7/16/2019 Shale or Clay Effect http://slidepdf.com/reader/full/shale-or-clay-effect 1/24 ROLE OF CLAY IN WELL-LOG INTERPRETATION BY M. R. J. WTLLIE ' IntroducHon. It is the intention of the writer to diseuss primarily the eleetroeheniieal properties of charged membranes and particularly shales as natural embodiments of such membranes. Attention will be given to the factors involved in the practical utilization of the properties of shale membranes as tools in the interpreta tion of electrical well logs. Conversely, it will be pointed out that the properties of electrical Mell logs appear to give information bearing on the properties of the clays in natural shales. Attention will be given to the role that clays play in the interpretation of electrical-resistivity logs. AVhereas in the interpretation of the S.P. (spontaneous or self potential) log the presence of clay in shales appears to give rise to a natural phenomenon of great practical utility, the pi'esence of clay or shale in permeable rocks such as sandstones or limestones constitutes a major bane. Although the title induces no such limitation upon it, the scope of this paper will not include the effect of clay.s on the interpretation of well logs other than elec trical well logs. This omission implies no derogation of the importance of radioactivity and other logs, but merely the recognition that the interpretation of elec trical logs, being presently of greater economic impor tance, has received more attention. The clay problems in electrical-log interpretation are certainly great; analogous problems involved in radioactivity logging may well be prodigious. The Self-Potential Log. Electrical well logging, or, as it was initially called, electrical coring, was invented by the brothers Conrad and Marcel Schlumberger in 1927, and the first electrical log run was made in the Pechelbronn field of Alsace. The initial logs consisted only of electrical resistivity logs; that is, a plot of the resistivitv of formations as a function of their depth bel o\v ground level. However, Marcel Schlumberger noted evidence of a natural electrical phenomenon oc curring in the borehole, and in ]98], while surveying a well in the Caucasus, Schlumberger engineers confirmed the existence of this phenomenon, which they called the self potential or S.P. From the beginning the S.P. curve proved very useful because it enabled a simple distinc tion to be made between permeable rocks and shales. It provided also a more precise method than any previously existing for determining the thicknesses of sandt and shale sequences. Also, the characteristic shape of the S.P. curve made it possible to correlate well logs over large areas with a much greater precision than had been po,ssible when only electrical resistivity logs of the crude original type were available. The method of running a self potential log is extraor dinarily simple. The basic equipment consists of a length of insulated wire to which are attached two electrodes. Generally these electrodes consist of lead wire bound on an insulating mandrel, although non-polarizing elec- * Gulf Research and Development Company, Pittsburgh, Pennsyl vania. t "Sand" is used throug^hout this paper in the petroleum technology sen.?e of permeable rock. trodes are to be preferred. In practice, one electrode is anchored at the surface in the mud pit or a pit arti ficially dug adjacent to the well-head and filled with fiuid. The other electrode is lowered down the borehole and the potential difference between the two electrodes is measured and recorded automatically as a function of the depth of the borehole electrode below surface level. Since the contact potential difference between the elec trodes and the fluids in which they are immersed may not be identical, it is customary to insert in the circuit between the two electrodes a means by which this po tential may be controlled. This control or bucking poten tial has no other role than to serve as a convenient method of arranging for the potential between the elec trodes at any particular datum level to be such that it can be plotted on the recording paper. During the log ging run it is essential that this bucking potential re main constant, and, as a consequence, what is recorded on the paper is the natural difference of potential be tween the borehole electrode and the surface or reference electrode as a function of the depth of the borehole electrode below surface level. The general scheme is shown in figure 1. It was found by the Schlumberger engineers to be an empirical fact that as the borehole RECORDING V F ^1 F 5ll= F • ' . V * • . . V llr * • llr NUD FIGURE 1. Schematic drawing of basic S.P. losging circuit. electrode was lowered into the hole its potential changed systematically with depth. In general, when the bore hole electrode passed a permeable bed its potential de flected in a negative direction; but when it passed into a non-permeable or shale bed its potential changed in the opposite direction. The most remarkable feature of this phenomenon was the fact that when the potential changed at the interface between a shale and a sand bed in a negative direction and at the interface between the sand bed and the shale below it in a positive direc tion, in practically all cases the magnitude of the nega tive change at the top of the bed was equal to the (282 )
IntroducHon. It is the inte ntio n of the wr ite r todiseuss primarily the eleetroeheniieal properties of charged membranes and particularly shales as naturalembodiments of such membranes. Attention will be givento the factors involved in the practical utilization of theproperties of shale membranes as tools in the interpretation of electrical well logs. Conversely, it will be pointedout that the properties of electrical Mell logs appear togive information bearing on the properties of the claysin natural shales.
Attention will be given to the role that clays play inthe interpretation of electrical-resistivity logs. AVhereasin the interpretation of the S.P. (spontaneous or self potential) log the presence of clay in shales appearsto give rise to a natural phenomenon of great practicalutility, the pi'esence of clay or shale in permeable rockssuch as sandstones or limestones constitutes a majorbane.
Although the title induces no such limitation upon it,the scope of this paper will not include the effect of clay.s on the interpretation of well logs other than electrical well logs. This omission implies no derogationof the importance of radioactivity and other logs, butmerely the recognition that the interpretation of electrical logs, being presently of greater economic importance, has received more attention. The clay problemsin electrical-log interpretation are certainly great;analogous problems involved in radioactivity loggingmay well be prodigious.
The Self-Potential Log. Electrical well logging, or,as it was initially called, electrical coring, was inventedby the brothers Conrad and Marcel Schlumberger in1927, and the first electrical log run was made in the
Pechelbronn field of Alsace. The initial logs consistedonly of electrical resistivity logs; that is, a plot of theresistivitv of formations as a function of their depthbel o\v gro und level. Howe ver, Marcel Schl umbe rgernoted evidence of a natural electrical phenomenon occurring in the borehole, and in ]98], while surveying awell in the Caucasus, Schlumberger engineers confirmedthe existence of this phenomenon, which they called theself potential or S.P. From the beginning the S.P. curveproved very useful because it enabled a simple distinction to be made between permeable rocks and shales. Itprovided also a more precise method than any previouslyexistin g for det erm ini ng the thicknesses of sa nd t andshale sequences. Also, the characteristic shape of theS.P. curve made it possible to correlate well logs over
large areas with a much greater precision than had beenpo,ssible when only electrical resistivity logs of the crudeoriginal type were available.
The method of running a self potential log is extraordinarily simple. The basic equipment consists of a lengthof insulated wire to which are attached two electrodes.Generally these electrodes consist of lead wire bound onan insulating mandrel, although non-polarizing elec-
* Gulf Researc h and Development Company, Pitts bur gh, Penn sylvania.
t "Sand" is used throug^hout this paper in the petroleum technologysen.?e of permeable rock.
trodes are to be preferred. In practice, one electrode isanchored at the surface in the mud pit or a pit artificially du g ad ja ce nt to the well -hea d an d filled wi thfiuid. The othe r elec trode is low ered dow n th e borehol eand the potential difference between the two electrodesis measur ed and r ecorded automat ically as a function of the depth of the borehole electrode below surface level.Since the contact potential difference between the electrodes and the fluids in which they are immersed maynot be identical, it is customary to insert in the circuitbetween the two electrodes a means by which this potential may be controlled. This control or bucking potential has no other role than to serve as a convenientmethod of arranging for the potential between the electrodes at any particular datum level to be such that itcan be plotted on the recording paper. During the logging run it is essential that this bucking potential remain constant, and, as a consequence, what is recordedon the paper is the natural difference of potential between the borehole electrode and the surface or referenceelectrode as a function of the depth of the boreholeelectrode below surface level. The general scheme isshown in figure 1. It was fou nd by the Sch lu mbe rg erengineers to be an empirical fact that as the borehole
RECORDINGV
F̂ 1F5ll=
F
• '. V * •
.
. V
llr* •
llr
NUD
FIGURE 1. Schem atic drawi ng of basic S.P. losging circuit.
electrode was lowered into the hole its potential changed
systematically with depth. In general, when the borehole electrode passed a permeable bed its potential deflected in a nega tive di rec tio n; but when it passed i ntoa non-permeable or shale bed its potential changed inthe opposite direction. The most remarkable feature of this phenomenon was the fact that when the potentialchanged at the interface between a shale and a sandbed in a negative direction and at the interface betweenthe sand bed and the shale below it in a positive direction, in practically all cases the magnitude of the negative change at the top of the bed was equal to the
P a r t V I I ] CIJAY TECHNOLOGY IX THE PETKOLEI;.\[ INDUSTRY 283
:S3^:
m,-'T,
OHM- I OH M- IaOm.v. ^ 0 METERS 20 METERS
0 20
FIGURE 2. A typical shalebaseline.
magiiitnde of the positive cliaiip'e at the bottom. If inthin beds, for example, this did not occur, it was usualto find that further down the borehole th e ])otentialopposite shales had again achieved a definite value. Thisdefinite shale potential, which is called th e shale baseline, is in the view of the writer a phenomenon of tremendous theoretical significance. A typical shale base
line is shown in figure 2.I t may be shown that baseline shifts occur. Some of
these will be discussed below. Xevertheless, the moststr iking feature of the S.P. log, and a feature whichmust be reconciled iu any theory of the S.P., is theexistence on almost all S.P. logs of a str ikingly constantshale baseline. The dominating significance of this factshould never be overlooked iu the consideration of S.P.phenomena.
