Determining resistivity of a formation adjacent to a borehole having casing using multiple electrodes and with resistances being defined between the electrodes

Methods of operation of different types of multiple electrode apparatus vertically disposed in a cased well to measure information related to the resistivity of adjacent geological formations from inside the cased well. The multiple electrode apparatus have a minimum of three spaced apart voltage measurement electrodes that electrically engage the interior of the cased well. Measurement information is obtained related to current which is caused to flow from the cased well into the adjacent geological formation. First compensation information is obtained related to a first casing resistance between a first pair of the spaced apart voltage measurement electrodes. Second compensation information is obtained related to a second casing resistance between a second pair of the spaced apart voltage measurement electrodes. The measurement information, and first and second compensation information are used to determine a magnitude related to the adjacent formation resistivity.

This invention provides improved methods and apparatus for measurement of 
the electronic properties of formations such as the resistivities, 
polarization phenomena, and dielectric constants of geological formations 
and cement layers adjacent to cased boreholes and for measuring the skin 
effect of the casing present. The terms "electronic properties of 
formations" and "electrochemical properties of formations" are used 
interchangeably herein. 
The oil industry has long sought to measure resistivity through casing. 
Such resistivity measurements, and measurements of other electrochemical 
phenomena, are useful for at least the following purposes: locating 
bypassed oil and gas; reservoir evaluation; monitoring water floods; 
measuring quantitative saturations; cement evaluation; permeability 
measurements; and measurements through a drill string attached to a 
drilling bit. Therefore, measurements of resistivity and other 
electrochemical phenomena through metallic pipes, and steel pipes in 
particular, are an important subject in the oil industry. Many U.S. 
patents have issued in the pertinent Subclass 368 of Class 324 of the 
United States Patent and Trademark Office which address this subject. The 
following presents a brief description of the particularly relevant prior 
art presented in the order of descending relative importance. 
U.S. patents which have already issued to the inventor in this field are 
listed as follows: U.S. Pat. No. 4,820,989 (Ser. No. 06/927,115); U.S. 
Pat. No. 4,882,542 (Ser. No. 07/089,697); U.S. Pat. No. 5,043,688 (Ser. 
No. 07/435,273); U.S. Pat. No. 5,043,669 (Ser. No. 07/438,268); U.S. Pat. 
No. 5,075,626 (Ser. No. 07/434,886); U.S. Pat. No. 5,187,440 (Ser. No. 
07/749,136); and Ser. No. 07/754,965 that issued as U.S. Pat. No. 
5,223,794 on Jun. 29, 1993. These seven U.S. Patents are collectively 
identified as "the Vail Patents" herein. 
The apparatus and methods of operation herein disclosed are embodiments of 
the Through Casing Resistivity Tool.TM. that is abbreviated TCRT.TM.. The 
Through Casing Resistivity Tool.TM. and TCRT.RTM. are Trademarks of 
ParaMagnetic Logging, Inc. in the United States Patent and Trademark 
Office. ParaMagnetic Logging, Inc. has its principal place of business 
located at 18730 - 142nd Avenue N. E., Woodinville, Wash., 98072, USA, 
having telephone number (206) 481-5474. 
An important paper concerning the Through Casing Resistivity Tool was 
published recently. Please refer to the article entitled "Formation 
Resistivity Measurements Through Metal Casing", having authors of W. B. 
Vail, S. T. Momii of ParaMagnetic Logging, Inc., R. Woodhouse of Petroleum 
and Earth Science Consulting, M. Alberty and R. C. A. Peveraro of BP 
Exploration, and J. D. Klein of Arco Exploration and Production Technology 
which appeared as Paper "F", Volume I, in the Transactions of the SPWLA 
Thirty-Fourth Annual Logging Symposium, Calgary, Alberta, Canada, Jun. 
13-16, 1993, sponsored by The Society of Professional Well Log Analysts, 
Inc. of Houston, Tex. and the Canadian Well Logging Society of Calgary, 
Alberta, Canada (13 pages of text and 8 additional figures). Experimental 
results are presented therein which confirm that the apparatus and methods 
disclosed in Ser. No. 07/434,886 that is U.S. Pat. No. 5,075,626 actually 
work in practice to measure the resistivity of geological formations 
adjacent to cased wells. To the author's knowledge, the SPWLA paper 
presents the first accurate measurements of resistivity obtained from 
within cased wells using any previous experimental apparatus. 
Other recent articles appearing in various publications concerning the 
Through Casing Resistivity Tool and/or the Vail Patents include the 
following: (A) in an article entitled "Electrical Logging: 
State-of-the-Art" by Robert Maute of the Mobil Research and Development 
Corporation, in The Log Analyst, Vol. 33, No. 3, May-June 1992 page 
212-213; and (B) in an article entitled "Through Casing Resistivity Tool 
Set for Permian Use" in Improved Recovery Week, Volume 1, No. 32, Sep. 28, 
1992. 
The Vail Patents describe the various embodiments of the Through Casing 
Resistivity Tool (TCRT). Many of these Vail Patents describe embodiments 
of apparatus having three or more spaced apart voltage measurement 
electrodes which engage the interior of the casing, and which also have 
calibration means to calibrate for thickness variations of the casing and 
for errors in the placements of the voltage measurement electrodes. 
U.S. Pat. No. 4,796,186 which issued on Jan. 3, 1989 to Alexander A. 
