RECALL DIRECT0242 00 06 00060243 06 03 .div.0244 07 12 DECIMAL POINT0245 07 05 50246 05 07 SKIP IF Y.gtoreq.X0247 04 07 SEARCH0248 02 00 02000249 05 14 GO IF LESS THAN 0.5 USE0250 06 05 .dwnarw. 0050251 04 07 SEARCH0252 02 00 02000253 04 08 MARK0254 01 09 01090255 07 01 10256 04 08 MARK0257 02 00 02000258 04 04 STORE DIRECT0259 03 07 03070260 04 15 RECALL Y BEARING BRADING0261 01 06 0106 EVALUATION.0262 07 08 80263 06 02 X0264 04 05 RECALL DIRECT0265 01 02 01020266 06 03 .div.0267 04 14 STORE Y0268 03 09 03090269 07 07 7 IS BEARING GRADING0270 05 07 SKIP IF Y.gtoreq.X GREATER THAN 7?0271 04 07 SEARCH0272 00 02 00020273 06 01 - IF BEARING GRADING IS0274 07 02 2 GREATER THAN 70275 07 00 0 CORRECT TORQUE FOR0276 07 00 0 DRAG0277 07 00 00278 06 02 X0279 04 05 RECALL DIRECT0280 04 02 X DIRECT0281 06 060282 06 01 -0283 06 05 .dwnarw.0284 04 04 STORE DIRECT0285 04 00 + DIRECT0286 04 15 RECALL Y0287 01 08 01080288 06 02 X0289 04 14 STORE Y0290 04 01 - DIRECT0291 04 07 SEARCH0292 02 01 02010293 04 08 MARK CORRECT TORQUE FOR T.sub.o0294 00 02 0002 (no drilling on bottom0295 04 05 RECALL DIRECT torque)0296 04 02 X DIRECT0297 04 00 + DIRECT0298 04 00 + DIRECT0299 04 15 RECALL Y0300 04 00 + DIRECT0301 04 05 RECALL DIRECT0302 01 08 01080303 06 02 X0304 04 14 STORE Y0305 04 01 - DIRECT0306 05 14 GO0307 05 14 GO0308 04 08 MARK NET KILOPOUNDS TURNS FOR0309 02 01 0201 2 FT.0310 04 15 RECALL Y0311 01 06 01060312 04 05 RECALL DIRECT0313 01 00 01000314 06 01 -0315 04 14 STORE Y0316 03 06 03060317 04 15 RECALL Y0318 02 07 02070319 04 05 RECALL DIRECT NET TIME FOR 2 FT.0320 00 08 00080321 06 01 -0322 06 05 .dwnarw.0323 04 06 DIRECT0324 05 06 INDIRECT0325 04 04 STORE DIRECT0326 05 08 SKIP IF Y<X0327 04 14 STORE Y0328 03 08 03080329 05 14 GO0330 05 14 GO0331 04 08 MARK CALCULATE T/WD0332 02 02 02020333 04 15 STORE Y0334 01 04 01040335 07 01 10336 07 02 20337 06 03 .div.0338 04 05 RECALL DIRECT0339 01 07 01070340 06 03 .div.0341 04 05 RECALL DIRECT0342 03 06 03060343 06 02 X0344 06 06 .dwnarw.0345 06 15 1/X0346 04 04 STORE DIRECT0347 02 00 02000348 05 14 GO0349 05 14 GO0350 04 08 MARK0351 00 04 0004 EVALUATION OF .theta.0352 07 04 40353 06 03 .div.0354 06 05 .dwnarw.0355 04 07 SEARCH CALULATION OF DE-0356 00 07 0007 NOMINATOR OF POROSITY0357 04 08 MARK EQUATION0358 00 06 00060359 07 02 20360 06 02 X0361 06 05 .dwnarw.0362 05 14 GO0363 05 14 GO0364 04 07 SEARCH0365 00 03 00030366 05 14 GO0367 05 14 GO0368 04 08 MARK0369 00 05 00050370 04 14 STORE Y0371 02 01 02010372 07 01 10373 04 01 - DIRECT0374 02 01 02010375 06 00 +0376 04 05 RECALL DIRECT0377 02 01 02010378 06 03 .div.0379 04 14 STORE Y0380 02 01 02010381 05 14 GO0382 05 14 GO0383 04 08 MARK0384 00 08 00080385 04 15 RECALL Y0386 01 03 01030387 04 05 RECALL DIRECT0388 02 03 02030389 06 02 X0390 04 05 RECALL DIRECT0391 02 02 02020392 06 01 -0393 04 05 RECALL DIRECT0394 00 05 00050395 06 02 X0396 04 05 RECALL DIRECT0397 