Investigation of the natiTre of the S.P. curve, andpar t icu lar ly th e natural potentials which gave rise to itsexistence, was first made by the Schlumberger organization ; and two early papers on the subject appeared,wr i t ten by the Schlumberger brothers and E. G. Leonar-don (1984, 1934a). Th e first paper ascribed the S.P.
wholly to electrokinetic eflfects, that is, a streamingpotential occurring as a result of the flow of mud fluidfrom th e borehole into a permeable formation. It may benoted here that in modern rotary dril l ing th e hydrostatichead of the column of mud contained in the borehole always exceeds th e hydrostatic pressure of the fluids inpermeable formations through which the borehole passes.However, it was soon realized by the Schlumberg'ers andLeonardon that electrokinetic phenomena, although theymight constitute a par t of the S.P., could not be responsible for the entire effect. These workers then investigated in the laboratory the potential which was set upat th e interface between a mass of plastic graj^ clay anda saline solution, and were able to show that a potentialexisted at this interface. This they recognized as an
electrochemical potential and they ascribed the S.P. toa combination of electrokinetic and electrochemicaleffects. This early view is now generally accepted as correct.
Although there is reason to believe that work was carried ou t within oil companies on the phenomenon of theS.P., it was not until some 10 years had elapsed thatanother paper appeared on the same subject. This paper,by Mounce and Rust (1945), in essence duplicated theearly work of the Schlumbergers and Leonardon, butshowed more clearly an d emphasized more definitely thatan electromotive force was set up when a shale separatedtwo saline solutions. It was shown that a chain consistingof a shale barrier separating tw o solutions differing inionic strength and with the two solutions in turn broughtin contact to form a l iquid junction was capable of
giving rise to the passage of an electric current. Unfortunately, Mounce and Rust made no at tempt to assess thereasons for the setting up of this current and morespecifically made no at tempt to measure th e potentialsquant i ta t ively as a function of the compositions of thesolutions separated bj' their shale membrane. Later II .G. Doll (1949) discussed in considerable detail th epotential distribution which existed in a borehole if theshale wa s able to act as a bat tery and cause the flow of electrical current. Doll showed that, since an electricalcurrent flowed at the junction between sands and shales
in a borehole, the action of the circulating electricalcurrents at these interfaces would involve ohmic changesin potential along the axis of the borehole. He showedthat it was these ohmic changes in potential which wererecorded by the borehole electrode. Uoll emphasized thatthe relative electrical resistances of the shale, sand, andborehole components in the path of the circulating
currents had a dominant effect on the magnitude of theS.P. recorded and on the shape of the S.P. curve. Inessence he was able to demonstrate that if sands andshales had effective resistances in the path of the circulatory currents which were small by comparison with theresistance constituted by the mud in the borehole, thechanges in potential between the shale baseline and themaximum deflections in the centers of permeable bedswere substantially equal to the total electromotive forcesgiving rise to the circulation of electrical currents. Sincethe effective resistances of the three legs of the circuit,i.e., a shale bed, a sand bed, and a column of boreholemud, were controlled both by their electrical resistivitiesand by their physical dimensions, Doll demonstratedthat only if a bed were thick by comparison with the
diameter of the borehole or if, for any given diameter of borehole, the resistance of the mud was exceptionallyhigh by comparison with the ett'eotive resistances of theshale and sand beds, would the total S.P. recorded besubstantiall.v the same as the electromotive force of thecell giving rise to the circulation of current. Thus themaximum S.P., as normally recorded, can never beexactly equal to the emf of the cell which is generatingcurrent, although in many cases it may be asymptoticto this value. These complications arise because the shalecell which gives rise to the potential is being measuredin ordinary S.P. practice on a closed electrical circuit;whereas for an exact measurement, as it would be madein a laboratory, the measurement should be made poten-tiometr ically, i.e., on open circuit. This state of affairs
has been partially rectified by an ingenious device whichrecords the so-called static S.P. log (Doll 1950). Thisdevice in effect makes in the borehole a potentiometricmeasurement of the S.P.
It is not the intention of the writer to discuss in thispaper the geometrical effects of the formations on themagnitude of the recorded S.P. These effects, thoughserious in electric log interpretation, are purely physical.They may be very largely overcome at the present timeby the application of static S.P. logging techniques oreven by the art of intelligent guess-work. For instance, infigure 2 the S.P. of the formation at 6450-6472' is probably cut back because of the high resistance effect of laminated thin beds. In an interpretation it would beunwise to take the recorded S.P. at the level of this bed
as the true S.P. The maximum S.P. above and belowthe bed is the same and probably is also the Static S.P.of the laminated bed.
There is every hope that in the future the positionmay be further improved. What seems to the writer tobe of critical importance is the nature of the mechanismwhereby the emf is set up, and particularly any quantitative relationship which may exist between this emf and the nature and composition of the fluids in permeable beds and in the borehole. It is imperative forthe proper interpretation of electrical well logs that the
electrical resistivity of the fluids within porous formations be obtained. Thus any informat ion concerningthese resistivities which can be derived from the S.P.log is of major practical importance.
Practical Utilization of S.P. Log Data. It was pointedout by the write r (Wyllie 1948) t hat if a portion of a
natural shale were interposed between two sodium chloride solutions, the potential which developed across theshale appeared to be related by the Nernst equation tothe activity of the sodium ions in the solutions separated.
BT ai E = /w —
F a-2
where
(1)
E = potential
BT := thermodynamic temp eratu re dependent para m-
F eter
0], (7o = single ion activities of the sodium ions in the
two solutions
It may be noted that the more dilute solution is positive,whereas when an ordinary liquid-junction potential isset up between the same solutions it is negative.
Table 1 shows some of the data obtained. In accordance with the more recent findings of both Kressman(1952) and the writer, the single ion activities which aretheoretically required by equation (1) have been replaced by activi ties based on mean activity coefficients.These coefBcients are taken from Harned and Owen(1950). While the use of mean activity coefficient mayinvolve a constant potential error, the magnitude of this error, if it exists, is not believed to be large. DeWitte (1950) seems to confirm the findings of the writer
regarding the applicability of the Nernst equation toshales. However, the unorthodox method used by deWitte to find the activity ratio of the sodium chloridesolutions he used and the uncertainty regarding theabsolute concentrations he employed (appa rentl y thesewere 0.01 N to 1.0 N) precludes the writer from givingdetailed consideration to his data.
Tahle ].
Shale type Ci molai C2 molal a i aa
Nernstpoten
tial (mv)
Observedpoten
tial (mv)
Conemangh 0.0480.0480.557
0.5571.0001.0002.0004.0002.0004.000
0.01120.01120.125
0.1250.4000.4000.5001.0000.6001.000
0.03960.03960.,370
0.3700.6540.6541.3303.1321.3303.132
0.0100.0100.096
0.0960.2700.2700.3400.6540.3400.654
34.734.734.1
34.122.322.331.039.631.039.6
32.732.7
ConemaiighWoodford _ _ -Conemaugh,,
0.0480.0480.557
0.5571.0001.0002.0004.0002.0004.000
0.01120.01120.125
0.1250.4000.4000.5001.0000.6001.000
0.03960.03960.,370
0.3700.6540.6541.3303.1321.3303.132
0.0100.0100.096
0.0960.2700.2700.3400.6540.3400.654
34.734.734.1
34.122.322.331.039.631.039.6
32.2
32.223.023.0
ConemanghConemangh _. ^Woodford
0.0480.0480.557
0.5571.0001.0002.0004.0002.0004.000
0.01120.01120.125
0.1250.4000.4000.5001.0000.6001.000
0.03960.03960.,370
0.3700.6540.6541.3303.1321.3303.132
0.0100.0100.096
0.0960.2700.2700.3400.6540.3400.654
34.734.734.1
34.122.322.331.039.631.039.6
14.39.9
34.228.9
0.0480.0480.557
0.5571.0001.0002.0004.0002.0004.000
0.01120.01120.125
0.1250.4000.4000.5001.0000.6001.000
0.03960.03960.,370
0.3700.6540.6541.3303.1321.3303.132
0.0100.0100.096
0.0960.2700.2700.3400.6540.3400.654
34.734.734.1
34.122.322.331.039.631.039.6
The data in table 1, which refer to a carbonaceousDevonian shale (Woodford) cored at a depth of 6808feet and a Pennsylvanian shale (Conemangh) cored ata depth of less than 100 feet, are typical of the labo-
Part yil] CLAY TECHNOLOGY IX THE PETROLEUM INDUSTRY 285
ratory data that are obtained with natural shale specimens. Two features of the data are particularly stressed.The first is that at low ionic strengths both shales givethe same potential and this potential is close to theNernst potential. At high ionic strengths the differencebetween the potential observed and that calculated fromthe Nernst equation increases, and this difference is not
the same for the two shale specimens. As will be shownbelow, a failure to give potentials conforming to theNernst equation at high ionic strengths of the solutionsused is typical of an imperfect membrane electrode.
The observation that shales separating sodium chloride solutions differing in activity give potentials whichtend to follow the Nernst potential suggests that theS.P. log may be used to calculate the salinity, and hencethe resistivity, of subsurface waters in permeable rockspenetrated by a borehole (Wyllie 1949). The methodhas been fur the r discussed and some of its limitationsoutlined by the author in several publications (Wyllie1949a, 1951, 1951a; Wyllie and Morgan 1951).