Kaufman entitled "Conductivity Determination in a Formation Having a Cased 
Well" also describes apparatus having three or more spaced apart voltage 
measurement electrodes which engage the interior of the casing and which 
also have calibration means to calibrate for thickness variations in the 
casing and for errors in the placements of the electrodes. This patent has 
been assigned to ParaMagnetic Logging, Inc. of Woodinville, Wash. In 
general, different methods of operation and analysis are described in the 
Kaufman Patent compared to the Vail Patents cited above. 
U.S. Pat. No. 4,837,518 which issued on Jun. 6, 1989 to Michael F. Gard, 
John E. E. Kingman, and James D. Klein, assigned to the Atlantic Richfield 
Company, entitled "Method and Apparatus for Measuring the Electrical 
Resistivity of Geologic Formations Through Metal Drill Pipe or Casing", 
predominantly describes two voltage measurement electrodes and several 
other current introducing electrodes disposed vertically within a cased 
well which electrically engage the wall of the casing, henceforth 
referenced as "the Arco Patent". However, the Arco Patent does not 
describe an apparatus having three spaced apart voltage measurement 
electrodes and associated electronics which takes the voltage differential 
between two pairs of the three spaced apart voltage measurement electrodes 
to directly measure electronic properties adjacent to formations. Nor does 
the Arco Patent describe an apparatus having at least three spaced apart 
voltage measurement electrodes wherein the voltage drops across adjacent 
pairs of the spaced apart voltage measurement electrodes are 
simultaneously measured to directly measure electronic properties adjacent 
to formations. Therefore, the Arco Patent does not describe the methods 
and apparatus disclosed herein. 
USSR Patent No. 56,026, which issued on Nov. 30, 1939 to L. M. Alpin, 
henceforth called the "Alpin Patent", which is entitled "Process of the 
Electrical Measurement of Well Casings", describes an apparatus which has 
three spaced apart voltage measurement electrodes which positively engage 
the interior of the casing. However, the Alpin Patent does not have any 
suitable calibration means to calibrate for thickness variations of the 
casing nor for errors related to the placements of the voltage measurement 
electrodes. Therefore, the Alpin Patent does not describe the methods and 
apparatus disclosed herein. 
French Patent No. 2,207,278 having a "Date of Deposit" of Nov. 20, 1972 
(hereinafter "the French Patent") describes apparatus having four spaced 
apart voltage measurement electrodes which engage the interior of borehole 
casing respectively defined as electrodes M, N, K, and L. Various uphole 
and downhole current introducing electrodes are described. Apparatus and 
methods of operation are provided that determines the average resistance 
between electrodes M and L. This French Patent further explicitly assumes 
an exponential current flow along the casing. Voltage measurements across 
pair MN and KL are then used to infer certain geological parameters from 
the assumed exponential current flow along the casing. However, the French 
Patent does not teach measuring a first casing resistance between 
electrodes MN, does not teach measuring a second casing resistance between 
electrodes NK, and does not teach measuring a third casing resistance 
between electrodes KL. The invention herein and other preferred 
embodiments described in the Vail Patents teach that it is of importance 
to measure said first, second, and third resistances to compensate current 
leakage measurements for casing thickness variations and for errors in 
placements of the voltage measurement electrodes along the casing to 
provide accurate measurements of current leakage into formation. Further, 
many embodiments of the Vail Patents do not require any assumption of the 
form of current flow along the casing to measure current leakage into 
formation. Therefore, for these reasons alone, the French Patent does not 
describe the methods and apparatus disclosed herein. There are many other 
differences between various embodiments of the Vail Patents and the French 
Patent which are described in great detail in the Statement of Prior Art 
for Ser. No. 07/754,965 dated Dec. 2, 1991 that is to issue as U.S. Pat. 
No. 5,223,794 on Jun. 29, 1993. 
An abstract of an article entitled "Effectiveness of Resistivity Logging of 
Cased Wells by A Six-Electrode Tool" by N. V. Mamedov was referenced in 
TULSA

The invention is described in three major different portions of the 
specification. In the first major portion of the specification, relevant 
parts of the text in Ser. No. 07/089,697 now U.S. Pat. No. 4,882,542, 
{Vail(542)} are repeated herein which describe apparatus defined in FIGS. 
1, 3, 4, and 5. The second major portion of the specification quotes 
relevant parts of Ser. No. 07/434,886 {Vail(626)} that describe the 
apparatus defined in FIG. 6. The third major portion of the specification 
herein is concerned with providing multi-electrode apparatus and methods 
of operation of the multi-electrode apparatus to measure formation 
resistivity from within cased wells that compensates for casing resistance 
differences and for errors in placements of the various voltage 
measurement electrodes. The definitions provided in FIGS. 1 through 6 are 
used to conveniently define many of the symbols appearing in FIGS. 7 
through 12. 
From a technical drafting point of view, FIGS. 1, 2, 3, 4, and 5 in Ser. 
No. 07/089,697 {Vail(542)}, now U.S. Pat. No. 4,882,542, and in those 
contained in this application are nearly identical. However, the new 
drawings have been re-done using computer graphics and the A-4 
International Size. The following excerpt is taken word-for-word from Ser. 