02 01 02010398 06 02 X0399 04 14 STORE Y0400 04 03 .div. DIRECT0401 05 14 GO0402 05 14 GO0403 04 08 MARK0404 00 09 00090405 04 15 RECALL Y0406 03 06 03060407 04 05 RECALL DIRECT EVALUATION OF POROSITY0408 02 04 02040409 06 03 .div.0410 04 05 RECALL DIRECT0411 01 04 01040412 06 03 .div.0413 04 05 RECALL DIRECT0414 02 00 02000415 06 02 X0416 07 09 90417 07 06 60418 06 02 X0419 04 05 RECALL DIRECT0420 04 03 .div. DIRECT0421 06 01 -0422 04 14 STORE Y0423 03 04 03040424 04 05 RECALL DIRECT0425 02 05 02050426 06 06 EVALUATION OF SDL0427 06 03 .div. (both ln and log)0428 07 01 10429 07 04 40430 07 04 40431 06 02 X0432 06 05 .dwnarw.0433 06 11 LOG.sub.e X0434 06 04 .uparw.0435 04 05 RECALL DIRECT0436 02 06 02060437 06 03 .div.0438 04 14 STORE Y0439 03 01 03010440 05 14 GO0441 05 14 GO0442 04 08 MARK0443 01 01 01010444 04 15 RECALL Y0445 03 06 03060446 04 05 RECALL DIRECT0447 03 07 03070448 06 12 ##STR3##0449 06 03 .div.0450 04 05 RECALL DIRECT0451 00 05 00050452 06 12 ##STR4##0453 06 03 .div.0454 04 05 RECALL DIRECT0455 02 09 02090456 06 03 .div.0457 04 14 STORE Y0458 03 02 03020459 06 05 .dwnarw.0460 06 11 LOG.sub.e X0461 04 15 RECALL Y0462 03 00 03000463 06 00 +0464 06 05 .dwnarw.0465 04 06 DIRECT0466 03 02 03020467 06 10 LOG.sub.10 X0468 04 04 STORE DIRECT0469 03 03 03030470 04 05 RECALL DIRECT0471 03 05 03050472 04 02 X DIRECT0473 03 03 03030474 04 12 WRITE ALPHA TYPEWRITER ON AND0475 12 00 TYPEWRITER ON CARRIAGE RETURN0476 01 08 RETURN CARRIAGE0477 04 13 END ALPHA0478 07 01 1 UPDATE AND TYPE LINE0479 04 00 + DIRECT NUMBER0480 01 01 01010481 04 05 RECALL DIRECT0482 01 01 01010483 04 11 WRITE0484 03 00 3 DIGITS0485 04 11 WRITE SPACE 3 TIMES0486 15 03 15030487 04 05 RECALL DIRECT TYPE DEPTH0488 00 05 00050489 04 11 WRITE0490 09 00 9 DIGITS0491 04 15 RECALL Y NEXT DEPTH EVALUATION0492 02 04 02040493 06 00 +0494 06 05 .dwnarw.0495 04 12 WRITE ALPHA DIVIDE X BY 10'0496 04 01 - DIRECT0497 06 08 INTEGER X0498 04 12 WRITE ALPHA MULTIPLY X BY 10'0499 07 01 10500 06 01 -0501 04 14 STORE Y0502 00 04 00040503 05 14 GO0504 05 14 GO0505 04 08 MARK0506 01 04 01040507 04 15 RECALL Y ROUND OFF AND TYPE0508 03 01 0301 POROSITY0509 07 12 DECIMAL POINT0510 07 00 00511 07 00 00512 07 00 50513 06 00 +0514 06 05 .dwnarw.0515 04 12 WRITE ALPHA0516 07 02 20517 06 08 INTEGER X0518 04 12 WRITE ALPHA0519 04 02 X DIRECT0520 04 11 WRITE0521 04 02 4 DIGIT,2 DECIMALS0522 05 14 GO0523 05 14 GO0524 04 15 RECALL Y ROUND OFF AND TYPE0525 03 03 0303 SDL (log)0526 07 12 DECIMAL POINT0527 07 00 00528 07 00 00529 07 05 50530 06 00 +0531 06 05 .dwnarw.0532 04 12 WRITE ALPHA MULTIPLY X BY 10.sup.20533 07 02 20534 06 08 INTEGER X0535 04 12 WRITE ALPHA DIVIDE X BY 10.sup.20536 04 02 X DIRECT0537 04 11 WRITE0538 04 01 X DIRECT0539 05 14 GO0540 04 14 GO0541 04 15 RECALL Y ROUND OFF AND TYPE0542 03 02 0302 SDL (ln)0543 07 12 DECIMAL POINT0544 07 00 00545 07 00 00546 07 05 50547 06 00 +0548 06 