A cell in the earth which gives rise to an S.P. deflection may be resolved into the following components. A
shale bar rie r tha t separa tes two solutions of differentionic activities and which gives rise to a potential of the kind previously discussed. The two solutions arerespectively the mud fluid in the borehole and the interstitial water in a permeable and porous rock. Thesetwo solutions make contact in the interstices of the porous rock thereby closing the electrical circuit and givingrise also, in ideal cases, to a normal liquid junctionpotential. Current circulates from the shale into theborehole, from the borehole into the permeable rock andfrom the rock back into the shale. This is shown infigure 3. If the activity of the fluid in the borehole isless than the interstitial water activity, and this is commonly the case, cations move from the shale into theborehole while anions simultaneously move across the
liquid junction formed in the permeable rock so as tomaintain an over-all electrical neutrality. The net effectis the transfer of salt from the more concentrated solu-
SHALE
ARROWS IN DIRECTION OFPOSITIVE CURRENT FLOW
-f
S.R CURVEFiGXJKE 3. Schematic view of the potentials, current flow, ion
movement and S.P. curve for a permeable bed containing a solution of activity ac, separating two shale beds and penetrated by aborehole containing mud of activity am. ac>am.
tion in the permeable formation to the more dilute solution in the borehole. The current flow is not large; intypical instances, it is of the order of milliamperes. Thecurrent density in the shale is very small.
The shale cell written in conventional fashion is
Mud//Interstitial waterShale/Mud
in the permeable rock/
If the mud and interstitial M-ater are both assumed tobe sodium chloride solutions differing only in ionicstrength, and if the shale potential is considered to follow the Nernst equation irrespective of the ionic strengthof the solutions separated, the cell may be formallywritten
NaCl/'/NaCl/Na^electrode/NaCl (2 )a i a-i
The expression for the potential of a cell of this nature involving as it does both the equivalent of a sodiitmelectrode potential and a liquid junction potential is
BT ai E = 2t. In —
F a2(3 )
whore t. is the transference number of the chloride ionand a, and «£ the mean ionic activities of the two sodiumchloride solutions.
For practical use equation (3) may be readily cast ina form in which the potential E is related to the activityratio (ai/a2) and temperature T. For this purpose it isonly necessary to assume some reasonable average sodium chloride concentration for which the value of thetransference number as a function of temperature canbe found. If E is now identified with the maximum orstatic S.P. on a log and the activity of the mud, ao, ismeasured, it is possible to arrive at a value of «], theactivity of the interstitial water. Knowing this activity
the salinity and hence resistivity of the interstitial water is easily found. Simple charts to accomplish thesesteps have been published (Wyll ie 1951).
Equ ation (3) thus forms the basis of a method of computing interstitial water resistivity. The method hasbeen used with success by the author (Wyllie 1949a)and is now standard practice in Gulf operations. Asimilar method was evolved independently by Tixier(1949) from a consideration of the S.P. phenomena andinterstitial water resistivities observed by him in theRocky Mountain area of the United States. Tixier'smethod, based purely on log data, so closely approximates the results of the writer's theoretical analysisthat it may be construed as lending support to the analysis made.
While the method is used with success within theGulf organization, others have not found it equally useful.* A major difficulty is certainly that of obtaininga fully developed S.P. deflection when geometrical effects, e.g., thin beds or excessive filtrate invasion, areconspiring to reduce the maximum S.P. deflection. Theformulae evolved by Doll (1949) for correcting the S.P.for .such geometrical effects are apparently too idealizedto be invariably successful in practice. However, staticS.P. logging will do much to overcome these difficulties,
while the interpretation of conventional S.P. logs maybe greatly improved if the maximum consistent S.P.deflection above an d below (for pref eren ce) or in thevicinity of the bed of interest, is selected. However, some judgment is recp ii red in th e use of thi s tec hn iq ue , fo r insome areas the salinity of interstitial waters may changeabruptly from bed to bed while in others the change is
gradual. Thus on the Gulf Coast the technique may bereliable, but in California it is hazardous.
It is the experience of the writer and his associatesthat in the United States the method may be used tocalculate a water resistivity sufficiently reliable for alog interpretation in about 70 percent of eases. In aneffort to improve this sitiiation and to determine to whatextent the results obtained have been fortuitous, attention has been given to the basic assumptions made in theformulatioh of equation (3) and the degree to whichthese assumptions may be relied upon in practical instances. This program is still continuing, but has devolved into two basic lines of inquiry. These are an investigation of the existence and magnitude of potentialsother than electrochemical potentials which are recorded
on the S.P. log, and the mechanism of the eleetrochemiealpotential. The latter problem has involved both thetheory of charged membrane electrodes and particularlythe problem of the bi-ionic potential.
Electrokinetic Potentials. In drilling operations usingrotarjr rigs, the borehole contains mud fluid. This fluidis designed to remove cuttings produced at the drill-bitand to seal off permeable beds while drilling proceeds.The density of the mud is maintained at a figure whichis sufficient to ensure that the hydrostatic pressure inthe mud column opposite any permeable bed exceedsthe pressure of the fluids in the bed. While this pressuredifference ensures that no bed yields its fluids into theborehole during drilling, it inevitably leads to the steadyinfiltration of drilling mud into all permeable beds. To
minimize this infiltration muds are designed to build onthe faces of permeable beds a filter cake having a permeab ili ty as low as the inge nui ty of the mud engine ercan devise. Nevertheless, no filter cake is impermeablean d in all wel ls th er e is a st ea dy flow of mu d filtratefrom the borehole through the filter cake into permeablebeds.
The pre ssu re diffe rent ial ca usi ng the flow of filtrateis a funct ion of the mud densit y, the formati on pres sureand the location of the bed in the borehole. While allthree factors vary, it may be said that in the depthranges now of interest in petroleum production the pressure differential is always of the order of hundreds of pounds per square inch and in deep wells it may beseveral thousand pounds per square inch.
There is also a range in resistivity of modern drillingmuds, but the present tendency seems to be for them tobe progressively lowered. Resistivities of the order of 0.5 ohm-meters to 1.5 ohm-meters at a temperature of abo ut 70° F are now commo n, alt houg h figures bot habove and below these limits are freq uent ly enco unte red.These resistivities imply ionic strengths of the order of 0.05 to 0.20 molal.
Such ionic strengths would not normally be consideredas liable to give rise to electrokinetic potentials of anymagnitude, but experiments have shown (Wyllie, 1951)that this assumption is not justified in well-logging.
Al th ou gh the high ionic st re ng th s of the filtrates wh ichare forced through the filter cakes sheathing permeablebeds are not themselves conducive to high streamingpotentials, they are more than outweighed in total effectby the high zeta pot ent ia ls of th e filter-cake ma te ri al san d the very large pre ssure differentials causin g fluidflow. The filter cakes are largely composed of montmoril-
lonite clay, the exchangeable ions generally being sodium; but probably some calcium also is present, particula rly in the case of modern lime-base mud s (Be rgm an,1952) . The cakes also contain weighting material in theform of barytes, along with silica and other solids arisingfrom the drilling operations. Oil in the filter cake ischaracteristic when oil-emulsion drilling muds are eni-ploj'ed.
It has been found t hat since it is deformabl e thepermeability of a filter cake is itself a function of thepressure differential across it; thus the streaming potential across a filter cake is not the usua l li nea r fun cti onof the pressure diff'erential inducing fluid flow. Thestreaming potential appears to follow a relationship of the form
E,, = A-P" (4)
Here Eg is streaming potential in mv, k a constant whichdepends primarily on the mud resistivity (and thus onthe mu d filter-cake res ist ivi ty since thes e are int er de pe nde nt ) a nd J/ is a const ant for any part ic ul ar mu dat a particular temperature. The value of y seems todepend upon the deformation ability of the filter cake;an average value is about 0.75. In figure 4 are shownsome average values for the streaming potential-pressurerelationships of drilling muds of different resistivities.The resistivities are expressed at a temperature of 25° C.
The fact that the constant k in equation (4) is approximately prop orti onal to the resistivity of the mud from
which a filter cake is derived is explicable if it is considered that the total non-conductive solid content of a filter cake is larg ely ind epe nde nt of resist ivity . Th esolid content is probably related to the mud weight.Hence k would be expected to be proportional to themud-filtrate resistivity if the surface density of thecha rge on th e filter-cake pa rt ic le s were eit her co nst antor filtrate-resistivity de pe nde nt . Da ta quo ted by Mar shall (1949) seem to show that the surface-chargedensity of kaolinite is practi cally c oncentration independent when the clay is in the sodium form, and thesame may be true of montmorillonite. Thus in the rangeof ionic strengths characteristic of drilling muds the surface-charge density of the montmoril lonite (bentonit e)which is invariably used may well be considered constant. If this is so, the comparatively systematic varia
tion with resistivity of the electrokinetic-potential characteristics of muds of widely differing types becomesexplicable. Nevertheless, the effect of temperature on thecha rge dens ity is not clear (AVyllie, 1951) and re mai nsto be investigat ed further .