No. 07/089,697: 
"FIG. 1 shows a typical cased borehole found in an oil field. The borehole 
2 is surrounded with borehole casing 4 which in turn is held in place by 
cement 6 in the rock formation 8. An oil bearing strata 10 exists adjacent 
to the cased borehole. The borehole casing may or may not extend 
electrically to the surface of the earth 12. A voltage signal generator 14 
(SG) provides an A.C. voltage via cable 16 to power amplifier 18 (PA). The 
signal generator represents a generic voltage source which includes 
relatively simple devices such as an oscillator to relatively complex 
electronics such as an arbitrary waveform generator. The power amplifier 
18 is used to conduct A.C. current down insulated electrical wire 20 to 
electrode A which is in electrical contact with the casing. The current 
can return to the power amplifier through cable 22 using two different 
paths. If switch SW1 is connected to electrode B which is electrically 
grounded to the surface of the earth, then current is conducted primarily 
from the power amplifier through cable 20 to electrode A and then through 
the casing and cement layer and subsequently through the rock formation 
back to electrode B and ultimately through cable 22 back to the power 
amplifier. In this case, most of the current is passed through the earth. 
Alternatively, if SW1 is connected to insulated cable 24 which in turn is 
connected to electrode F, which is in electrical contact with the casing, 
then current is passed primarily from electrode A to electrode F along the 
casing for a subsequent return to the power amplifier through cable 22. In 
this case, little current passes through the earth. 
Electrodes C, D, and E are in electrical contact with the interior of 
casing. In general, the current flowing along the casing varies with 
position. For example, current I.sub.C is flowing downward along the 
casing at electrode C, current I.sub.D is flowing downward at electrode D, 
and current I.sub.E is flowing downward at electrode E. In general, 
therefore, there is a voltage drop V1 between electrodes C and D which is 
amplified differentially with amplifier 26. And the voltage difference 
between electrodes D and E, V2, is also amplified with amplifier 28. With 
switches SW2 and SW3 in their closed position as shown, the outputs of 
amplifiers 26 and 28 respectively are differentially subtracted with 
amplifier 30. The voltage from amplifier 30 is sent to the surface via 
cable 32 to a phase sensitive detector 34. The phase sensitive detector 
obtains its reference signal from the signal generator via cable 36. In 
addition, digital gain controller 38 (GC) digitally controls the gain of 
amplifier 28 using cable 40 to send commands downhole. The gain controller 
38 also has the capability to switch the input leads to amplifier 28 on 
command, thereby effectively reversing the output polarity of the signal 
emerging from amplifier 28 for certain types of measurements. 
The total current conducted to electrode A is measured by element 42. In 
the preferred embodiment shown in FIG. 1, the A.C. current used is a 
symmetric sine wave and therefore in the preferred embodiment, I is the 
0-peak value of the A.C. current conducted to electrode A. (The 0-peak 
value of a sine wave is 1/2 the peak-to-peak value of the sine wave.) 
In general, with SW1 connected to electrode B, current is conducted through 
formation. For example, current .DELTA.I is conducted into formation along 
the length 2 L between electrodes C and E. However, if SW1 is connected to 
cable 24 and subsequently to electrode F, then no current is conducted 
through formation to electrode B. In this case, I.sub.C =I.sub.D =I.sub.E 
since essentially little current .DELTA.I is conducted into formation. 
It should be noted that if SW1 is connected to electrode B then the current 
will tend to flow through the formation and not along the borehole casing. 
Calculations show that for 7 inch O.D. casing with a 1/2 inch wall 
thickness that if the formation resistivity is 1 ohm-meter and the 
formation is uniform, then approximately half of the current will have 
flowed off the casing and into the formation along a length of 320 meters 
of the casing. For a uniform formation with a resistivity of 10 
ohm-meters, this length is 1040 meters instead." These lengths are 
respectively called "Characteristic Lengths" appropriate for the average 
resistivity of the formation and the type of casing used. A Characteristic 
Length is related to the specific length of casing necessary for 
conducting on approximately one-half the initial current into a particular 
geological formation as described below. 
One embodiment of the invention described in Ser. No. 07/089,697 
{Vail(542)}, now U.S. Pat. No. 4,882,542, provides a preferred method of 
operation for the above apparatus as follows: "The first step in measuring 
the resistivity of the formation is to "balance" the tool. SW1 is switched 
to connect to cable 24 and subsequently to electrode F. Then A.C. current 
is passed from electrode A to electrode F thru the borehole casing. Even 
though little current is conducted into formation, the voltages V1 and V2 
are in general different because of thickness variations of the casing, 
inaccurate placements of the electrodes, and numerous other factors. 
However, the gain of amplifier 28 is adjusted using the gain controller so 
that the differential voltage V3 is nulled to zero. (Amplifier 28 may also 
have phase balancing electronics if necessary to achieve null at any given 
frequency of operation.) Therefore, if the electrodes are subsequently 
left in the same place after balancing for null, spurious effects such as 
thickness variations in the casing do not affect the subsequent 
measurements. 
With SW1 then connected to electrode B, the signal generator drives the 
power amplifier which conducts current to electrode A which is in 
electrical contact with the interior of the borehole casing. A.C. currents 
from 1 amp o-peak to 30 amps o-peak at a frequency of typically 1 Hz are 
introduced on the casing here. The low frequency operation is limited by 
electrochemical effects such as polarization phenomena and the invention 
can probably be operated down to 0.1 Hz and the resistivity still properly 
measured. The high frequency operation is limited by skin depth effects of 
the casing, and an upper frequency limit of the invention is probably 20 
Hz for resistivity measurements. Current is subsequently conducted along 
the casing, both up and down the casing from electrode A, and some current 
passes through the brine saturated cement surrounding the casing and 
ultimately through the various resistive zones surrounding the casing. The 
current is then subsequently returned to the earth's surface through 
electrode B." 
