CA2037563C - Electronic measurement apparatus movable in a cased borehole and compensating for casing resistance differences - Google Patents

Abstract

The invention describes new methods of operation of an apparatus having at least two pairs of voltage measurement electrodes vertically disposed in a cased well to measure the resistivity of adjacent geological formations from inside the cased well. During stationary measurements with the apparatus at a fixed vertical depth within the cased well, the invention herein discloses methods of operation which include a measurement step and subsequent first and second compensation steps respectively resulting in improved accuracy of measurement. The invention also discloses multiple frequency methods of operation resulting in improved accuracy of measurement while the apparatus is simultaneously moved vertically in the cased well. The multiple frequency methods of operation disclose a first A.C. current having a first frequency that is conducted from the casing into formation and a second A.C. current having a second frequency that is conducted along the casing. The multiple frequency methods of operation simultaneously provide the measurement step and two compensation steps necessary to acquire accurate results while the apparatus is moved vertically in the cased well.

Description

An Electronic Measurement Apparatus Movable In A Cased Borehole and Compensating for Casing Resistance Differences , This invention was made with co-funded financial support from: (a) U.S. Department of Energy (DOE) Grant No. DE-FG19-88BC14243 entitled "Proof of Feasibility of Thru Casing Resistivity Technology"; and (b) Gas Research Institute (GRI) Contract No. 5088-212-1664 entitled "Proof of Feasibility of the Through Casing Resistivity Technology". The U.S. government and the GRI have certain rights in this invention.

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 methods disclosed in the application provide for improved measurement accuracy in the presence of corroded casing while performing stationary measurements within cased wells. Furthermore, apparatus and methods are disclosed which enable such improved measurements to be performed while the apparatus is being moved vertically in cased wells which is typically desirable in the industry.
The oil industry has long sought to measure resistivity through casing. Such resistivity measurements, and measurement 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. Patent No. 4,820,989 issued to the inventor, and' U.S. Patent 4,882,542 issued to the inventor, are henceforth to be referenced together as the "Vail patents". These Vail patents predominantly describe apparatus having two pairs of voltage measurement electrodes which engage the interior of the casing, and which have a calibration means to calibrate for thickness variations and errors in the placements of the electrodes.
The detailed descriptions of several particular methods of operation which are disclosed in the Vail patents have certain limitations in.measurement accuracy due to "second order errors" that will be described in detail in the remaining portion of the application. Furthermore, while the Vail patents do, briefly discuss taking data while moving in the well, the application herein provides detailed methods and apparatus for that purpose.
U.S. Patent No. 4,796,186 which issued on January 3, 1989 to Alexander A. Kaufman entitled "Conductivity Determination in a Formation Having a Cased Well" also mostly describes apparatus having two pairs of 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. In general, different methods of operation are described in the Kaufman patent compared to the Vail patents cited above. The particular methods of 'operation in the Kaufman patent do not thoroughly describe how~to eliminate all types of "second order errors", nor does the Kaufman patent describe how to build and operate an apparatus which takes data while moving vertically in the well.

1~~''~' U.S. Patent No. 4,837,518 which issued on June 6, 1989 to Michael F. Gard, John E. Kingman, and James D.
Klein, .assigned to the Atlant~.c Richfield Company, entitled "Method and Apparatus for Measuring the Electrical Resistivity of Geologic Formations Through, Metal Drill Pipe or Casing", describes multiple voltage measurement electrodes within a cased well which engage the wall of the casing, henceforth referenced as "Arco's patent". However, Arco's patent does not describe an apparatus with two pairs of adjacent voltage measurement electrodes and associated electronics which takes the voltage differential between these two pairs to directly measure electronic properties adjacent to formations.
Therefore, Arco's patent does not describe the methods and apparatus disclosed herein.
USSR Patent No. 56,426, which issued on November 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 two pairs of voltage measurement electrodes which positively engage the interior of the casing.
However, the Alpin patent does not have any suitable calibration means to calibrate f or thickness variations nor errors in the placements of the electrodes.
'Cheref ore, the Alpiri patent does not describe the methods and apparatus disclosed herein.
U.S. Patent No. 2,729,784, issued on January 3, 1956 having the title of "Method and' Apparatus for Electric Well Logging", and U.S. Patent No. 2,891,215 issued on June 16, 1959 having the title of "Method and Apparatus for Electric Well Logging", both of which issued in the name of Robert E. Fearon, h.ezzcef orth called the "Fearon patents", describe apparatus also having two pairs of ~~ '~ YJ ~i~ P.r voltage measurement electrodes which engage the interior of the casing. However, an attempt is made in the Fearon patents to produce a "virtual electrode" on the Casing in an attempt to measure leakage current into formation wYy ch provides for methods and apparatus which are unrelated to the Kaufman and Vail patents cited above. The Fearon patents neither provide calibration means, nor do 'they provide methods similar to those described an either the Kaufman patent or the Vail patents, to calibrate for thickness variations and errors in the placements of the electrodes. Theref ore, the Fearan patents do not describe the methods and apparatus disclosed herein.
Accordingly, an object of the invention is to provide new and practical methods of measuring the resistivity of geological formations adjacent to cased wells which compensate far s~cand order errors of measurement.
Zt is yet another object of the invention to provide new and practical methods of measuring the resistivity of geological formations adjacent to cased wells which compensate far second order errors of measurement and which are also particularly adapted f or acquiring data while moving vertically in the well.
And it is another object of the invention to provide new, and practical apparatus capable of providing measurements of the resistivity of geological formations adjacent_to cased wells which compensate f or second order errors of measurement and which also are capable of acquiring data while moving vertically in the well.
And further, it is another object of the invention to provide new and practical methods and apparatus capable of measuring electrochemical phenomena through casing which ~~ ~,i~ E7 '~ '».J J cj compensate f or second order errors of measurement.
And finally, it is another object of the invention to provide new and practical methods and apparatus capable of measuring electrochemical phenomena through casing which compensate f ox second order errors of measurement and which are also particularly adapted for acquiring data while moving vertically. in the well.