The char ge on th e filter cake is such th a t th e filtratewhich penetrates a filter cake is positive with respectto the mud from w hich it is filtered. Thi s mea ns t ha twhen the electrochemical S.P. is negative, the S.P. deflection is nume ric all y increased by the str eam ing potential. The maximum S.P. or Static S.P., which is
Par t VII ] CLAY TECHNOLOGY IN THE PETROLE UII INDUSTRY 287
100.0
2 0 0
y •^y y ^v y y
Y y y
y y^ y
y yy yl ^y^X \y.y y
y Xy ̂ X y Xy
y^y^x
5 ^I 10 100 lOO
PRESSURE DIFFERENTIAL (P.S.I.)
FIGURE 4. Average streaming potential-differential pressurerelationships for aqueous drilling muds.
assumed in the pra cti cal applic atio n of equa tion (3)to be wholly electrochemical in origin, is in fact thealgebraic sum of an electrochemical potential and anelectrokinetic potential. The magnitude of the electro-
kinetic component of the total S.P. cannot always beconsidered negligible as the data of figure 4 reveal. Forhigh mud resistivities in particular, and even for compar ati vel y low mu d resistivities if the pressur e differential is high, the electrokinetic component may be farfrom negligible. Thus in deep wells, particularly, itwould seem that allowance must be made for the electrokinetic potential .
From a purely practical standpoint, assuming that asan approximation no correction for the electrokinetic potential is being made, it is interesting to note that theerror in the computation of an activity ratio from equation (3) will not be a function of the ionic strength of the inter stitia l water. This fact is shown graphical ly infigure 5. Thi s figure revea ls, for exampl e, th at the ra ti o
of apparent activity of interstitial water to true activityof interstitial water is 1.65 whether the true activityof the interstitial water is either twice or one hundredfold greater than the mud activity.* It also shows thatto use equation (3) empirically, by arb itr ari lj ' adjus tingthe value of 2f- RT/F to allow for the effects of electrokinetic potentials, is not practicable since the empirical constant would be a parameter contingent upon
* However, the error in the calculation of interstitial water resistivity is less for high absolute interstitial-water activities. Both theshape of the resistivity-salinity curve at hish salinities and thenature of the activity-salinity relationship at hig-h activities contribute to this fact.
the absolute activity of the interstitial water. This procedure is mentioned since it appears to have been attempted in field practice.
The only practical method of reducing errors resultingfrom electrokinetic potentials, without making a specificcorrection for the electrokinetic component of the S.P.,is to lower the mud resistivity. This has been discussed
previously (Wyllie, 1951).Another method of reducing the streaming potential
is to adjust the exchangeable ion on the montmorillonitein the filter cake, possibly bj' svibstitut ing a po lyva lention for the predominant sodium ion. However, this seemsimpracticable both because of the expense involved andbecause the large zeta potential itself contributes desirable properties to the mud as a plastering agent andas a suspending medium for drill cuttings. Also, as willbe discussed below, the presence of any substantialquantities of polyvalent ions in the drilling mud wouldseriously complicate the interpretation of the electrochemical component of the S.P. curve.
Investigations of the electrokinetic component inactual field operations are now being carried on using a
device (Wyllie, 1951b) which makes use of tlie hydrostatic pressure in the borehole to build a filter cake onthe exterior of a porous container. The container volumeis sufficiently large that its internal pressure is not seriously increased by the accumulation within it of mudfiltrate. As th e device is lowe red down t he boreh ole, th estreaming potential between a reversible electrode withinthe container and a similar electrode outside is automatically recorded as a function of depth. Since theinternal pressure of the container is almost constant,the streaming potential across the filter cake is recordedas a function of the external hj-drostatic borehole pressure. Using this device the electrokinetic potential characteristics of muds can be logged in the borehole. Thisprocedure eliminates the effects of mud aging which may
occur when mud samples are transferred to the labora-
tory for testing. Also it is possible to attain readilydifferential pressures of the order of thousands of pounds per square inch. For technical reasons suchpressure differentials are not readily obtained in thelaboratory. Tests of this device appear to confirm theaccuracy of equation (4). They may also lead to furtherknowledge concerning the range of pressure differential
over which the exponent y in the relationship E^ = fcP"may be considered constant (AVjdlie, 1951).
In exceptional cases where pressure differentials arevery high and the interstitial water activity is lowerthan that of the mud, it appears that the streamingpotential may be sufficiently large to effect an entirereversal of the S.P. curve. Thus in figure 6 the S.P. of the sand at 10,215 to 10,155 feet is —38 mv. Waterwas actually produced from this formation and had asalinity of 2,083 mg/1 of which 622 mg/1 were sodiumions, 5.8 mg/1, magnesium and 23.2 mg/1, calcium. Themeasured pressure differential across the filter cake was1950 psi. For the mud resistivity used, 1.55 ohm-metersat 25° C (mud filtrate resistivity 0.66 ohm-meters),figure 4 indicates a streaming potential of about —60
mv. This implies an electrochemical potential of -[-22mv, which for a formation temperature of 194° F leadsto a salini ty, based on equation (3) a nd the curves givenin Wyllie *(1951), of about 3,000 gm/1. The agreementhere is satisfactory, but it may be noted that no allowance has been made for the possible effect of temperature on the electrokinetic characteristics of the drillingmud filter cake. While preliminary experiments appearto indicate that such a temperature effect is not large,it is not yet possible to state whether or not this is generally true.
In fine, however, it appears that streaming potentialscannot be neglected if equation (3) is to be used for thepurposes of practical computation. Thus methods of logging the streaming potential in the borehole or of
otherwise allowing for it should be fur the r investigated.This is particularly true for regions such as Venezuelaand parts of California where the low natural salinityof interstitial waters contributes to the use of relativelyhigh resistivity natural drilling muds. Where drillingmud resisitivities at 25° C are 0.50 ohm-meters or less,
FiGUKE 6. A revers al of elec trochemical S.P .which resul ts fi-om high electrokineti c S.P. (electrochemical S.P. at 1012.5-10155' is positive).
it is probably permissible to forego any streaming potential correction unless pressure differentials are knownto exceed about 1,000 psi.
Nevertheless, the prac tica l use of equation (3 ), assuming that a true electrochemical potential can be obtained,is contingent upon its validity. The question of the validity of equation (3) is discussed below.
Shale as a Membrane Electrode. Wyllie and Patnode(1950) suggested that the electrochemical properties of natural shales could be rationalized if it were consideredthat these materials represented natural embodimentsof charged membranes. They also presented a brief discussion of what they believed was the essential electrochemical structure of shale membranes, drawing an analogy between the structure of shales and the structureof heterogenous membranes prepared by bonding artificial cation-exchange materials with inert and insulatingplastics. It is proposed here to amplify these concepts.It may be noted that there has been no alternative to thestructure tentatively proposed other than one by Williams (Wyllie, 1949), who in a discussion of an early
paper by the writer, appeared to suggest that the electrochemical energy of the shale cell was less a function of the properties of the solutions separated by the membrane than a property of the membrane itself. InWilliams' view the shale is in equilibrium with the salinewater contained in its interstices. He suggested that thechloride ion is more strongly adsorbed than the sodiumion, so that the former is constrained by adsorbtiveforces while the sodium constitutes the counter ion.When in contact with a dilute salt solution, the sodiumions are conceived as diffusing away from the clay particles in the shale before the corresponding chloride ionsare desorbed. He suggested that the "leading" of thecounter ions gave rise to the potential effects observed.This view accorded with his belief that the shale potential was relatively transient. It also served to explainhis observations that the potential was in large measuredependent on the nature of the shale membrane used.
While certain aspects of Williams' theory are in broadaccord with prevailing concepts of the action of membrane electrodes, the statement that the potential istransient is not in accordance with other experimentalobservations. Provided no physical leaks or cracks in ashale occur, the observed potential is maintained if theactivities of the solutions separated by a shale membraneare maintained constant. If, of course, the potential ismeasured on closed circuit, the flow of current itself tends to equalize the concentrations of the two solutionsand hence diminish the observed potential. Nor didAVilliams appear to take cognizance of the quantitativeagreement between the potentials observed and those
demanded by the Nernst equation. This agreement, thepotentials observed using sandy shale specimens, and thebehavior of shale membranes when in contact with solutions containing cations other than sodium, all suggestthat a shale barrier behaves as a typical cliarged-mem-brane electrode.
The Electrochemical Properties of Charged Mem-hrancs. In any discussion of the properties of chargedmembranes or, as they are sometimes termed, membranesof high ionic selectivity, it would be invidious to neglect
P ar t VI I ] CLAY TECHNOLOGY IN THE PETROLE UII INDUSTRY 289
to mention the pioneer work of Leonor Miehaelis. Fortun ate ly, a rec ent review by Sollner (1 950) , who hashimself made a great eontribntion to the subject, givesadeq\iate referenees to work carried out prior to the lasttwo years.
Although imperfect in several respects, the best theorynow extant covering the properties of charged mem
branes is the so-called Meyer-Sicvers-Teorell thcorj '(M.S.T.) suggested independentlv bv Meyer and Sievers(1936) and Teorell (1935).
The membranes to be considered may be conceived asbeing porous, the size of the pores being of the orderof a few Aniistriim units. In their internal structure thepores may be visualized as being geometrically similar,for example, except in their size, to the pores in anyunconsolidated or consolidated porous medium. However,along the pore walls are irregularly arranged fixedcharges. These charges may be either positive or negative and are electrically neutralized by appropriate anionor cation counter ions. Thus a charged membrane maybe expected to exhi bit cation excha nge, altho ugh t hemagnitude of this exchange capacity need not necessarily
be large. AVhether the charge on the membrane is positive or negati ve does not affect its fun dam ent al behavio r.For convenience of presentation, since shale membranesappear to be negatively charged, attention will here begiven to membranes of this tj'pe.
e0
e »—s ®^.-^®
e
®
ee
0
FlGUKE 7. Cross-section through pores of a negatively chargedmembrane of high cationie selectivity.