Quoting further from Ser. No. 07/089,697 {Vail(542)}, now U.S. Pat. No. 
4,882,542: "FIG. 2 shows the differential current conducted into formation 
.DELTA.I for different vertical positions z within a steel cased borehole. 
Z is defined as the position of electrode D in FIG. 1. It should be noted 
that with a voltage applied to electrode A and with SW1 connected to 
electrode B that this situation consequently results in a radially 
symmetric electric field being applied to the formation which is 
approximately perpendicular to the casing. The electrical field produces 
outward flowing currents such as .DELTA.I in FIG. 1 which are inversely 
proportional to the resistivity of the formation. Therefore, one may 
expect discontinuous changes in the current .DELTA.I at the interface 
between various resistive zones particularly at oil/water and oil/gas 
boundaries. For example, curve (a) in FIG. 2 shows the results from a 
uniform formation with resistivity .rho..sub.1. Curve (b) shows departures 
from curve (a) when a formation of resistivity .rho..sub.2 and thickness 
T.sub.2 is intersected where .rho..sub.2 is less than .rho..sub.1. And 
curve (c) shows the opposite situation where a formation is intersected 
with resistivity .rho..sub.3 which is greater than .rho..sub.1 which has a 
thickness of T.sub.3. It is obvious that under these circumstances, 
.DELTA.I.sub.3 is less than .DELTA.I.sub.1, which is less than 
.DELTA.I.sub.2. 
FIG. 3 shows a detailed method to measure the parameter Vo. Electrodes A, 
B, C, D, E, and F have been defined in FIG. 1. All of the numbered 
elements 2 through 40 have already been defined in FIG. 1. In FIG. 3, the 
thickness of the casing is .tau..sub.1, the thickness of the cement is 
.tau..sub.2, and d is the diameter of the casing. Switches SW1, SW2, and 
SW3 have also been defined in FIG. 1. In addition, electrode G is 
introduced in FIG. 3 which is the voltage measuring reference electrode 
which is in electrical contact with the surface of the earth. This 
electrode is used as a reference electrode and conducts little current to 
avoid measurement errors associated with current flow. 
In addition, SW4 is introduced in FIG. 3 which allows the connection of 
cable 24 to one of the three positions: to an open circuit; to electrode 
G; or to the top of the borehole casing. And in addition in FIG. 3, 
switches SW5, SW6, and SW7 have been added which can be operated in the 
positions shown. (The apparatus in FIG. 3 can be operated in an identical 
manner as that shown in FIG. 1 provided that switches SW2, SW5, SW6, and 
SW7 are switched into the opposite states as shown in FIG. 3 and provided 
that SW4 is placed in the open circuit position.) 
With switches SW2, SW5, SW6, and SW7 operated as shown in FIG. 3, then the 
quantity Vo may be measured. For a given current I conducted to electrode 
A, then the casing at that point is elevated in potential with respect to 
the zero potential at a hypothetical point which is an "infinite" distance 
from the casing. Over the interval of the casing between electrodes C, D, 
and E in FIG. 3, there exists an average potential over that interval with 
respect to an infinitely distant reference point. However, the potential 
measured between only electrode E and electrode G approximates Vo provided 
the separation of electrodes A, C, D, and E are less than some critical 
distance such as 10 meters and provided that electrode G is at a distance 
exceeding another critical distance from the casing such as 10 meters from 
the borehole casing. The output of amplifier 28 is determined by the 
voltage difference between electrode E and the other input to the 
amplifier which is provided by cable 24. With SW1 connected to electrode 
B, and SW4 connected to electrode G, cable 24 is essentially at the same 
potential as electrode G and Vo is measured appropriately with the phase 
sensitive detector 34. In many cases, SW4 may instead be connected to the 
top of the casing which will work provided electrode A is beyond a 
critical depth . . . ". 
Quoting further from Ser. No. 07/089,697 {Vail(542)}, now U.S. Pat. No. 
4,882,542: "For the purposes of precise written descriptions of the 
invention, electrode A is the upper current conducting electrode which is 
in electrical contact with the interior of the borehole casing; electrode 
B is the current conducting electrode which is in electrical contact with 
the surface of the earth; electrodes C, D, and E are voltage measuring 
electrodes which are in electrical contact with the interior of the 
borehole casing; electrode F is the lower current conducting electrode 
which is in electrical contact with the interior of the borehole casing; 
and electrode G is the voltage measuring reference electrode which is in 
electrical contact with the surface of the earth. 
Furthermore, V.sub.o is called the local casing potential. An example of an 
electronics difference means is the combination of amplifiers 26, 28, and 
30. The differential current conducted into the formation to be measured 
is .DELTA.I." The differential voltage is that voltage in FIG. 1 which is 
the output of amplifier 30 with SW1 connected to electrode B and with all 
the other switches in the positions shown. 
Further quoting from Ser. No. 07/089,697 {Vail(542)}, now U.S. Pat. No. 