Figure 1 is a sectional view of one preferred embodiment of the invention of the Thru Casing Resistivity Tool (TCRTJ.
Figure 2 shows QI vs. z~which diagrammatically depicts the response of the to01 to different formations.
Figure 3 is a sectional view of a preferred embodiment of the invention which shows how Vo is to be measured.
Figure 4 is a sectional view of an embodiment of the ' invention which has voltage measurement electrodes which are separated by different distances.
Figure 5 is a sectional view of an embodiment of the invention which has electrodes which are separated by different distances and which shows explicitly how to measure Vo.
Figure 6 is a sectional view of an embodiment of the invention which is adapted to take measurements while moving vertically in the cased well.
The invention herein is described in two major different portions of the specification. Tn the first major portion of the specification the apparatus defined in Figures 1, 3, 4, and 5 is described. Such apparatus are perhaps ideally suited as stop-hold-and-lock , apparatus for stationary measurements (although their applications are certainly not limited to stop-hold-and-lock situations). New and precise methods of measurement are then disclosed in this first portion of the text which provide for improved measurement accuracy of an apparatus in the presence of corroded casing while performing stationary measurements within cased wells. The second major portion, of the specification herein is concerned with providing both apparatus and methods which enable such improved measurements to be performed while the apparatus is being moved vertically in cased wells which is typically desirable in the industry.

Fig. l 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. ~.'he 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 SWl 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 connect ed to electrode F, which is in electrical contact with the casing, then current is passed primarily from elect rode 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 IC is flowing downward along the casing at electrode C, current ID is,flowing downward at electrode D, and current IE is flowing downward at electrode E. In general, 'therefore, there is a voltage drop Vl 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. Wi.th~switches SWZ arid 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 J , f,l ~~ Cod 32 to a phase sensitive detector 34 (PSD?. 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 cantroller 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 fox 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 i5 the 0-peak value of the A.C. current conducted to electrode A. (The 0-peals value'of a sine wave is 1/2 the peak-to-peak value of the sine wavo.l In general, with SW1 connected to electrode B, current is conducted through formation. For example, current gI,is conducted into formation along the length 2L between electrodes C and E. However, if SWl is connected to cable 24 and subsequently to electrode F, then no current is conducted through formation to electrode B. In this case, IC ID = IE sznce essentially little current t1T is conducted into formation.
Tt should be noted that if SWl 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 thic)tness 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.
One embodiment of the invention 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 f or null, spurious effects such as thickness variations in the casing do not affect the subsequent measurements.
With SW1 then connected to electrode H, 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 amps o-peak to 30 amps o-peak at a frequency of typically 1 Hz is introduced on the casing here. The low frequency operation is limited by electrochemical effects such as polarizatrion phenomena and the invention can probably be operated down to .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 H."
Therefore, in a preferred method of operation, first the tool is "balanced" for a null output from amplifier 30 when SW1 is connected to cable 24, and then the departure of the signal from null when SW1 is instead connected to electrode B provides a measure of the leakage current into formation. Such a method of operation does not automatically eliminate all "second order errors of measurement". An improved method of operation is described in a later section of this application which does automatically eliminate these "second order errors of measurement".
Fig. 2 shows the differential current conducted into formation 6I 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 (iI in Fig. 1 which are inversely proportional to the re~istivity of the formation. Therefore, one may expect f ~ '-'.! ~ G
discontinuous changes in the current t1I at the interface between various resistive zones particularly at oillwater and oil/gas boundaries. Far example, curve (a) in Fig. 2 shows the results from a uniform formation with resistivity p1 . Curve tb) shows departures from curve (a) when a formation of resistivity p2 and thickness T2 is intersected where p2 is less than pl. And curve tc) shows the opposite situation where a formation is intersected with resistivity 'p3 which is greater than pl which has a thickness of T3. It is obvious that under these circumstances, ~I3 is less than ~I1, which is less than ~I2.
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 T1, the thickness of the cement is TZ, 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 rAference 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 f low.
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 SW? 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, SWS, 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 lO.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 SWl 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.
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, Vo 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 DI. The differential voltage is that voltage in Figure 1 which is the output of amplifier 30 with SW1 connected to electrode B and with all the other switches in the positions shown.
Fig. 4 is nearly identical to Fig. 1 except the electrodes C and D are separated by length Ll, electrodes D and E are separated by L2, electrodes A~and C are separated by L3 and electrodes E and F are separated by the distance L4.
In addition, rl 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 L1~ L2' L3, L4, rl, and z are explicitly shown. In addition, r2 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 Ll and L2 are not equal. And f or many types of measurements, the distances L3 and L4 are not very important provided that they are not much larger in magnitude than Ll and L2.

An improved method of operation of a preferred eznbodimewt of 'the invention is now described in terms of Figure 1. Using this "Preferred Method of Operation"
disclosed herein, the apparatus can be placed in any one of three states: tl) the Preferred Measurement State;
(2) the Preferred Null State ; and (3) the Preferred Calibration State.
The three states defined in this Preferred Method of Operation of the invention are therefore defined as f of lows :
(1) The Preferred Measurement State of the apparatus in Figure 1 is defined by the following configuration:
SW1 is connected to electrode B; switch SW2 is closed; arid switch 5W3 is closed.
(2) The Preferred Null State of the apparatus in Figure 1 is defined by the following conf9.guration: SWl is connected to cable wire 24 and therefore is electrically connected to electrode F; switch SW2 is closed; and switch SW3 is closed.
(3) The Pref erred Calibration State of the apparatus in Figure 1 is defined by the following configuration:
SW1 is connected to cable 24 and therefore is electrically connected to electrode F; switch SW2 is open; and switch SW3 is closed.
. The purpose of the, following analysis is to determine a method of operation to acquire the experimental quantity 6T in Figure 1 which is relatively accurate, which is relatively unaffected by even substantial thickness variations in the casing, and which is~ not materially affected by inaccurate placements of the electrodes.