In figure 7 is shown schematically a cross-section of two pores in a membrane of high ionic selectivity immersed in an aqueous solution containing positive andnegative ions. The fixed negative charges shown may bea residual electrostatic charge (analagous to the chargeson clays) or maj^ be a negative group such as a sulphonicacid group. The latter is characteristic of many syntheticcation-exchange materials. Bach negative group is balanced by an adjacent positive ion, although these ionsmay be conceived as possessing reasonable mobility. Thecharge balancing is dynamic and statistical rather thanstatic and exact. Around each fixed negative charge azone may be conceived into which, due to electrostaticrepulsion effects, an anion cannot effect entry. If this
10—91001
zone of rep ul sio n effectively fills a pore (i.e., fills it to anextent which does not permit a particular size of anionto find unrestricted passage between the periphery of the repulsion zone and the pore wall), that pore will beeffectively blocke d to anions. Clea rly then, three factorsaffect this situation; the magnitude of the negativecharge, the effective size of the anion and the manner in
which the negative charge is disposed in relation to theinternal structure of the pore. These are the so-calledsteric-geometrical effects discussed by SoUner (1945).If complete pore blocking is achieved, the membrane becomes impervious to anions and it will conduct only bythe passage of cations. This means that the cation-transference num ber is unit y, the anion-transference numb erzero. Such a membrane will give potentials which obeythe Nernst equation exactly when separating two solutions having different activities but with a cation incommon. Such a potential will also be stable since nocontinuous passage of cations through the membranecan take place. This follows because the separation of charge which would be involved would be too prodigiousto be permissible.*
A similarlj^ perfect membrane separting two solutionsin which the cations are not the same would also giverise to a potential, the so-called bi-ionic potential( B . I .P . ) . Although reproducible B.I.P.'s are easily determined, this type of potential is inherently unstable,since the two cations will tend to diffuse through themembrane until their mixed concentrations are identicalon both sides. There is no electrostatic barrier to thismutual diffusion. The reproducible B.I.P. which isinitially measured (when no difftision has occurred) appears to be a function of the activities of the cationsseparated by the membrane and their transference numbers and activity coefficients within the membrane.
Membranes have been made in the laboratory by theprocess of compacti ng a powdered artificial or na tur al
cation-exchange material (clay) under high pressureand bonding the compacted particles by filling the interstices between them Avith an insulating jjlastic. The bestof these mem bra nes ap pea r to be almost perfect. Suchmembranes have a cation-transference ninnber which isvery close to unity, i.e., they have only a very smallanion "leak." In general, however, most membranes arenot perfect and in such cases the passage of anions intothe membrane pores becomes possible. The distributionof anions and cations within and without the membraneis then controlled by a Donnan distribution. In such adistribution the product of the cation and anion activities inside the membrane is equal to the same productin the solution in which the membrane is immersed.Owing to the presence of fixed negative charges within
the pores, it follows that the cation activity within themembrane is higher and the anion activity lower thanin the external solution. The ionic strength is now alsoa factor of considerable importance. The higher the ionic
* It is also of interest to note that if such a membrane has a finitehydraulic permeability, water forced through the membrane willnot contain salt. This ha s been experimentally verified. Thus aperfectly ion-selective membrane would be a perfect sieve to remove salt from water or to concentrate salt on one side. It maybe noted that if natural shale membranes ar e substantially impervious to anions (as their electrochemical performance indicates) they would affect the saturation of salts in waterexpressed from them during- compaction. This would serve to explain thermodynamically a property of shales that was postulated as a necessity by de Sitter (19 47) in his theory of thediagenesis of oil-field hrines.
strength of the external solution, the greater the anionactivity (and concentration) within the membrane.
If a membrane of imperfect ionic selectivity is usedto separate, for example, two sodium chloride solutions,then each face of the membrane adjusts itself so as to bein Donnan equilibrium with the solution in contact withit. "Within the membranes is formed a liquid junction
potential between the different concentrations of anionsand cations characteristic of these two Donnan distributions. Tf the ionic activity of the fixed charges withinthe membrane, expressed as gram moles per 1,000 gramsof water within the pores of the membrane, is A, it ispossible to compute the potential across the membraneas a function of A, the concentrations of the externalsolutions and the mobilities of the anions and cationswithin the membrane. This calculation forms the basis of the M.S.T. theory of membrane behavior. The totalpotential is composed of three separate components; aDonnan potential at each membrane face and a liquid
junc tion potent ial within the membrane.
For NaCl solutions this may be represented as
-Membrane
Solution 1
Na* = Oi
CI- = rti
-A + V A' + 4a,' CI- = ' Cl-
2 1
Na* = CI- + 4 1 Xa<
A + V A- + 4ar
— > •
-A + VA- + 403-
2
= CI- + .1
A + V A- + 402=
Solution 2
Nil* = oa
Cr = (I.
DonnanPotential
#1
Liquid.JunctionI'otential
RT
DonnanPotential
#2
Donnan Potential # 1 = InF
V ' )
Liquid Junction Potential
RT -V-in T V A= + 4ai'> + VA~\
RT
Donnan Potential #2 = In -
^ / A + VA^ — 4 a / \
V 2 )
Here V =z where Z/NH and Z7ci are the sodium
and chloride ion mobilities within the membrane.
The total potential is thus
RT ai- A + -^ A^ + iaiB = ]» — •
F 02 A + V A" + iax^
^T p v A^ + 4ai= + VA~\ Ulnl I
F \j^'A^+ 4:02^ + VAJ • + VA_
(5)
If A » «! or a2 eqiiation (5) reduces to the Nernstequation, BT/F In a^/d'l- On the other hand if A « a-^or a2equation (5) reduces to the ordinary liquid-junction potential E == BT/F TJln ai/a-y- These potentialsthus represent the upper and lower limits possible.
Equation (5) shows that when a\ or a2 are small bycomparison with A the potential developed across acharged membrane may be expected to approximatecloselj^ to the Nernst potential. The larger the absolute
THEORETICALPOTENTIAL
4731
-0.5 0.0 0.5 1.0
-LOG NaCI NORMALITYFIGURE 8. Potentia ls across sandy shales separating O.OIN NaCl
solutions from NaCl solutions of increasing concentrations.
value of A, the higher will be the permissible activities(concentrations) which may be used before the potentialdeveloped seriously diverges from the Nernst potential.Thus it may be seen that, qualitatively at least, the datatabulated in table 1 are indicative of two charged membranes of which one, the Woodford shale, has a highereffective charge, A, than the Conemaugh shale. Whileboth shales tend to give potentials obeying the Nernstequation when the activities tt] and a2 are small, theConemaugh shale diverges more from the Nernst equation than does the Woodford when these activities become larger.
A more convenient way of showing this effect is tomaintain one activity, a2, at a constant and small figureand progressively to increase the activity ai. Then a plotof potential on a linear scale against activity, ai, on alogarithmic scale will give a straight line having a poten-
P ar t VI I ] CLAY TECHNOLOGY IX THE PETROLEU^F IXDT'STRY 291
tial cliang-e equal to (RT/F) or 59.17 mv at 25° C foreach tenfold increase in «i if the Nernst equation isobeyed. Fi gu re 8 shows some typic al result s obtaine d ona series of somewhat sa ndy shales tak en from differentdepths in the same well. All but one of these shalesgive potentials which follow the Nernst equation whenthe activities are small. The potentials diverge progres
sively fr(mi the Nernst equation as the activity of theone solution is progressively' increased. The potentialsat high activities are always lower than the Nernstpotential as would be expected if an increasing proportion of current were being carried by anions.
Clearly the shales which gave rise to the data infigure 8 are very far from be ing ideal me mb ra ne electrodes. Although superior to these in their behavior, theWoodford and the Conemaugh shales used to obtainthe da ta of table 1 are likewise not ideal. Th e w rit erand his associates have now tested the electrochemicalperformance of large numbers of shale samples obtainedfrom wells in all parts of the world, and it can be saidthat only a few of these specimens were superior to theWoodford shale specimen used to obtain the data of
table 1. The great majority of shale specimens gavepotentials, when separating solutions of high ionicstrength, which were considerably below the theoreticalNernst potential .
The data obtained indicate that when measured inthe laboratorj' most shale specimens do not act as idealmembranes through which electric current is effectivelycarried only by cations. The data and the previous discussion also serve to explain the observation of Williamsnoted above. Unless a systematic investigation is made,the potentials given by different shale specimens whenseparating identical pairs of solutions appear quite unpredictable and entirely a function of the nature of theshales employed. And indeed these potentials are a function of the shales, or at least of their structure, since theshale composition probably controls the extent of anionleak. Alternatively, the physical and chemical nature of the shales, following the lines of the M.S.T. theory, maybe said to control the magnitude of the charge, A, andthe eation/anion intramembrane mobili ty ratio.