4,882,542: "FIG. 4 is nearly identical to FIG. 1 except the electrodes C 
and D are separated by length L.sub.1, electrodes D and E are separated by 
L.sub.2, electrodes A and C are separated by L.sub.3 and electrodes E and 
F are separated by the distance L.sub.4. In addition, r.sub.1 is the 
radial distance of separation of electrode B from the casing. And Z is the 
depth from the surface of the earth to electrode D. FIG. 5 is nearly 
identical to FIG. 3 except here too the distances L.sub.1, L.sub.2, 
L.sub.3, L.sub.4, r.sub.1, and Z are explicitly shown. In addition, 
r.sub.2 is also defined which is the radial distance from the casing to 
electrode G. As will be shown explicitly in later analysis, the invention 
will work well if L.sub.1 and L.sub.2 are not equal. And for many types of 
measurements, the distances L.sub.3 and L.sub.4 are not very important 
provided that they are not much larger in magnitude than L.sub.1 and 
L.sub.2." 
FIG. 6 was first described in Ser. No. 07/434,886 {Vail(626)} which states: 
"For the purpose of logical introduction, the elements in FIG. 6 are first 
briefly compared to those in FIGS. 1-5. Elements No. 2, 4, 6, 8, and 10 
have already been defined. Electrodes A, B, C, D, E, F, G and the 
distances L.sub.1, L.sub.2, L.sub.3, and L.sub.4 have already been 
described. The quantities .delta.i.sub.1 and .delta.i.sub.2 have already 
been defined in the above text. Amplifiers labeled with legends A1, A2, 
and A3 are analogous respectively to amplifiers 26, 28, and 30 defined in 
FIGS. 1, 3, 4, and 5. In addition, the apparatus in FIG. 6 provides for 
the following: 
(a) two signal generators labeled with legends "SG 1 at Freq F(1)" and "SG 
2 at Freq F(2)"; 
(b) two power amplifiers labeled with legends "PA 1" and "PA 2"; 
(c) a total of 5 phase sensitive detectors defined as "PSD 1", "PSD 2", 
"PSD 3", "PSD 4", and "PSD 5", which respectively have inputs for 
measurement labeled as "SIG", which have inputs for reference signals 
labeled as "REF", which have outputs defined by lines having arrows 
pointing away from the respective units, and which are capable of 
rejecting all signal voltages at frequencies which are not equal to that 
provided by the respective reference signals; 
(d) an "Error Difference Amp" so labeled with this legend in FIG. 6; 
(e) an instrument which controls gain with voltage, typically called a 
"voltage controlled gain", which is labeled with legend "VCG"; 
(f) an additional current conducting electrode labeled with legend "H" 
(which is a distance L.sub.5 --not shown--above electrode A); 
(g) an additional voltage measuring electrode labeled with legend J (which 
is a distance L.sub.6 --not shown--below electrode F); 
(h) current measurement devices, or meters, labeled with legends "I1" and 
"I2"; 
(i) and differential voltage amplifier labeled with legend "A4" in FIG. 6." 
Ser. No. 07/434,886 {Vail(626)}, now U.S. Pat. No. 5,075,626, further 
describes various cables labeled with legends respectively 44, 46, 48, 50, 
52, 54, 56, 58, 60, 62, and 64 whose functions are evident from FIG. 6. 
Ser. No. 07/434,886 {Vail)626)}, now U.S. Pat. No. 5,075,626, further 
states: "The outputs of PSD 1, 2, 3, and 4 are recorded on a digital 
recording system 70 labeled with legend "DIG REC SYS". The respective 
outputs of the phase sensitive detectors are connected to the respective 
inputs of the digital recording system in FIG. 6 according to the legends 
labeled with numbers 72, 74, 76, 78, and 80. One such connection is 
expressly shown in the case of element no. 72." 
Ser. No. 07/434,886 {Vail(626)}, now U.S. Pat. No. 5,075,626, teaches in 
great detail that it is necessary to accurately measure directly, or 
indirectly, the resistance between electrodes C-D (herein defined as "R1") 
and the resistance between electrodes D-E (herein defined as "R2") in 
FIGS. 1, 3, 4, 5 and 6 to precisely measure current leakage into formation 
and formation resistivity from within the cased well. Please refer to 
Equations 1-33 in Ser. No. 07/434,886 {Vail(626)}, now U.S. Pat. No. 
5,075,626, for a thorough explanation of this fact. The parent 
application, Ser. No. 06/927,115 {Vail(989)}, now U.S. Pat. No. 4,820,989, 
and the following Continuation-in-Part application Ser. No. 07/089,697 
{Vail(542)}, now U.S. Pat. No. 4,882,542, taught that measurement of the 
resistance of the casing between voltage measurement electrodes that 
engage the interior of the casing are very important to measure formation 
resistivity from within the casing. 
Using various different experimental techniques that result in current flow 
along the casing between current conducting electrodes A and F in FIGS. 1, 
3, 4, 5, and 6 result in obtaining first compensation information related 
to a first casing resistance defined between voltage measurement 
electrodes C and D. Similarly, using various different experimental 
techniques that result in current flow along the casing between current 
conducting electrodes A and F in FIGS. 1, 3, 4, 5, and 6 result in 
obtaining second compensation information related to a second casing 
resistance between voltage measurement electrodes D and E. FIGS. 1, 3, 4, 
5, and 6 all provide additional means to cause current to flow into 
formation, and the measurements performed while current is flowing into 
the formation is called the measurement information related to current 
flow into formation. Such measurement information is used to determine a 
magnitude relating to formation resistivity. FIGS. 7-12 in the remaining 
application also provide various means to provide measurement information, 
and respectively first and second compensation information, along with 
additional information in several cases. 
