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: μ = ratio of total porosity to the porosity effecting the atmospheric compressive strength

ln = natural logarithm of

N = rotational speed of bit

T = torque

P_e = effective confining pressure

D = bit diameter

R = penetration rate

W = weight on bit

σca 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 "φ" stands for porosity; "μ" stands for the ratio of total porosity to the porosity effecting the atmospheric compressive strength; "ln" stands for "natural logarithm of"; and "σca" 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_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

α = slope of torque vs. weight on bit

D = bit diameter

R = penetration rate

T = torque

σca 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 α 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 "σca max" and the "P_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 ×0402 × DIRECT              0603 ÷0403 ÷ DIRECT  0604 ↑0404 STORE DIRECT  0605 ↓0405 RECALL DIRECT 0606 ↓↑0406 ⃡ DIRECT              0607 | X |0407 SEARCH        0608 INTEGER X0408 MARK          0609 π0409 GROUP 1       0610 Log10 X0410 GROUP 2       0611 Loge X 0411 WRITE         0612                    ##STR1##0412 WRITE ALPHA   0613 10x0413 END ALPHA     0614 ex0414 STORE Y*      0615 1/x0415 RECALL Y*              0700 00500 + INDIR       0701 10501 - INDIR       0702 20502 × INDIR 0703 30503 ÷ INDIR   0704 40504 STORE INDIR   0705 50505 RECALL INDIR  0706 60506 ⃡ INDIR              0707 70507 SKIP if Y≧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 X20513 LOAD PROG     0174 RECALL RESIDUE0514 GO            0715 CLEAR X0515 STOP              *ENTERED BY TOGGLE0600 +             SWITCH SETTING__________________________________________________________________________FOR MODEL 720 ONLY*CodeOperation     *Code                   Operation__________________________________________________________________________1200 + DIRECT (+100)              1205 RECALL DIRECT(+100)1201 - DIRECT (+100)              1206 ⃡ DIRECT(+100)1202 × DIRECT (+100)              1214 STORE Y (+100)1203 ÷ 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 1010402    × DIRECT   Divide X by 1020403    ÷ DIRECT     Divide X by 1030404    STORE DIRECT     Divide X by 1040405    RECALL DIRECT    Divide X by 1050406    ⃡ DIRECT                    Divide X by 1060407    SEARCH           Divide X by 1070408    MARK             Divide X by 1080409    GROUP 1          Divide X by 1090400    + DIRECT         Divide X by 10100701    1                Multiply X by 1010702    2                Multiply X by 1020703    3                Multiply X by 1030704    4                Multiply X by 1040705    5                Multiply X by 1050706    6                Multiply X by 1060707    7                Multiply X by 1070708    8                Multiply X by 1080709    9                Multiply X by 1090700    0                Multiply X by 1010______________________________________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 ≠ 00610    Log10 X     Skip if X positive0611    Loge X      Skip if X = O0710    SET EXP          Skip if X negative0711    CHANGE SIGN      Skip if X ≠ 0______________________________________Miscellaneous0615    1/X              Pause0514    GO               180/π0515    STOP             π/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 θ)0008    00 03   00030009    06 04   ↑0010    07 03   30011    07 06   60012    07 00   00013    06 03   ÷0014    06 05   ↓0015    06 08   INTEGER X0016    06 01   -0017    07 04   40018    06 02   X0019    06 05   ↓0020    06 08   INTEGER X0021    06 01   -0022    04 12   WRITE ALPHA     (Cosine test) 002306 12    ##STR2##        "0024    06 09    π0025    06 02    X0026    07 02    20027    06 03    ÷0028    06 05    ↓0029    07 13    X20030    04 04   STORE DIRECT0031    00 03   00030032    07 01   10033    07 06   60034    06 04   ↑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   ↓0045    04 03   ÷ DIRECT0046    00 00   00000047    07 01   10048    06 01   -0049    06 05   ↓0050    07 11   CHANGE SIGN0051    04 03   ÷ 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 θ0077    00 07    00070078    04 12   WRITE ALPHA     ARC TAN 90° TEST0079    07 15   CLEAR X0080    06 04    ↑0081    07 12   