r3 ~.~ ~..1 e~
Therefore, assume that the gains of amplifiers 26, 28, and '30 in Figure 1 are respectively.given by al, a2, and a3.
Furthermore, assume 'that the resistance of the casing in ohms between electrode C and D is given by R1; and that the resistance of the casing in ohms between electrodes D
and E is given by R2. In 'the following analysis, for the purposes of simplicity only, it is assumed that: (a) there is no phase shift between amplifiers; (b) there is no phase shift between the voltages appearing on the casing and the~current conducted through the earth (caused by polarization effects, skin effects, or other electrochemical processes); and (c) that therefore 'the magnitudes representative of the amplitudes of low frequency A.C. quantities may be used in the following simplified analysis.
The average resistance of the casing between electrodes D and E is defined as the quantity RA, which is given as the follows:
RA - y R1 + R2 1 / 2 Equation 1.
Therefore, there is a departure from average resistance of the first section of the casing between electrodes C and D defined as ~ Rl such that:
Rl - RA ~. pRl Equation 2.
Furthermore, there is a departure from the average resistance of the second section of the casing between electrodes D and E defined as Q R2 such that:
R2 _ RA .~ nR2 Equation 3.

u, ~~f '~ ;~ t'~ y ~y '~~ e.i~ 3 .~ i5 e,~
In the Preferred Null State of the apparatus, a current called the Null Current (defined as "IN") is passed along the casing between electrodes C and E. Since relatively little current is expected t o flow 'through formation in this slat e, then essentially the same current IN flows between electrodes C and D and between electrodes D and E. Therefore, the output voltage from amplifier 30 in this situation defined as VN, which is given by the following:
to VN _ a3 ~ a2 IN ( RA + QR2 y -- al IN ( RA + aRl ) 1 Equation 4.
Re-arranging terms in Equation 4, one obtains:
VN _ a3,'y IN Equation 5.
The quantity Y in Equation 5 is given by the following algebraic formula:
Y = ~ a2 ( RA + QR2 ) - al ( RA + ~R1 ) ?
Equation 6.
In the Preferred Measurement State of the apparatus, a "Total Measurement Current", defined as IT, is passed between electrode A .and electrode B on the surface of the earth. Only a portion of that Total Measurement Current is conducted downward along the casing between electrodes C and D, and~that portion is called simply the "Measurement Current", defined as the quantity IM. If TM
is passing between electrodes C and D, then a certain current will leak off the casing between electrodes D and E which is defined as the quantity d:i2. Therefore, the current passing downward at electrode E, which is the quantity IE, is given by the following:
TE = T~ -- 8 i2 Equation 7 .
Therefore, the output voltage from amplifier 30 in this situation is defined as.VM. which in a lumped component model approximation is given by the following:
VM = a3 C a2 ( IM - &i2) ( R~ -~- 4R2) -- al IM ( R~ -~ dRl)1 Equation B.
Equation 8 simplifies to the following:
VM _ a3 Y I~ _ a2 a3 g i2 ( RA -h L1R2 ) Equation 9.
In the Preferred Calibration State of the apparatus, the.calibration current, ICS, is passed along the casing between electrodes C and E. Since relatively little current is expected to flow through f ormatian in this state, then essentially the same current TCA flows between electrodes C and D and between electrodes D and E. In the Preferred Calibration State, SW2 is open, so that the output from amplifier 30 in this state, VCS, is given by the following:
VCA - " al a3 ICA ( R,~ -~ 4R1 ) / D
Equation 10.
Here, the parameter D is a gain reduction parameter. or divider factor, to avoid saturation of amplifier 30 if SW2 is open, la ~~'~':~~~r although the means to do so is not explicitly shown in Figure 1. Basically, when SW2 is open, then the output of amplifier 30 is divided by the parameter D which was found to be useful during field tests. In this embodiment, the gain controller 3n in Figure 1 has at least the ability to open and close switches SW2, SW3, and t o divide the output of amplifier 30 by the factor D.
There are three fundamentally different independent measurements performed which are summarized in the f ollawing equations: Equation 5, Equation 9, and Equation 10. The gains al, a2, and a3 are assumed to be known to an accuracy of 0.1%. The following currents are measured during the various different states: IN, IM, and IUD. Therefore, Equations No. 5,,9, and 10 contain essentially three fundamental unknowns: di2, Rl, and R2.
Three equations with three unknowns always have a unique solution. One such solution used in practice that minimizes certain types of required measurement accuracies is described in the following.
A convenient parameter to calculate for the analysis herein is called AV, which is defined as follows:
A V - V~ - VN Equation 11.
Using VM from Equation 9, and VN .from Equation 5, then the quantity AV is given as follows:
A V - a3 Y ( IM - TN ) - a2 a3 fi i2 t RA + a.R2 ) Equation 12.

f., r, ~.~ ~ ~i '3 ~J P~a Using Equation 10, and solving for the quantity RA:
RA _ ~ - D VCA / ( al a3 ICA ) ~ - 6 R.~
Equation 13.
Substituting RA from Equation 13 into Equation 12, then the quantity ~V becomes:
aV - ( a2 / al ) ( d i2 ! FICA ) ~ VCA CTerm A~1 + a3 y ( IM - IN) GTerm B3 - a2 a3 d i2 ( D R2 - ~ R1 > CTerm C:7 Equation 1~.
Equat:iAn l~ is the central result of this analysis.
'.Germs A, B. and C appear in sequence in Equation 14 and are identa..fied by the square brackets adjacent to each respective term. Term A describes useful information related to measuring the leakage current flowing into formation. Term B is a first order error term which is present if the measurement current IM is not equi alent to the null current IN and if there are different resistances in different portions of the casing. Term C is the second order error term which is due to the product of the difference in resistances between different sections of casing times the leakage current f lowing into formation.
Term C is called a second order term because it is the product of two quantities which can each be very small under ideal circumstanices.