FIG. 7 is closely related to FIG. 6. However, in FIG. 7, amplifier A3 that 
is shown in FIG. 6, which can be either downhole, or uphole, has been 
removed. Further, the Error Difference Amp, cable 60, and the VCG have 
also been removed. In FIG. 7, the output of amplifier A1 at frequency F(1) 
is measured by PSD 4 and the output of amplifier A1 at frequency F(2) is 
measured by PSD 2--as was the case in FIG. 6. However, in FIG. 7, the 
output of amplifier A2 at F(1) is measured by PSD 1 and the output of 
amplifier A2 at F(2) is measured by PSD 3. In FIG. 7, current at the 
frequency of F(1) is conducted into formation resulting in measurement 
information being obtained from PSD 1 and PSD 4. Current at the frequency 
of F(2) is caused to flow along the casing between electrodes H and F to 
provide compensation for casing thickness variations and to provide 
compensation for errors in the placement of the voltage measurement 
electrodes. First compensation information related to the casing 
resistance between electrodes C and D is obtained from PSD 2. Second 
compensation information related to the casing resistance between 
electrodes D and E is obtained from PSD 3. Analogous algebra exists for 
the operation of the apparatus in FIG. 7 to Equations 1-33 in Ser. No. 
07/434,886, now U.S. Pat. No. 5,075,626, {Vail(626)} that provides 
compensation for casing resistance differences and for errors of 
placements of the three spaced apart voltage measurement electrodes C, D, 
and E. 
FIG. 8 is similar to FIG. 7 except that electrode D in FIG. 7 has been 
intentionally divided into two separate electrodes D1 and D2. D1 and D2 do 
not overlap and are separated by a distance L9. Electrodes C and D1 are 
separated by distance L1*. Electrodes D2 and E are separated by the 
distance L2*. If D(1) and D(2) overlap, then the invention has the usual 
configuration described in FIGS. 1, 3, 4, 5, 6, and 7. Then consider the 
situation wherein electrodes D(1) and D(2) do not overlap. Suppose they 
are separated by 1 inch. Then suppose that the separation distance between 
C to D(1) is 20 inches and suppose that the separation distance between 
D(2) to E is also 20 inches. Then clearly, the invention will still work, 
although there will be some error in the current leakage measurement 
caused by the lack of measurement information from the 1 inch segment. 
Perhaps the error shall be on the order of 1 inch divided by 20 inches, or 
on the order of an approximate 5% error. FIG. 8 shows an apparatus having 
four spaced apart voltage measurement electrodes that compensates for 
casing thickness variations and for errors in placements of electrodes by 
providing measurements of the casing resistance R1 between electrodes C 
and D1 at the frequency of F(2) by PSD 2 and by providing measurements of 
the casing resistance R2 between electrodes D2 and E at the frequency F(2) 
by PSD 3. 
FIG. 8 may be operated in a particularly simple manner. The signal between 
electrodes C-D1 can be used to control current flowing along the casing at 
the frequency F(1) (by using electronics, not shown, of the type used to 
control currents in FIG. 6). Then the signal between electrodes D2-E can 
be used to measure information related to current flow along the casing 
and into the formation at the frequency of F(1). Despite the fact that 
electrodes C-D1 are used to "control current", nonetheless, the apparatus 
so described requires at least 3 spaced apart voltage measurement 
electrodes and is therefore another embodiment of the invention herein. 
FIG. 9 shows certain changes to the apparatus defined in FIG. 8. Changes 
from FIG. 8 includes cables 88 and 90 that are meant to convey signals to 
the appropriate phase sensitive detectors shown in FIG. 8 for the purposes 
of simplicity; extra variable resistor labeled with legend "VR1" placed in 
series with current meter labeled with legend "I1" connected to cable 92 
that provides current at the frequency of F(1) to the upper current 
conducting electrode here defined as A1; extra variable resistor labeled 
with legend "VR2" placed in series with another current meter labeled with 
legend "I3" connected to cable 94 that provides current at the frequency 
of F(1) to new electrode A2. Electrodes H and F are shown connected to 
cables 98 and 100 respectively which operate as shown in FIG. 8, but many 
of the details are omitted in FIG. 9 in the interest of simplicity. In 
FIG. 9, current at the frequency of F(2) is passed between electrodes H 
and F as in FIG. 8 which provides first compensation information related 
to current flow through the casing resistance ("R1") between electrodes 
C-D1 and second compensation information related to current flow through 
the casing resistance ("R2") between electrodes D2-E, although many of the 
details are not shown in FIG. 9 for the purposes of simplicity. The 
purpose of electrodes A1 and A2 in FIG. 9 are to provide simultaneously 
upward and downward flowing currents along the casing at the frequency of 
F(1). Such simultaneously upward and downward flowing currents along the 
casing are hereinafter defined as "counter-flowing currents". Such 
counter-flowing currents in the vicinity of the voltage measurement 
electrodes C, D1, D2, and E minimize the "common mode signal" input to the 
amplifiers A1 and A2. Therefore, the signal output of amplifiers A1 and A2 
in the presence of such counter-flowing currents tends to be more 
responsive to the current actually flowing into formation and less 
responsive to the relatively larger currents flowing along the casing. 
Other apparatus showing methods of introducing counter-flowing currents on 
the casing include FIGS. 22 and 23 of Ser. No. 07/089,697 , now U.S. Pat. 