DECIMAL POINT0082    07 05    50083    05 07   SKIP IF Y ≧ X0084    04 12   WRITE ALPHA     ARC TAN 45° TEST0085    07 13    X20086    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    ÷0095    06 05    ↓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    ↑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    ↓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   ÷ DIRECT0135    00 03    00030136    04 05   RECALL DIRECT0137    00 02    00020138    04 12   WRITE ALPHA     SKIP if X = 00139    06 11   LOGEe 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/π0148    05 14    GO0149    06 02    X0150    07 04    40151    07 05    50152    04 12   WRITE ALPHA     AVERAGE TANGENT SET0153    06 13   10X0154    06 05    ↓0155    04 12   WRITE ALPHA     SET SIGN0156    05 12   END PROGRAM0157    04 07   SEARCH0158    05 06     INDIRECT0159    04 08   MARK            TRANSFER OF COS θ 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 θ 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    ↑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    ↑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    ÷0224    06 05    ↓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    ÷0244    07 12   DECIMAL POINT0245    07 05    50246    05 07   SKIP IF Y≧X0247    04 07   SEARCH0248    02 00    02000249    05 14    GO             IF LESS THAN 0.5 USE0250    06 05    ↓       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    ÷0267    04 14   STORE Y0268    03 09    03090269    07 07    7              IS BEARING GRADING0270    05 07   SKIP IF Y≧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    ↓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 To0294    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   ↓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    ÷0338    04 05   RECALL DIRECT0339    01 07    01070340    06 03    ÷0341    04 05   RECALL DIRECT0342    03 06    03060343    06 02    X0344    06 06    ↓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 θ0352    07 04    40353    06 03    ÷0354    06 05    ↓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    ↓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    ÷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   ÷ 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    ÷0410    04 05   RECALL DIRECT0411    01 04    01040412    06 03    ÷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   ÷ 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    ÷          (both ln and log)0428    07 01    10429    07 04    40430    07 04    40431    06 02    X0432    06 05    ↓0433    06 11   LOGe X0434    06 04    ↑0435    04 05   RECALL DIRECT0436    02 06    02060437    06 03    ÷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    ÷0450    04 05   RECALL DIRECT0451    00 05    00050452    06 12    ##STR4##0453    06 03    ÷0454    04 05   RECALL DIRECT0455    02 09    02090456    06 03    ÷0457    04 14   STORE Y0458    03 02    03020459    06 05    ↓0460    06 11   LOGe X0461    04 15   RECALL Y0462    03 00    03000463    06 00    +0464    06 05    ↓0465    04 06     DIRECT0466    03 02    03020467    06 10    LOG10 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    ↓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    ↓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    ↓0532    04 12   WRITE ALPHA     MULTIPLY X BY 1020533    07 02    20534    06 08   INTEGER X0535    04 12   WRITE ALPHA     DIVIDE X BY 1020536    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    ↓0549    04 12   WRITE ALPHA     MULTIPLY X BY 1020550    07 02    20551    06 08   INTEGER X0552    04 12   WRITE ALPHA     DIVIDE Y BY 1020553    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    ↓0589    04 12   WRITE ALPHA     MULTIPLY X BY 1010590    07 01    10591    0608   INTEGER X0592    04 12   WRITE ALPHA     DIVIDE X BY 1010593    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 1020601    07 02    20602    05 14    GO0603    06 08   INTEGER X0604    04 12   WRITE ALPHA     DIVIDE X BY 1020605    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    ↓0631    04 12   WRITE ALPHA     DIVIDE X BY 1010632    04 01   - DIRECT0633    06 08   INTEGER X0634    04 12   WRITE ALPHA     MULTIPLY X BY 1010635    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.