~,J f,. ~fi ,~
~~ ~ ~ ...1 fj r3 For the purpose of showing the relative numerical sizes of Terms A, B, and C, and their relative importance, these terms are now calculated for 'the following values:
al. _ a2 -. A
a3 - 10 Equation 15 pRl - - O.1 RA
p R2 - -!- 0 . 3 RA
- ~cA - . ~o Furthermore, for the purpose of conveying the importance of the first order error Term B above, it is assumed that the currents T~ and 1N are almost, but not quite equal, as follows:
1M - IN - - 0.01 To Equation 16.
Equation 10 is first used to calculate the quantity VCA ~.n Term A o:~ Equation 14; then Equations 15 and 16 are substituted into Equation 14; and using Equation 6 f or the quantity y ; then Equation 14 becomes:
Term A - --0:90 A a3 8iZ RA Equation 17.
Term B - -0.004 A a3 Io RA Equation ld.
Term C - -0.40 A a3 di2 RA Equation 19.
35.

~~~~r Tn this e~cample, the second order error term, Term C
is significant. Keeping in mind that Term A has the information desired related to current leakage from the casing:
Term C l Term A - 0.44 Equation 20.
The second order error term causes a 44% error in computing the leakage current if onl r.~erm A of Equation 14 is used to calculate leakage current into formation.
Theref ore, it is concluded that methods for compensation of second order errors are important for improved measurement accuracy.
~lith a leakage current of ,about 30 milliamps, and with current T~ of 5, amps, then the ratio of Terms ~i to A
becomes:
Term S / Term A - 0.74 Equation 21.
Therefore, if ythe currents TM and TN are equal to only 1% as in Equation 16, 74% measurement errors are to be expected in this example if onl Term A in Equation 14 is used to calculate the leakage current flowing into formation.
The result in Equation 21 also points up an important aspect of this analysis. Tf the currents TM and TN were different by 50% as is typically the case if the total currents delivered to the casi_~ _throuah current meter 42 were kept_constant for different switch positions of SW1, then errors on the order of at least 25 times the size of the quantity to be measured would be present in the example cited. To compensate f or such large errors, the resistances R1 and R2 would have to be measured to an accuracy approaching 5 significant decimal places far the required measured accuracy of the leakage currentl This place accuracy is difficult to achieve because of cross-talk in the wirelines, magnetic pick-up, and other 5 effects that are to be discussed in another related application. Hy contrast, the method of operation described above only requires consistent measurement accuracy of the various quantities to typically 3 decimal places which is much easier to achieve in practice.
Therefore, in practice in one embodiment of the .
invention, the currents IM and I~ are to be made equal to an accuracy of one part in one thousand (0.1%) to give acceptable measurement errors of the leakage current to accuracies better than 10% if Term B in Equation 14 is to be neglected. during interpretation of the data.
Consequently, in practice to avoid first order errors of measurement if Term B is to be neglected tand.al = al = A):.
Absolute Magnitude of (IM - IN) '~ .001 Ta Equation 22.
Equation 14 is the central result and is used to interpret the data. Now that the importance of the various terms have been established, the following logic is used to put Equation 14 in a farm that is used in practice in one embodiment of the invention. In particular, if the gains of amplifiers 26 and 28 are equal, then the following is used to simplify Equation 14:
al _ a2 _ ~, Equation 23.

;.~'~~e~~a.J~:9e.~
Substituting Equation 23 into Equation 6 for the quantity Y gives the following that may be used to simplify Term B in Equation 14:
y = A ( ~R2 - ~R1) Equation 24.
Term C in Equation 14 can be put into another form more useful for this analysis if Equation 23 is substituted into Equations 5 and 6 thereby providing:
( ~R2 - 4R1 ) - VN / ( a3 A IN ) Equation 25.
Therefore, Equation 24 is used to simplify Term B in Equation 14, and Equation 25 is used to simplify Term C in Equation 14r 'thereby providing:
0V - di2 C ( D VCA f xCA ) - ( VN / TN ) 1 + a3 - A C ( T~ - IN ) ( ~R2 - ~Rl ) 1 Equation 26 The first line of Equation 26 has the corresponding Terms A and C from Equation 14. The second line of Equation 26 corresponds to Term B of Equation 14. Please notice that this second term is the mathematical product of the difference in resistances between various sections of casing times the difference between the measurement and null currents, which in general is a first order error term that is very large unless the measurement and null currents are deliberately chosen to be equal for reasons discussed above.

~0~°~
Tn a. preferred method of operation the invention, the experimental parameters may be set such thats IM - IN - ~TCA " To Equation 27.
In practice, these currents are made equal by demanding that the voyage from amplifier 3U with SW2 open, and SW3 closed, be the same voltage f or both possible states of SWI. For each position of SWl, suitable adjustments are made on the,output voltage of the signal generator 14 in Figure 1 such that the current flowing between electrodes C and D is always the.same for each position of SW1 in this preferred embodiment of the invention.

If Equation 27 is exactly valid, 'then Term B in Equation 26 is zero. Using Equata.on 11 to eliminate the quantity ~V :Ln.Equation 26, then Equation 26 becomes the following:
8 i 2 - T o ( VM - VN ) / ( D VCA -- VN ) Equation 28.
This is the primary result which,provides the quantity di2 which is not affected by second order errors of measurement caused by different resistances in adjacent regions of the casing. The quantity di2 is also not affected by first order errors of measurement.
Therefore, at least three measurements of different quantities are necessary to eliminate significant measurement errors. and to provide accurate results. In the case shown above, three independent~measurements result 3n measuring three experimentally independent quantities: di2, Rl, and R2. Put another way, first and _sP_cond compensation measurements are performed to correct a third measurement of the current leakin into formation from 'the casino to obtain accurate results.
Furthermore. the apparatus has bean used in three different configurations providing a first compensation means (Preferred Null State) and then a second compensation means (Preferred Calibration State) to obtain accurate measurements of the leakage current (in the Preferred Measurement State).