It follows then, if all shale specimens examined in thelaboratory are found to deviate to greater or lesser extents from the ideal behavior quantitatively expressedby the Nern st equation, that equation (3) , which isbased on ideal behavior, is not generally applicable.Specifically, apart from any other disabilities fromwhich it might suffer, such as the assumption that thecritical ions affecting the shale are sodium ions only,equation (3) would be expected to hold fairly generallyonly if interstitial waters were of low ionic strength.Fr om a practi cal stan dpoi nt equation (3) would thenbe worthless.
Clearly the question of the ideality of shales as membrane electrodes when in situ in the earth represents,from a practical standpoint, the crux of the entireproblem.
The Ideality of Shale Beds in Situ as Membrane Electrodes. To settle the question whether shale beds insitu can be considered as substanti ally perfect negativelycharged membranes is not easy. Several approaches arepossible. Certain of these are direct, others involve
purely deductive reasoning. None are entirely satisfactory.
The direct appr oach is clearl y to check equat ion (3)by actual measurement. That is, to compare salinitiescomputed using equation (3) with those actually measured . To achieve this sat isfa ctor ih' a nd with th e de greeof accuracy required for a truly valid test is not easy. It
is impera tive th at the total S.P. be accurat ely measure dopposite a verj ' thick clean forma tion if a st an da rd S.P.log is used, or preferably by using a static S.P. log. Thetotal S.P. must then be corrected for an electrokineticpotential component if one exists. The activity of themud must be measured. This may be done using a synthetic membrane electrode of very high ionic selectivity(Wjdlie and Patnode, 1950). While there are indications that a rather good activity may be derived fromthe res ist ivi ty of the mu d filtrate b y con side rin g thefiltrate as a pu re solut ion of sodi um chlori de, sufficientexperience has not yet been accumulated to suggestthat this is invariably true. Some of the data obtainedto date are given in table 2. Theoretically, however,unl ess th e filtrate is composed onlj^ of soluble sodium
salts, the properties of the membrane must influencesomewhat the activit y measured. Tha t is, the activit ywith respect to the measuring electrode is theoreticallynot exactly its activity with respect to shales unless thefiltrate solu tion is mono cati onic. The reason for thi s willbe shown below. However, unless there is a considerablepercentage of ions other than sodium dissolved in themud the error is likely to be negligible by comparisonwith other errors.
Tahle 2. Relationship Itetween mud activity directly measured using an Amherlite IH-100/pohjstyrene electrode (mud against standard SaCl solution) and the activity computed from the mud
filtrate resistivity assuming the filtrate to he a sodium chloridesolution.
Nature of mud
Mud resistivity and
temperatureohm-meters
Mud filtrateresistivity andtemperatureohm-meters
Measuredactivitymolality
.Activityfrom filtrate resistivitymolality
Caustic-quebracho1.7 at ,50°F1.8 at 70°F0.9 at 70°r1.5 at 60°F7.9 at 76"^2.0 at 76°r
0.93 at SOT0.97 at 70°F0.56 at 70°F0.98 at 60°r5.9 at 76''r2.0at 76°F
0.10450.0880.14S0.0990.01370.053
0.1051.7 at ,50°F1.8 at 70°F0.9 at 70°r1.5 at 60°F7.9 at 76"^2.0 at 76°r
0.93 at SOT0.97 at 70°F0.56 at 70°F0.98 at 60°r5.9 at 76''r2.0at 76°F
0.10450.0880.14S0.0990.01370.053
0.081BentoniteBentoniteNatural - . ..Natural ^ ,
1.7 at ,50°F1.8 at 70°F0.9 at 70°r1.5 at 60°F7.9 at 76"^2.0 at 76°r
0.93 at SOT0.97 at 70°F0.56 at 70°F0.98 at 60°r5.9 at 76''r2.0at 76°F
0.10450.0880.14S0.0990.01370.053
0.1350.0920.01050.038
Trials fulfilling these rigid conditions have been few.The data from one, held in a well in Oklahoma, are givenin table 3. In tab le 3 the calcul ation s of the electrochem
ical S.P. were based on sodium chloride solutions of concentrations equal to the total dissolved solid contents of the waters produced. The streaming potentials werederived from laboratory measurements made on mudsamples taken at the time of logging. These samples wereheated during the measurements to the temperaturesAvhich obt ain ed in the hole opposi te the forma tio ns. Mu dactivities were measured with Amherlite IR-lOO/Poly-styr ene electrodes. Pre ssur e differentials across the filtercakes were determined by direct measurement of theformation pressures and the hj'drostatic pressure of themud column.
Tuhte 3. Comparixon ietween theoretical electrochemicul and electrokinetic S.P. and measured S.P.
[Bull. 169
SectionInterstitial
water activityac
Mud activityam
ae/aniTlieoretical
clectroclieniicalemf
Theoreticalelectrokinetic
emf
Totaltheoretical
emf
Maximummeasured
S. P.Trial number
Feet m v mv mv mv
1254-13001254-1300
0.360.360.360.360.36
1.651.651.651.65
0.06880.06880.08790.09830.1185
0.06880.08790.09830.1185
5.245.244.103.663.04
24.018.816.813.9
52.052.044.540.535.0
100.593.089.083.5
6.27.06.05.58.5
8.07.06.5
10.0
58.259.050.546.043.5
108.5100.095.593.5
55.555.046.545.543.0
111.0103.086.5
108.5
12
1254-13001254-13001254-1300
2358-2375 _
0.360.360.360.360.36
1.651.651.651.65
0.06880.06880.08790.09830.1185
0.06880.08790.09830.1185
5.245.244.103.663.04
24.018.816.813.9
52.052.044.540.535.0
100.593.089.083.5
6.27.06.05.58.5
8.07.06.5
10.0
58.259.050.546.043.5
108.5100.095.593.5
55.555.046.545.543.0
111.0103.086.5
108.5
345
22358-2375--
0.360.360.360.360.36
1.651.651.651.65
0.06880.06880.08790.09830.1185
0.06880.08790.09830.1185
5.245.244.103.663.04
24.018.816.813.9
52.052.044.540.535.0
100.593.089.083.5
6.27.06.05.58.5
8.07.06.5
10.0
58.259.050.546.043.5
108.5100.095.593.5
55.555.046.545.543.0
111.0103.086.5
108.5
32358-2375__ _._
0.360.360.360.360.36
1.651.651.651.65
0.06880.06880.08790.09830.1185
0.06880.08790.09830.1185
5.245.244.103.663.04
24.018.816.813.9
52.052.044.540.535.0
100.593.089.083.5
6.27.06.05.58.5
8.07.06.5
10.0
58.259.050.546.043.5
108.5100.095.593.5
55.555.046.545.543.0
111.0103.086.5
108.54
2358-2375 ^.
0.360.360.360.360.36
1.651.651.651.65
0.06880.06880.08790.09830.1185
0.06880.08790.09830.1185
5.245.244.103.663.04
24.018.816.813.9
52.052.044.540.535.0
100.593.089.083.5
6.27.06.05.58.5
8.07.06.5
10.0
58.259.050.546.043.5
108.5100.095.593.5
55.555.046.545.543.0
111.0103.086.5
108.5 5
0.360.360.360.360.36
1.651.651.651.65
0.06880.06880.08790.09830.1185
0.06880.08790.09830.1185
5.245.244.103.663.04
24.018.816.813.9
52.052.044.540.535.0
100.593.089.083.5
6.27.06.05.58.5
8.07.06.5
10.0
58.259.050.546.043.5
108.5100.095.593.5
55.555.046.545.543.0
111.0103.086.5
108.5
Water analyses.
Ions (mg/1) 1254-1300 ft. 2358-2376 ft.
SO4CIHCO3Na -. -- ---
1,14018,364
38111,691
446210
nil96,780
24
48,982CaMg
1,14018,364
38111,691
446210
8.3102,254
34,050 156,35034,050
The five trials recorded were made at intervals duringthe course of about one month during which the hole wasbeing deepened. The formations were cored and werefound to be relatively free of shale or clay contamination.
Considering the assumptions made, table 3 reflects reasonably good agreement between potentials based onequation (3) and those actually measured. It may benoted that the ionic strength of the 2358-2375 feet formation water is large.
An analysis made by the writer (1949a) showed thatin a number of different regions in Kentucky, Oklahomaand Illinois the agreement found between the S.P. measured and that based on equation (3) was good. In theseregions the salinities of the interstitial waters ranged ashigh as 172,350 mg/1. Nevertheless, in this examinationno correction was made for possible streaming potentials, and mud activities were not actually measured.
I t has been noted previously that the total S.P. iswidely and rather successfully used in the routine employment of equation (3). While perhaps suggestive of the basic accuracy of equation (3), this fact cannot beconsidered a direct substantiation of its validity sinceelectrokinetic potential corrections are not normallymade nor accurate activities used. The possibility that
the agreement is dependent upon a fortuitous compensation of error has already been noted (Wyllie, 1951).
Indirect approaches to the basic problem, whether ornot shales * can be considered perfect membranes, maynow be considered.
* The writer is aware th at a shale Is difficult to define rigidly. Atwhat point does a shale become a sandy shale and the latter ashaly sand? In this paper shale, unqualified, is deemed to meanan argillaceous material which, if free of geometrical effects,would give on a log a S.P. shale basel ine. The classification isadmittedly arbitrary and could even be unrealistic geologically,since a section of sandstone in which every pore was entirelyfilled with shale could, under certain circumstances, give a perfect shale baseline.