No. 4,882,542, {Vail(542)}. The current actually flowing into the 
formation at the frequency of F(1) generates voltages across amplifiers A1 
and A2 responsive to the current flow into formation that results in 
measurement information at the frequency of F(1) from phase sensitive 
detectors as shown in FIG. 8. That measurement information is used to 
determine a magnitude relating to formation resistivity, including 
information related to the resistivity of the adjacent geological 
formation. 
FIG. 10 improves the measurement accuracy of the apparatus defined in FIG. 
9. FIG. 10 is similar to FIG. 9 except that in FIG. 10 extra voltage 
measurements P, Q, R, and S have been added. The purpose of additional 
voltage measurement electrodes P and Q are to sense the current flowing 
along the casing at the frequency of F(1) between P and Q. Further 
electronics, not shown, are used to control the variable resistor VR1 such 
that the current flowing along the casing remains relatively constant at 
the frequency of F(1). Please recall that electrodes H and F are used to 
conduct current along the casing at the frequency of F(2) and therefore, 
measurements of the potential difference between P and Q can be used to 
measure the casing resistance between P and Q that is called "R3" which is 
therefore used as necessary information to keep the current flowing at the 
frequency F(1) through R3. FIG. 6 has already provided means to maintain 
equality of currents flowing along the casing, and similar apparatus can 
be adapted herein to maintain the equality of current flow at the 
frequency of F(1) between P and Q. Similarly comments can be made 
regarding new electrodes R and S which can be used to keep the current 
flowing along the casing at the frequency of F(1) constant through the 
casing resistance between electrodes R and S, that is "R4" by controlling 
the variable resistor VR2. If the current flowing through R3 at F(1) is 
held constant as the device vertically logs the well, then that shall 
serve to minimize the influence of the lack of information caused by the 
separation of electrodes D1 and D2. Similarly, if the current flowing 
through R4 at F(1) is held constant, that too serves to minimize the 
influence of the lack of information caused by the separation between 
electrodes D1 and D2. Consequently, extra current control means have been 
provided to control the current flow along the casing at the F(1) to 
minimize the influence of the lack of information from portions of the 
casing having no voltage measurement electrodes present. With suitably 
added amplifiers, these new electrode pairs can be used to independently 
monitor the counter-flowing currents at the measurement frequency at the 
positions shown. In particular, electrode pairs P-Q and R-S can be 
provided with amplifiers and feedback circuitry that drives the currents 
to A1 and A2 such that the counter-flowing current at the measurement 
frequency (for example, 1 Hz) is driven near zero across the voltage 
measurement electrodes C-D1 and D2-E. Regardless of the details of 
operation chosen however, the invention disclosed in FIG. 10 provides four 
spaced electrodes means that provides measurement information related to 
current flow into formation, and respectively, first and second 
compensation information related to measurements of R1 and R2 between 
respectively electrodes C-D, and D-E that are used to determine a 
magnitude related to formation resistivity. Altogether, FIG. 10 shows a 
total of 8 each voltage measurement electrodes operated as pairs of 
voltage measurement electrodes. 
FIG. 11 is similar to FIG. 10 except that electrodes D1 and D2 have been 
re-combined back into one single electrode D herein. However, the extra 
potential voltage measurement electrodes P-Q, and R-S remain in FIG. 11 to 
maintain equality of the magnitude of the counter-flowing currents along 
the casing at the frequency of F(1). Maintaining the equality of 
counter-flowing currents along the casing at F(1), and ideally causing the 
counter-flowing currents to approach the limit of zero net current flowing 
up or down the casing at the frequency of F(1) will result in improved 
measurement accuracy. Regardless of the details of operation chosen 
however, the invention disclosed in FIG. 11 provides a minimum of 3 spaced 
electrodes means that provides measurement information related to current 
flow into formation, and respectively, first and second compensation 
information related to measurements of R1 and R2 between respectively 
electrodes C-D, and D-E that are used to determine a magnitude related to 
formation resistivity. Altogether, FIG. 11 shows a total of 7 each voltage 
measurement electrodes operated as 4 pairs of voltage measurement 
electrodes. 
FIG. 12 is similar to FIG. 11 except that the extra potential voltage 
measurement electrodes P-Q and R-S have been removed. It should be noted 
that the apparatus defined in FIG. 12 results in knowledge of the 
measurement current leaking into formation, knowledge of the resistance R1 
between voltage measurement electrodes C-D, and the knowledge of the 
resistance R2 between voltage measurement electrodes D-E. Therefore, the 
apparatus in FIG. 12 provides knowledge of the net current at F(1) flowing 
through resistor R1 between electrodes C-D. Similarly, the apparatus in 
FIG. 12 provides knowledge of the net current at F(1) flowing through 
resistor R2 between electrodes D-E. Extra control circuitry, not shown, 
can be adapted as in FIG. 6 to minimize the net counter-flowing currents 
flowing by the combined resistors R1 and R2 to improve measurement 
accuracy. Regardless of the details of operation chosen however, the 
invention disclosed in FIG. 12 provides a minimum of 3 spaced apart 
electrode means that provide measurement information related to current 
flow into formation, and respectively, first and second compensation 
information related to measurements of R1 and R2 between respectively 
electrodes C-D, and D-E that are used to determine a magnitude related to 
formation resistivity. 
The apparatus in FIG. 12 may be operated in a particularly simple manner. 