It is to be briefly noted that Equation 6 in U.S.
patent No. 4,796,186 is directed toward eli.minatinc~
various types of measurement errors. That equation has been analyzed using the above concepts. In the language contained herein, Equation 6 in U.S. Patent No. 4,796,186 does in fact eliminate first order errors of measurement like Term :B in Equation 14. However. it does not eliminate second order errors of measurement like Term C in Equation 14. This does make sense since U.S.
patent No. 4,796,186 emphasizes making two independent measurements to obtain data (one compensation step, and one measurement step). The application herein has shown that ~sacond order measurement errors are of importance which therefore requires a method having two independent compensation steps and one final measurement step to eliminate those second order measurement errors.
U.S. Patent No. 4,820,989 defines a method of analysis which gives the resistivity of adjacent formations. See particularly Equations 6, 8, and Equation 9 (as corrected in a Certificate of Correction). However, in'that U.S. patent, the quantity ~I is discussed which is the combined current loss between both electrodes C - D
and between electrodes D ° E. However, here, this method of operation distinguishes between the current loss between electrode C and D which is bil, and the current loss between electrodes D and E which is di2. Therefore, using a lumped component model approx:i.mation:
d:i2 - Q.1 - d~il Equation 29.
To obtain the resistivity of the adjacent formation, the following analysis is needed. The contact resistance Rc of a cylindrical electrode of length t and of diameter d in contact with a formation of resistivity p is given theoretically' by the following (Earth Resistances, G. I°.
Tagg. Pitman PubJ.is)i~:ng Corporation, N.Y. 194, pg. 96):
Rc = p ~ Ln (~t/d) J /(2 ~r t) Equation 30.
.- p C
The geometric constant C is defined from theoretical considerations in Equation 30. The experimentally measured value~of the contact resistance, Rc, is given by the following:
Rc - Vo / S~i2 Equation 31.
Vo in Equation 31 is given by the measured potential voltage on the casing for the current Io defined in Equation 28. Therefore, the resistivity p is given by the following:
p = Vo / ( C ai2 ) Equation 32.

It is most convenient to define a new parameter K
where:
K - 1 f C Equation 33.
Then Equation 32 becomes:
p - K Vo / ai2 Equation 34.
Using the definition of Rc from Equation 31, then Equation 34 finally becomes:
p - K RC Equation 35.
Equation 35 provides the final result used to interpret the data for the preferred method of operation herein. Please notice that the parameter K has units of meters which is sensible because RC has units of ohms, and resistivity is measured in the units of ohm-meters. It should be noted that any calculated values of the parameter K from Equations 30 and 33 for a given diameter of casing and separation of voltage measurement electrodes would rely upon the validity of the argument that the section of caging of length. t may be approximated by an ellipsoid of revolution described by Tagg. It is therefore to be expected that the any value of K
calculated from such an analysis may not be highly accurate because of this approximation. It is reasonable, however, to expect that the parameter K could be empirically determined with considerable accuracy.
Calibrating the apparatus against a formation with known resistivity adjacent to a casing that was measured before ~~~'~K~~.
the casing was sot is sufficient for the purpose of empirically determining the parameter K. From Equations 30 and 33, it is expected that the parameter K is to be a function o~ the diameter of the pipe. From those two same equations, the parameter K is also expected to be a function of the spacing between the voltage measurement electrodes.
The second major portion of the specification is used to describe Figure 6 which presents an apparatus adapted to take data while moving which allows utilization of the preceding fundamental analysis. A preferred apparatus optimally adapted to take data while moving which uses the above fundamental methods of analysis requires a machine which simultaneously -acquires data analocrous to that provided above in the Preferred Measurement State; the Preferred Null State; and in the Preferred Calibration State. The apparatus in Figure 6 is adapted to acquire data in the analogous Preferred l~leasurement State at a first frequency of operation, called ,"F(1)" (perhaps 1 Hz for example); is adapted to simultaneously acqux.re data a.n the analogous Preferred Null State of the apparatus at a second frequency of operation, called "F(2)" (perhaps 2 Hz for example); and that is adapted to simultaneously provide data in the analogous Preferred Calibration State which ultimately is used to )seep the current flowing betweem electrodes C and D at the two frequencies of operation to be the same. as required by the conditions of Equation 27 above.
For the purpose of logical introduction, the elements in Figure 6 are first briefly compared to those in Figures 1-5. This introduction also serves to identify the various legends used in Figure 6. hlements No. 2, 9, 6, 8, and 10 have already been defined. Electrodes A, B, C, r~e3 a~c)~.~eJ
D, E, F, G and the distances L1, L2, L3, and Lq have already been described. The quantities ail and ai2 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 Figures 1, 3, ~1, arzd 5. Tn addition, the apparatus i11 Fig. 6 provides for the following:
(a) two signal, generators 7.abeled with legends "SG 1 at Freq F(1)" and "SG 2 at Freq F(2)'~';
(b) two power amplifiers labeled faith legends "PA 1"
and "PA 2";
(c) a total of 5 phase sensitive detectors labeled with legends "PSD 1", "PSD 2", "'PSD 3", "PSD 4", and "PSD 5", which respectively have inputs for measurement labeled with legends "STG", which have inputs for reference signals labeled with legends "REF", which have oLitpLlts defined by lines having arrows pointing away from the re~spoct~.ve units, and which are capable oL reiectinc~
_a11 signal -voltages at freauencies which are not ecLzal to ' that t~rovided by the respective reference signals;
(d) an "Error Difference Amp" so labeled with this legond in Fig. 6;
(e) an instrument which controls gain with voltage, typically called a "voltage controlled gain", lJh:iCh i.S
. labeled with legend "VCG";
(f) an additional current conducting electrode labeled with legend "11" (which is a distance L5 - not shown - above electrode A).
(g) an additional voltage measuring electrode labeled with legend "J" (which is a distance L6 - riot shown - below electrode F).
(h) current measurement devices, or meters, labeled with legends "T1" and "T2";
(i) and differential voltage amplifier labeled with legend "A9" in Fig. 6.