If a shale is not a perfect membrane then any shalewhich is sandwiched between two horizontal permeablebeds which contain different salinities of interstitialwater would not only develop a potential between thetwo permeable beds but would permit current to flowfrom one bed to the other in a perpendicular direction.
The current would flow in such a direction as eventuallyto equalize the salinities of the waters in the two permeable beds. The rapidity with which this equalizationwould take place would depend upon the thickness of the intervening shale bed and the difference in thesalinities of the waters in the two permeable beds. Thegreater the salinity difference and the thinner the shalebed, the higher the potential gradient across the shaleand the more rapid the rate of ionic migration. However,for thick beds and for relatively small differences ininterstitial water salinities the rate of equalization wouldnot be high and even geologic time would probably beinsufficient to effect substantially complete equalization.Thus the fact that shale beds are known to separate permeable beds which have interstitial waters of differentsalinities is not valid evidence of their complete anionimpermeability. Indeed the fact that in many regions thesalinity of interstitial waters changes very slowly withdepth might tend to indicate rather that the contrarywere true and that shales were relatively inefficient asanion impermeable membranes.
Perhaps the most suggestive fact which bears on thequestion of the efficiency of shale as membranes is theobserved constancy of shale baselines on logs made inevery part-of the world. On the great majority of logs,it is possible to draw a consistent shale baseline overmany thousands of feet of log. This baseline on the usuallog is drawn through the most positive excursions of the S.P. curve, and it is defined in most reasonablyshale-rich sections by numerous shale beds. When the
fact is considered that any change in the contact potential of the borehole electrode with the mud fluid affectsthe baseline, it may be said that eac^h of these shale bedspossess an electrochemical property which, within a fewmillivolts, is identical. Here, then, is a measure of consistency which in any one well is possesed by shaleslaid down at what mus t often have been widely differinggeologic times. Nor arc these shales physically identical.They generally differ in the amounts of clays, organicmaterials and silts which they contain and the extent towhich they have been lithified.
Part VII] CLAY TECHNOLOGY IX THE PETROLETTM INDUSTEY 293
For simplicity a clean, shale-free permeable bedseparating two shale beds may be considered. It will beassumed, as seems generally to be the case, that withinthe permeable bed the salinity of the interstitial water isuniform. Then the S.P. deflection at the top of the permeable bed results from a chemical interaction betweenthe mud and interstitial water with the shale lying
above the permeable bed. This interaction leads to theproduction of an emf which in turn causes the S.P.curve to deflect a definite amount. If the permeable bedis sufficiently thick, the ohmic potential changes in theborehole which affect the borehole electrode potential donot persist over the entire bed thickness. The S.P. deflection climbs to a plateau and the borehole potentialdoes not alter until the electrode is subjected to theetfeets of current circulation which result from the electrochemical interaction of the lower shale bed with theinterstitial water and mud. The potential change is nowin a sense opposite to that experienced by the electrodeat the top of the bed and the S.P. deflects from itsplateau opposite the permeable bed, finally attaining afresh value opposite the lower shale bed. If the potential opposite the lower shale bed is identical with thatopposite the upper, that is, if there is a constant shalebaseline, it follows that the potential given by the electrochemical interaction of the lower shale bed is identicalwith that given by the upper. By the same token, if theshale baseline is maintained over thousands of feet, itfollows that each shale which separates a permeable bedbehaves in an identical fashion* electrochemically.
This point may be further clarified if it is noted, aspointed out by Doll (1949), that the S.P. curve is symmetrical. A constant "sand line," that is a line drawnthrough the maximum negative excursions of a conventiona l log, is 7101 obtained unless all i nte rst iti al watersin permeable beds are identical. Such sand lines are obtained (fig. 2) bu t genera lly over small distances com
pared with shale baselines. Thus, as noted above, theexistence of a constant shale baseline extending over anentire S.P. log implies remarkable electrochemical homogeneity amongst all the shales in the borehole.
Now the electrochemical potential developed by eachshale above and below a permeable bed is controlled bythe same two fluids, the mud and the same interstitialwater. If the two shales are imperfect, this implies thateach shale possesses an identical anionic leak. On thebasis of the M.S.T. theory each possesses the same charge, A, and the same ratio of cation and anion mobilities.Figure 8 shows that leaky membranes do not show thesame electrochemical potentials when separating identical solutions except in the range of concentration inwhich they follow the Nernst equation. Figure 8 may
be considered typical of resul ts obtained with imperfectmembranes. Even when membranes are made from identical percentages of identical cation exchange materialand plastic and are moulded in an identical manner, itis extremely rare for two membranees to give identicalpotentials in the concentration range in which the Nernstpotential is not followed. It is, however, pertinent to notethat in the range where the Nernst equation is obeyed
* The fact t hat certai n thin shale beds do not retur n to the baseline obtained In conventional S.P. logging- is purely a geometrical effect and does not affect the argument developed. Doll(1949) has adequately treated this point.
CONNATE WATER
^zzzzzzzza)
HYDROUS MICA
<@KAOLIN
oSILICA
FiGL'RE 0. Electrochem ical s tru ctu re of sliale.
the physical nature of a non-homogeneous electrode, orthe amount or tj'pe of cation exchange material it contains are of no importance. This is to be expected theoretically and has been demonstrated experimentally(Wyllie and Patrode, 1950).
The weight of existing evidence seems to indicate thatshales in situ in the earth do act as perfect membraneelectrodes. In this event equations of the type of equation (3) may be expected to be applicable to the electrochemical potentials developed when all conditions for
their application are fulfilled. Nevertheless, it must bepointed out that if further research on the nature of shales and on the structure of charged membranes shoulddisclose that the value of A and the cation/anion mobility ratio in all shales could reasonably be identical, thisconclusion could no longer be sustained. In this paperthe fact that shales in situ do obey the Nernst equationwill be assumed and the consequences of that assumptionwill be examined.
A Tentative Electrochemical Structure for Shales. Infigure 9 is given a tentative two-dimensional physicalpicture of the essential structure of shales from the electrochemical standpoint. For this purpose the principalcon.stituents of shale are assumed to be silica, hydrousmica, and kaolin. These components, for the marineshales which are of patrieular importance in petroleumexploration, have been found by the writer's colleaguesto be typical. These components appear also to be inessential agreement with the results reported by others(Millot, 1952). In most shales, the silica particles varyin size, many being similar in size to the clay particles.The plate-like structure of the clays makes them tendto orientate themselves parallel to the bedding planesof the shale. In figure 9 the particles of hydrous micaare drawn surrounded by a water sheath in which arelocated the exchangeable ions. In this same sheath therewill, therefore, exist a considerable negative electrostaticcharge, a force repelling anions. Between the particlesof clay and silica there is water containing dissolvedsalts. In the figure the line of demarcation between thewater sheaths surrounding the clay particles and theinter-particle water has been drawn for convenience of presentat ion. Actuall y this is artificial and a swarm of ions gradually changing in composition is to be expected.
Under the enormous pressure of compaction resultingfrom the weight of overlying strata, the particles of allkinds are forced tightly together. If the pressure is suchthat all continuous paths for ions through the shaleinvolve at some point passage through tlie water sheatlisurrounding a clay particle, it will mean that within the.shale will exist a surface across which electric current
Part VII] CLAY TECHNOLOGY IX THE PETROLEU JI INDUSTRY 295
can only be carried by cations; i.e., the anion transference will be zero. Prom a thermodynamic standpoint, if there is such a surface in the shale, the shale will function as a perfect negativelj' charged membrane.
It is, perhaps, not immediately obvious that the concentration of the connate water in the shale, whichlargely controls its electrical resistivity, does not affect
the potential developed. Thus, marine shales frequentlyshow a lower resis tivity than non-marine shales (Clan-det, 1950) although electrochemically both shale typesmay behave similarly. This fact may be demonstratedif a system is considered composed of a niimber of perfect membranes separated by solutions of different concentration. For convenience all the solutions will be considered to consist of NaCl, but the result can be readih-generalized. Consider:
NaCl
Then the potential is
NaCI
Membranes -
RT a, RT «2 RT a-^ RT a^ E = In 1 In \ In 1 In —F tto F ao, F tti F a.-,
RT oi In —
F a.(6)
That is, only the exterior solutions affect the over-all potential developed. The electrical resistivity of the systemis a function of the resistivities of the membranes andthe solutions. If the conducting paths in the membranesare small by comparison with the paths through thesolutions, the latter will be dominant. This appears tobe the physical situation in shales.
If overburden pressure is removed from a shale, a
certain degree of elastic expansion is to be anticipated.This alone will tend to give rise to leak paths availableto anions, for the general effect will be to decrease theeffective charge, A, of the membrane. For while thecharges on the clays are not altered, the effective volumein which they are disposed will be increased, leading toa diminution in the molal activity, A. In laboratorypractice this effect is frequently reinforced by unavoidable drj'ing and cracking of the shale which gives riseto even larger leak paths. Hence it is not surprisingthat the electrochemical performances of shale sampleswhen tested in the laboratory are often inferior to theirapparent performances in situ.
Experimental verification has been found of the postulated effect of pressure. Thus membranes formed by
moulding powdered shale in lucite under a pressure of 5,000 psi have been found to possess an electrochemicalperformance superior to that of the shale samples beforepowdering (Wyllie and Patnode, 1950). An analogouseffect appears to be obtained when using synthetic sul-phonated phenol formaldehyde cation exchange resins(Wyllie, 1952).