Information from pair C-D can be used to control the magnitude of the 
current flowing along the casing at the frequency of F(1), and keep it 
constant. Then information from pair D-E can be used to infer geophysical 
parameters from measurements of the current at the frequency of F(1). 
Despite the fact that the first pair C-D is used primarily herein "to 
control current", the apparatus so described nonetheless requires 3 spaced 
apart voltage measurement electrodes which engage the interior of the 
casing and is therefore simply another embodiment of the invention herein. 
FIG. 13 is functionally identical to FIG. 26 from Ser. No. 07/089,697 that 
is U.S. Pat. No. 4,882,542, showing an apparatus having multiple voltage 
measurement electrodes engaging the interior of the casing that is marked 
with the legend "Prior Art". Individual potential voltage measurement 
electrodes k, l, m, n, o, p, q, r, s, and t electrically engage the 
casing. In principle, any total number Z of such potential voltage 
measuring electrodes can be made to electrically engage the interior of 
the casing. During the calibration step described in Vail(542), current is 
passed along the casing resulting in the knowledge of the respective 
casing resistances between each potential voltage measurement electrode. 
The casing resistance between electrodes k and l is defined herein as 
R(k,l). The casing resistance between electrodes l and m is defined herein 
as R(l,m). The casing resistance between m and n is defined herein R(m,n). 
The casing resistance between n and o is defined herein as R(n,o). By 
analogy, the casing resistances R(o,p), R(p,q), R(q,r), R(r,s) and R(s,t) 
are defined herein. In principle, any number of casing resistances can be 
defined for any number Z of electrodes which electrically engage the 
interior of the casing. The distance along the casing between electrodes k 
and l is defined herein as L(k,l). The distance along the casing between 
electrodes l and m is defined herein as L(l,m). The distance along the 
casing between electrodes m and n is defined herein as L(m,n). The 
distance along the casing between electrodes n and o is defined herein as 
L(n,o). By analogy, the distances of separation of appropriate electrodes 
are defined herein as L(o,p), L(p,q), L(q,r), L(r,s,) and L(s,t). In 
principle, any number of distances can be defined between any number Z 
electrodes which electrically engage the interior of the casing. The 
distance of separation between electrodes can be chosen to be any 
distance. They may be chosen to be equal or they can be chosen not to be 
equal, depending upon chosen function. For example, L(k,l) can be chosen 
to be 3 inches. L(l,m) can be chosen to be 6 inches. L(m,n) can be chosen 
to be 12 inches. L(n,o) can be chosen to be 20 inches. L(o,p) can be 
chosen to be 52 inches. L(p,q) can be chosen to be 60 inches. L(q,r) can 
be chosen to be 120 inches. Further, electrodes s and t can be 
disconnected. Such an array can measure the potential voltage distribution 
along the casing or the potential voltage profile along the casing in 
response to calibration currents primarily flowing along the casing and in 
response to the measurement currents flowing along the casing and into the 
formation. The calibration current can be at chosen to be the same 
frequency as the measurement current as originally described in Vail(989) 
or can be at a different frequency as described in Vail(626). The above 
described variable spacing can be used to infer the vertical and radial 
variations of the geological formation, the vertical distribution of 
geological beds, and other geological information. Regardless of the 
details of operation chosen however, the invention disclosed in FIG. 13 
provides a minimum of 3 spaced apart voltage measurement electrode means 
that provide measurement information related to current flow into 
formation, and respectively, first and second compensation information 
related to measurements of at least two casing resistances respectively 
between the three voltage measurement electrodes, wherein said measurement 
information and the first and second compensation information are used to 
determine a magnitude related to formation resistivity. FIG. 12 and the 
text herein further shows that a plurality of spaced apart electrodes 
along the casing, which may be chosen to be spaced at various different 
intervals, provide multiple measurements of quantities related to current 
flow into formation, and provide multiple measurements of the resistances 
of the casing spanned by the particular number of chosen spaced apart 
electrodes that may be used to infer geophysical information including the 
resistivity of the adjacent formation. 
It should also be noted that Ser. No. 07/089,697, now U.S. Pat. No. 
4,882,542, describes many different means to measure voltage profiles on 
the casing including those shown in FIG. 25, 26, 27, 28, and 29 therein. 
Those drawings describe several other apparatus geometries having multiple 
electrodes. 
Various embodiments of the invention herein provide many different manners 
to introduce current onto the casing, a portion of which is subsequently 
conducted through formation. Various embodiments herein provide many 
different methods to measure voltage levels at a plurality of many points 
on the casing to provide a potential voltage profile along the casing 
which may be interpreted to measure the current leaking off the exterior 
of the casing from within a finite vertical section of the casing. 
Regardless of the details of operation chosen however, the invention 
herein disclosed provides a minimum of 3 spaced apart voltage measurement 
electrode means that provides measurement information related to current 
flow into the geological formation, and respectively, first and second 
compensation information related to measurements of at least two separate 
casing resistances between the three spaced apart voltage measurement 
electrodes, wherein the measurement information and the first and second 
compensation information are used to determine a magnitude related to 
formation resistivity. 
While the above description contains many specificities, these should not 
be construed as limitations on the scope of the invention, but rather as 
exemplification of preferred embodiments thereto. As has been briefly 
described, there are many possible variations. Accordingly, the scope of 
the invention should be determined not only by the embodiments 
illustrated, but by the appended claims and their legal equivalents.