r The apparatus works as follows. Analogously to the '°Preferred Measurement State", SG 1 provides the basic signal voltage to the VCG which determines the output level of PA 1 which therefore conducts current at frequency F(1) through meter I1, through cable 4~ to electrode A, and then betcaeen electrodes A and B through the geological formation, and from electrode t3 through cable ~G back to PA 1. Therefore, a voltage drop at the frequency F,.(.1) appears along the casing between electrodes C-D and D-E.~::.',~tmplifier A1 takes' the difference in voltage between electrodes C-D; amplifier A2 takes the difference in voltage between ,electrodes D-E; and amplifier A3 takes the voltage difference, between the outputs in voltage from respectively amplifiers A2 and A1 which is ser7t uphole to PSD 1 and PSD 3 by cable 98. The voltage rneasured :by PSD 1 is that analogous to VM above.
Analogously to the "Preferred Null State", SG 2 provides the basic signal voltage which determines the output level of. PA 2 which therefore conducts current at frequency F(2) tYrrough meter I2, through cable 50 to electrode H, through a section of casing to electrode F, and th en back through cable 52 to PA 2. Therefore, a voltage drop at the frequency F(2) also appears along the casing between electrodes C-D and D-E. Amplifier A1 takes the difference in voltage between electrodes C-D;
amplifier A2 takes the difference in voltage between electrodes D-E; and amplifier A3 takes the voltage difference between the outputs in voltage from respectively amplifiers A2 and A1 which is sent uphole to PSD 1 and PSD 3 by cable 98. The voltage measured by PSD 3 is analogous to VN defined above.
Analogously to the Preferred Calibration State, the voltage appearing across electrodes C-D is amplified by ~~'~~~~
amplifier A1 which 15 then Sellt via cable 5~ to both PSD 2 and PSD ~. PSD ~1 measures a quantity related to the current at frequency F(1) flowing through the casing between electrodes C-D. PSD 2 measures a quantity related to the current at frequency P'(2) flowing through the casing between electrodes C-D. The outpLZts from PSD 2 and PSD ~ are sent by cables respectively 56 and 58 to the Error Difference Amp, which provides an error signal to the VCG through cable 60. The voltage provided to the VCG
by SG 1 on cable 62 provides tl~ze:basic level of current passing through meter I1. However, the error voltage provided to the VCG by cable 60 provides adjustments in the current passing through I1 such that the currents at freawencies F(1) and at F(2) passing through the section of casing between electrodes C and D are eaual to ttie level of ~~recision defined in Equation 22 above.
To get resistivity, the potential voltage Vo is needed. 'fherefore,~electrode J provides one of two input voltages to amplifier A~, the other coming from electrode G. The differential voltage output of amplifier A4 is sent to PSD 5 via cable 69. PSD 5 obtains its reference voltage from SG 1 at frequency F(1). Vo is measured at the frequency F(1) by PSD 5. Therefore, sufficient information is provided to the recording and computing system to calculate the resistivity in a form analogous to Equation 32 above.
For the purposes of clarity please notice that SG 1 provides an output voltage at frequency F(1) which is connected to voltage node 66 which in turn is connected to the reference inputs of PSD 1, PSD4, and PSD 5.
Furthermore, please also notice that SG 2 provides a voltage output at frequency F(2) which is connected to voltage node 68 which in turn is connected to the reference inputs of PSD 2 and PSD 3.
Digital Recording System 70 is labeled with legend "DTG REC SXSTEM°'. It is capable of acquiring data, is capable of performing computations with an internal computer, and is capable of providing final processed data outputs in the form of "logs" as is characteristic of the well lagging industry. The output of PSD 5 is connected to the input of the Digital Recording System with wire 72.
Similarly the output of PSD 1 is.connected to the input of the Digital Reco>~ding System with mire 74. However, to avoid unnecessary complexity in Figure 6, only the segment of the wire emerging from PSD 1 is shown with an outgoing arrow (labeled with 74) and only that portion of the wire immediately adjacent to the input of Digital Recording System is shown with an input arrow (also labeled with 74). xn general, an outgoing numbered arrow on a phase sensitive detector is to represent a wire attach ed to its output. An inward pointing arrow into the Digital Recording System is to represent a wire attached to its izyput. The outgoing arrow from a phase sensitive detector having a given number is to be connected with a~wire to the corresponding input arrow on the Digital Recording System. Therefore, the output of PSD 3 is connected to the input of the Digital Recording System with wire 76.
The output of PSD 2 is to be connected to the input of the .Digital Recording System with wire 78. The output of PSD
4 is to.be connected to the input of the Digital Recording System with wire 80. Tn addition, wire 82 connects the output of amplifier A2 to an input of amplifier A3. Many recent phase sensitive detectors have digital outputs.
Such digital outputs are ideal to provide digital data to the computer within the Digital Recording System. On the other hand, many older phase sensitive detectors have oz~zly analogue outputs. In such a case, the corresponding ,.~ , 1" ~,, ., , ~~.~~y~r~
inputs of the Digital Recording System must obviously be analogue-to-digital converters to communicate with the internal computer withiau the Digital Retarding System.
That internal computer is capable of performing standard mathematical computations. The data so provided yield sufficient information to calculate a leak age current analogous to that c'lefined in Equation 2B. The exact algebraic equation appropriate for the apparatus depends upon the gains chosen for amplifiers A1, A2, A3, and A4, but an equation closely analogous to Equation 2B for the moving system can easily be determined. The computer is then able to calculate the leakage current flowing into formation. The infarma-tion provided to the Digital Recording System is also sufficient to determine the potential voltage Vo. The computor is then able to calculate th a resistivity of the adjacent geological formation using Equation 3~. The resistivity vs. ctepth in the well is then provided in the form of a typical "lag"
characteristic of the well lagging industry.
To briefly to summarize: PSD 1 measures a quantity analogous to VM; PSD 3 measures a quantity analogous to VN; PSD 2 and PSD 4 are used to keep the current constant at the two frequencies between electrodes C and D; and PSD 5 measures Vo. The recording and computing system then computes the current leakage into formation, the local casing potential voltage, and the resistivity of the adjacent geological formation while the system is being drawn vertically upward in the well.