05 .dwnarw.0549 04 12 WRITE ALPHA MULTIPLY X BY 10.sup.20550 07 02 20551 06 08 INTEGER X0552 04 12 WRITE ALPHA DIVIDE Y BY 10.sup.20553 04 02 X DIRECT0554 04 11 WRITE0555 04 02 X DIRECT0556 05 14 GO0557 05 14 GO0558 04 11 WRITE SPACE 5 TIMES0559 15 05 15050560 04 05 RECALL DIRECT TYPE N (TURNS) AND0561 02 08 0208 UPDATE REGISTER0562 04 11 WRITE0563 09 00 9 DIGITS0564 04 06 DIRECT0565 00 09 00090566 05 14 GO0567 05 14 GO0568 04 05 RECALL DIRECT TYPE WN AND UPDATE0569 01 06 0106 REGISTER0570 04 11 WRITE0571 09 00 9 DIGITS0572 04 06 DIRECT0573 01 00 01000574 05 14 GO0575 05 14 GO0576 04 058 RECALL DIRECT TYPE TIME AND UPDATE0577 02 07 0207 REGISTER0578 04 11 WRITE0579 09 00 9 DIGITS0580 04 06 DIRECT0581 00 08 00080582 04 15 RECALL Y ROUNDOFF AND TYPE0583 04 01 - DIRECT TN(TORQUE X TURNS)0584 07 12 DECIMAL POINT0585 07 00 00586 07 05 50587 06 00 +0588 06 05 .dwnarw.0589 04 12 WRITE ALPHA MULTIPLY X BY 10.sup.10590 07 01 10591 0608 INTEGER X0592 04 12 WRITE ALPHA DIVIDE X BY 10.sup.10593 04 01 - DIRECT0594 04 11 WRITE0595 08 01 8 DIGITS, 1 DECIMAL0596 04 11 WRITE SPACE 5 TIMES0597 15 05 15050598 04 05 RECALL DIRECT ROUNDOFF AND TYPE0599 02 00 0200 T/WD0600 04 12 WRITE ALPHA MULTIPLY X BY 10.sup.20601 07 02 20602 05 14 GO0603 06 08 INTEGER X0604 04 12 WRITE ALPHA DIVIDE X BY 10.sup.20605 04 02 X DIRECT0606 04 11 WRITE0607 05 02 5 DIGITS,2 DECIMALS0608 04 05 RECALL DIRECT TYPE MUD WEIGHT0609 01 03 01030610 04 11 WRITE0611 05 02 5 DIGITS,2 DECIMALS0612 04 05 RECALL DIRECT TYPE BIT SIZE0613 01 04 01040614 04 11 WRITE0615 02 03 2 DIGITS, 2 DECIMALS0616 04 05 RECALL DIRECT0617 03 07 0307 TYPE TOOTH GRADING0618 04 11 WRITE0619 03 03 3 DIGITS, 3 DECIMALS0620 04 05 RECALL DIRECT TYPE BEARING GRADING0621 03 09 03090622 04 11 WRITE0623 03 03 3 DIGITS, 3 DECIMALS0624 04 05 RECALL DIRECT TYPE TORQUE (NET)0625 04 02 X DIRECT0626 04 11 WRITE0627 04 02 4 DIGITS, 2 DECIMALS0628 04 15 RECALL Y SPACE IF 10TH FT.0629 00 05 00050630 06 05 .dwnarw.0631 04 12 WRITE ALPHA DIVIDE X BY 10.sup.10632 04 01 - DIRECT0633 06 08 INTEGER X0634 04 12 WRITE ALPHA MULTIPLY X BY 10.sup.10635 07 01 10636 05 09 SKIP IF Y = X0637 04 07 SEARCH0638 01 05 01050639 04 12 WRITE ALPHA0640 01 10 LINE INDEX0641 04 13 END ALPHA0642 05 14 GO0643 05 14 GO0644 04 08 MARK0645 01 05 01050646 04 12 WRITE ALPHA TYPEWRITER OFF0647 12 01 TYPEWRITER OFF0648 04 13 END ALPHA0649 04 07 SEARCH0650 01 06 01060651 05 12 END PROGRAM__________________________________________________________________________
the foregoing has been illustrated and described in considerable detail in accordance with the applicable statues. However, this is not to be taken as in any way limiting the invention, but merely as being illustrative thereof.

Number	Name	Date	Kind
3898880	Kelseaux et al.	Aug 1975
3916684	Rundell	Nov 1975

Method and system for determining formation porosity

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