Uther components typically used in the wireline industry are to be provided with the apparatus which are not shown, but which include: depth control instrumentation; logging vehicles and w:irelin es; pressure housings for the downhole instrumentation, etc. It is ~~':~n:~~
assumed that the accustomed art in the industry :is to be implemented in th a invention for the blue-print type design of the invention and for the fabrication of the invention. Typical methods of ''de-bugging" the apparatus are to be employed including empirically determining the maximum vertical draw rate of the apparatus by successively moving at faster and faster~speeds until a critical speed is reached whereby tl~e results no longer agree with results at stationary or slower speeds of movement.
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 axe many possible variations. Furthermore, the apparatus and methods described may be used 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. Accordingly, the scope of tlae invention should be determined not only by the embodiments illustrated, but by the appended claims and their legal equivalents.

Claims (21)

1. An apparatus for measurement of the electrochemical properties of formations adjacent to a wellbore that is surrounded by a conductive borehole casing comprising:
a plurality of three vertically spaced apart voltage measuring electrodes disposed at substantially equal intervals within said wellbore, each said voltage measuring electrode being m electrical contact with said casing and positioned adjacent to a formation of interest;
a first current conducting electrode disposed within and engaged in electrical contact with said casing on a first vertical side of said voltage measuring electrodes;
a second current conducting electrode disposed within and engaged in electrical contact with said casing on a second vertical side of said voltage measuring electrodes opposite the first current conducting electrode;
an earth contacting electrode in electrical contact with the surface of the earth;
first current conducting means for applying a first sinusoidal alternating current having a first frequency to said first current conducting electrode in a manner requiring at least a portion of the first alternating current to pass from said first current conducting electrode through said formation of interest to said earth contacting electrode;
second current conducting means for simultaneously applying a second sinusoidal alternating current having a second frequency to said first current conducting electrode in a manner that requires a majority of the second alternating current to pass through the portion of the casing between said first and second current conducting electrodes wherein said second frequency is a different frequency than said first frequency;
measurement means for measuring the magnitudes of said first and second applied alternating currents;
first amplifier means for amplifying the voltage difference at said first frequency between a first pair of said voltage measuring electrodes and producing an output indicative thereof and for amplifying the voltage difference at said second frequency between the first pair of said voltage measuring electrodes and producing an output indicative thereof;
second amplifier means for amplifying the voltage difference at said first frequency between a second pair of said voltage measuring electrodes and producing an output indicative thereof and for amplifying the voltage difference at said second frequency between the second pair of said voltage measuring electrodes and producing an output indicative thereof;
first detector means for measuring the voltage differential between said first and second amplified outputs at said first frequency;

second detector means for measuring the voltage differential between said first and second amplified outputs at said second frequency to provide information concerning the electrochemical properties of formations.

2. An apparatus as recited in claim 1 wherein the first pair of electrodes is vertically the upper pair of said three voltage measuring electrodes and wherein the second pair of electrodes is vertically the lower pair of said three voltage measuring electrodes; and wherein the portion of the output from said first amplifier means at said first frequency provides a measure of the magnitude of current at the first frequency flowing through the casing between the upper pair of electrodes; and wherein the portion of the output from said first amplifier means at said second frequency provides a measure of the magnitude of the current at the second frequency simultaneously flowing through the casing between the upper pair of electrodes; and wherein said apparatus also has current comparison means and electronics means that measures, controls, and maintains the equality of the magnitudes of the respective currents at said first and second frequencies flowing between the upper pair of electrodes.

3. The apparatus as recited in claim 2 wherein the equality of the magnitudes of the currents at said first and second frequencies flowing between said upper pair of electrodes is maintained to an accuracy exceeding 0.1% of the magnitudes of said respective currents.

4. An apparatus as recited in claim 1 wherein the electrochemical property measured by said apparatus is the resistivity of formations adjacent to said wellbore.

5. An apparatus as recited in claim 1 wherein said first frequency is 1 Hz and said second frequency is 2 Hz.

6. An apparatus as recited in claim 1 particularly adapted to take data while moving vertically upward in the conductive borehole casing.

7. An apparatus for measuring the resistivity of a predetermined specific formation adjacent to a section of borehole casing comprising:
first introduction means for causing a first sinusoidal alternating current having a first frequency and first phase to enter the casing at a point in the proximity of the predetermined specific formation of interest;
first receiving means for receiving at least a portion of the first alternating current at a point sufficiently remote from the current entry point to ensure that a majority of the current introduced by said first current introduction means enters the formation from the casing;
second introduction means located vertically above said first introduction means, and. second receiving means located a distance vertically below said first introduction means for simultaneously causing a second sinusoidal alternating current having a second frequency and second phase to flow through the section of casing between the second introduction means and the second receiving means;

at least vertically spaced apart voltage electrode measurement means located vertically below said first introduction means and vertically above said second receiving means for simultaneously detecting the magnitudes and phases of the first varying voltage drops along the casing at said first and said frequencies, said disposition of electrode measurement means defining the section of casing which is adjacent to the specific formation to be measured; and electronic control means to adjust and make equivalent the magnitudes of the time varying voltage drops along the casing at said first and second frequencies of provide information about the predetermined specific formation of interest.

8. An apparatus as recited in claim 1 wherein there are three vertically spaced apart voltage measuring electrode means located vertically above said first introduction means and vertically above said second receiving means for simultaneously detecting the magnitudes and phases of the time varying voltage drops along the casing at said first and said frequencies.

9. A method for measuring electrochemical phenomena of formations adjacent to a cased borehole comprising the steps of:
applying a first sinusoidal alternating current having a first frequency and a first phase to the casing at a first entry point in the proximity of the specific portion of the formation to be tested;
selectively receiving at least a portion of said first alternating current at a point sufficiently remote from said first entry point to insure that a significant portion of said first current introduced at the first entry point enters the formation along the length of the borehole casing;
detecting the voltage levels present at a plurality of at least three spaced apart voltage measuring points along the casing, wherein the disposition of voltage measuring points defines a portion of the casing that is adjacent to the specific portion of the formation to be tested;
simultaneously conducting a second alternating current having a second frequency and a second phase from a second entry point on the casing, through said portion of the casing defined by said spaced apart voltage measuring points, and to a first exit point on the casing, said second entry point and said first exit points being located on opposite sides of said portion of the casing defined by said spaced apart voltage measuring points;
simultaneously measuring the magnitude and phases of the differential voltages between a plurality of discrete pairs of said spaced apart points at the first and second frequencies; and simultaneously controlling the magnitudes of the differential voltages at said first and second frequencies from at least one pair of said spaced apart points to measure electrochemical phenomena of the formations.

10. The method as recited in claim 9 wherein the magnitudes and phases of the differential voltages between a first pair of said spaced apart points on the casing at the first and second frequencies are used to control and maintain the equality of the magnitudes of the currents at said first and second frequencies that are flowing through the casing between said first pair of said spaced apart points.

11. A method for measuring the resistivity and changes in the resistivity of a formation adjacent to the exterior of a particular section of metallic pipe that is cemented in place in a geological formation comprising the steps of:
applying a sinusoidal electric field having a first frequency and a first phase to the exterior of the particular section of metallic pipe whereby said electric field has at least a component which is perpendicular to the section of pipe thereby causing a total time varying current at said first frequency to be conducted rom the metallic pipe through any cement present that is m electrical contact with the metallic pipe and through the surrounding geological formation;
simultaneously conducting alternating current having a second frequency and a second phase through said particular section of metallic pipe; and simultaneously measuring the A.C. voltage differences and phase differences at said first frequency between two adjacent vertical pairs of spaced apart voltage measuring electrodes which are in electrical contact with the interior of the particular section of borehole casing adjacent to the geological formation of interest; and simultaneously measuring the A.C. voltage differences and phase differences at said second frequency between the two adjacent vertical pairs of spaced apart voltage measuring electrodes whereby said A.C.
voltage measurements provide a measure of the resistivity and changes in the resistivity of said formation of interest.

12. A method as recited in claim 11 wherein the two adjacent vertical pairs of said spaced apart measuring electrodes are comprised of an upper vertical pair of electrodes and a lower vertical pair of electrodes, and wherein the magnitudes and phases of the voltages at the first and second frequencies between the upper vertical pair of said electrodes are used to maintain the equality of the magnitudes of the currents at said first and second frequencies that are flowing through the casing between the upper pair of electrodes.

13. A method for measuring electrochemical phenomena of formations adjacent to a cased borehole comprising the steps of:
applying a first sinusoidal alternating current having a first frequency and a first phase to the casing at a first entry point in the proximity of the specific geological formation to be tested;
selectively receiving at least a portion of said first alternating current at a point sufficiently remote from said first entry point to insure that a significant portion said first current introduced at the first entry point enters the formation along the length of the borehole casing;
detecting the voltage levels present at a plurality of at least three spaced apart voltage measuring points along the casing, wherein the disposition of voltage measuring points defines a portion of the casing that is adjacent to the specific geological formation to be tested;
simultaneously conducting a second alternating current having a second frequency and second phase from a second entry point on the casing, through said portion of the casing defined by said spaced apart voltage measuring points, and to a first exit point on the casing, said second entry point and said first exit point being located on opposite sides of said portion of the casing defined by said spaced apart voltage measuring points; and simultaneously measuring the magnitudes and phases of the differential voltage between a plurality of discrete pairs of said spaced apart points at the first and second frequencies;
using the measurements of said second frequency to determine the variable resistances of two different section of the casing between two respective spaced apart voltage measuring points and determining two compensation properties of two different section of the casing related to measurements at said second frequency; and using said two compensation properties to interpret measurements at said first frequency that are used to determine the electrochemical properties of the adjacent geological formation that includes the measurement of the resistivity of the specific geological formation to be tested.

14. A method for determining resistivity of a formation of interest that is adjacent to a borehole having casing, comprising:
applying a first signal having a first frequency to the casing adjacent to the formation of interest;
receiving at least portions of said first signal using at least first and second electrodes;
applying a second signal having a second frequency to the casing adjacent to the formation of interest, said second frequency being different from the first frequency;
receiving at least portions of said second signal using at least said first and second electrodes and with the magnitude of said second signal portions being substantially equal to the magnitude of said first signal portions; and determining a magnitude relating to the resistivity of the formation of interest using said first and second signal portions.

15. A method, as claimed in claim 14, further including:
moving a measuring apparatus while applying said first and second signals wherein at least portions of the measuring apparatus are used in at least one of the steps of applying said first and second signals and receiving said first and second signal portions.

16. A method, as claimed in claim 14, wherein:
said steps of applying said first and second signals are conducted at substantially the same time.

17. An apparatus for determining resistivity of a formation of interest that is adjacent to a borehole having casing comprising:
first means for applying a first signal having a first frequency to the casing adjacent to the formation of interest;
second means for applying a second signal having a second frequency to the casing adjacent to the formation of interest at substantially the same time said first signal is applied, said second frequency being different from said first frequency;
third means, responsive to at least portions of said first and second signals, for measuring electrical related information, said third means including at least first and second electrode means; and fourth means for processing said electrical related information for use in determining a magnitude relating to the resistivity of the formation of interest, said fourth means including means for maintaining substantially the same magnitude of first and second signal portions through said first and second electrode means.

18. An apparatus, as claimed in claim 17, wherein:
said fourth means includes means for compensating for variations in the resistivity of the casing.

19. An apparatus, as claimed in claim 17, wherein:
said third means includes a plurality of electrode means for use in providing signals having voltage related information.

20. An apparatus, as claimed in claim 19, wherein:
said plurality of electrode means includes first, second and third electrodes with each of said electrodes being spaced from each other.

21. An apparatus, as claimed in claim 20, wherein:
said fourth means includes means for providing substantially the same current flow at the second frequency between said first and second electrodes and said second and third electrodes.