Shale Baseline Shifts. An abrupt shift of the shalebaseline is sometimes observed. Although the phenomenon is comparatively rare it unquestionably exists. AVhenconsidering such shifts, it is wise to concentrate on those
which are characteristic of a particular environmentand which are reproduced on all logs run in a particularfield. Isolated shale baseline shifts on logs are more oftenthe consequence of an instrumental fault in the loggingequipment than the manifestation of a genuine phenomenon.
In figure 10 is reproduced a log which shoAVS a well-
defined shale baseline shift. This shift is characteristic of all logs in the area. Prom figure 10 it maj^ be seen toamount to +60 mv.
On the log there is a good shale baseline down to1760 feet and another below 1875 feet. The maximumS.P. deflection of the permeable beds above 1760 feetis rather constant and amounts to —37 mv. The maximum deflection of the beds at 1835-1860 feet with reference to the lower shale baseline is —97 mv. The mudactivity is 0.033 g moles/1000 g water. Application of equation (3) gives an interstitial water activity of about 0.064 corresponding to —37 mv and 0.74 corresponding to —97 mv. These activities in turn correspondto NaCl solutions with salinities of about 5,000 mg/1and 66,000 mg/ 1 respectively. At the format ion tempera
ture of 86° F, solutions with these salinities would haveresistivities of about 1.0 ohm-meter and 0.09 ohm-meters.It has been established that in the section 1680-1780
feet the formation factor (1942) of the permeable sections is rather constant. Thus the slope of the resistivitycurves between these depths appears to reflect a rathersteady change in interstitial water resistivity. The resistivity charge is from about 1 ohm-meter to 10 ohm-meters, a ratio of about 10 to 1. This ratio agrees closelywith the ratio of the calculated water resistivities, 1 ohm-meter and 0.09 ohm-meters. Figure 10 appears to be anexcellent example of a shale baseline shift which resultsbecause the salinity of the water in a series of rathershaly permeable beds changes, so that the water in contact with the shale which constitutes a part of the upper
shale baseline is very different from the water in contactwith shale which constitutes a part of the lower shalebaseline. However, both the upper and lower shales apparently have electrochemically identical properties.
The change in salinity which is shown in figure 10may readily be discerned on the log. Hence the conclusions drawn from the S.P. curve can be easily checkedagainst the data of the resistivity curves. Were thischange to have taken place within a very thin permeablebed, as may be possible under suitable conditions of flushing from an outcrop, conclusions based on the formof the S.P. curve would be almost impossible to check on the resistivity curves and the shift would be correspondingly more inexplicable. It is difficult to say howmany baseline shifts are the result of salinity changes
in permeable beds and how many result from genuinedifferences in shale nature. It does not seem unreasonableto expect a shale baseline shift at a facies change, particularly from marine to nonmarine, and it is believedthat these have been observed. Such ett'ects appear to bebound up with the theory of the bi-ionic potential.
It has been assumed in the foregoing discussion andcalcidations that interstitial waters and mud fluids canbe treated as sodium chloride solutions. This is an oversimplification and must introduce errors. The errors introduced may be divided into two parts. Those arisingfrom the effect of cations other than sodium on the
29 6 C L A Y S A N D C L A Y T E C H N O L O G Y [Bu l l . 1 6 9
p o t e n t i a l a c r o s s t h e s h a l e a n d t h o s e a r i s i n g f r o m t h e
effect o f b o th ca t i o n s an d an io n s , o th er t h a n so d iu m an dc h l o r i d e , o n t h e l i q u i d - j u n c t i o n p o t e n t i a l w h i c h i sf o r m e d b e t w e e n t h e i n t e r s t i t i a l w a t e r a n d t h e m u d .
\ Y h e n a fo r m a t io n i s sh a l e - f r ee t h e l a t t e r m ay ea s i l yb e a s s e s s e d i f l i q u i d - j u n c t i o n p o t e n t i a l s b e t w e e n s o l u t i o n s h av in g - co m p o s i t i o n s ak in t o t h o se ac tu a l l y en
c o u n t e r e d i n t h e f i e l d a r e c o m p u t e d . T h e s e p o t e n t i a l sm a y b e c o m p a r e d w i t h t h e l i q u i d - j u n c t i o n p o t e n t i a l sco m p u ted fo r so d iu m ch lo r id e so lu t i o n s o f s im i l a r i o n i cs t r e n g t h . T h e l a t t e r is t h e a s s u m p t i o n g e n e r a l l y m a d e a s
a p r a c t i c a l c o n v e n i e n c e t o p e r m i t t h e s o l u t i o n o f e q u a t i o n ( 3 ) . T h e e r r o r i n v o l v e d i s g e n e r a l l y m i n o r .
I f t h e fo r m a t io n i s n o t su b s t an t i a l l . y sh a l e - f r ee , t h e
e r r o r b eco m es m o re d if f icu l t t o as sess . Th e o re t i c a l l y ,h o w e v e r , a s h a l y p e r m e a b l e b e d i s m e r e l y a s h a le w i t hl a r g e a n i o n l e a k p a t h s . T h i s c o n c e p t i s g i v e n f o r m a lt r e a t m e n t b e l o w .
T h e p r o b l e m o f f o r m u l a t i n g e q u a t i o n s t o d e f in e t h eB . I . P . h a s b e e n c o n s i d e r e d hy b o t h M a r s h a l l ( 1 9 4 8 ) a n dS o l l n e r ( 1 9 4 9 ) . T h e w o r k of S o l l n e r is p e r h a p s t h e
m o r e e x t e n s i v e . S o l l n e r c o n s i d e r s t h a t i n a m e m b r a n e i n
w h i c h c a t i o n t r a n s f e r e n c e i s u n i t y t h e s i g n a n d m a g n i t u d e o f t h e B . I .P . a r e co n t ro l l ed b y t h e r a t i o o f t h e
a d s o r b a b i l i t i e s of t h e t w o io n s w i t h i n th e m e m b r a n e a n db y t h e r a t i o o f t h e i r i n t r a m e m b r a n e d i f f u s i o n v e l o c i t i e s .S t e r i c h i n d r a n c e e ff e ct s w i t h i n t h e m e m b r a n e m a y a l s op l a y a p a r t . F o r e x a m p l e , i f c e r t a i n p o r e s i n a m e m
b r a n e a r e s o s m a l l t h a t t h e y w i l l a d m i t o n l y o n e of t h et w o i o n s b e i n g c o n s i d e r e d , t h e a d s o r b a b i l i t y o f t h es m a l l e r i o n s in s u c h p o r e s w i l l b e m i ic h g r e a t e r t h a n
t h e i r a d s o r b a b i l i t y e l s e w h e r e i n t h e m e m b r a n e . B a s i c a l l y , h o w e v e r , S o l l n e r a p p e a r s to c o n s i d e r t h a t t h ed i s t r i b u t i o n o f t h e t w o i o n s w i t h i n t h e m e m b r a n e i se v e r j ' w h e r e t h e s a m e . M a r s h a l l h a s f o r m a l l y t r e a t e d b i -
i o n ic p o t e n t i a l s a s a l i q u i d j u n c t i o n p o t e n t i a l t o w h i c ht h e H e n d e r s o n e q u a t i o n m a y b e a p p l i e d . A n i o n m o b i l
i t i e s a r e c o n s i d e r e d t o b e z e r o . T h i s t r e a t m e n t i s q u i t ep e r m i s s i b l e t h e r m o d y n a m i c a l l y a n d i ts v a l i d i t y i s n o td e p e n d e n t u p o n a n y d e t a i l s o f t h e e l e c t r o d e m e c h a n i s m se x c e p t f or t h e i m p l i c i t a s s u m p t i o n t h a t t h e d i s t r i b u t i o no f t h e i o n s t o wh ich t h e m em b ran e i s se l ec t i v e i s i d en t i
c a l o n t h e m e m b r a n e f a c e s i n c o n t a c t w i t h t h e s o l u t i o n sa n d i n t h e s o l u t i o n s t h e m s e l v e s . T h i s a s s u m p t i o n d o e sn o t s e em t o i n v o l v e an jr n u m e r i c a l e r r o r s w h e n m o n o
v a l e n t i o n m i x t u r e s a r e c o n s i d e r e d . H o w e v e r , t h e c o n c e p td o e s n o t s e em t o b e t h e o r e t i c a l l y s o u n d w h e n m i x t u r e so f m o n o v a l e n t a n d d i v a l e n t i o n s a r e c o n s i d e r e d , f o rin su ch cases i t i s we l l k n o wn th a t t h e d iv a l en t i o n i s
p r e f e r e n t i a l l y a d s o r b e d b y a n i o n - e x c h a n g e m a t e r i a lw h e n t h e i o n i c s t r e n g t h o f t h e m i x t u r e of m o n o v a l e n ta n d d i v a l e n t i o n s i s s m a l l . I n g e n e r a l t h e d i s t r i b u t i o n
o f i o n s o n t h e io n - e x c h a n g e m a t e r i a l i s n o t i d e n t i c a l w i t hth e d i s t r i b u t i o n o f t h e sam e io n s i n a so lu t i o n i n co n t ac tw i t h t h e i o n - e x c h a n g e m a t e r i a l b u t i s a f u n c t i o n o f t h era t i o of co n c en t r a t i o n s o f t h e two io n s i n t h e s o lu t i o n
a n d i t s i o n i c s t r e n g t h .
Th e p o t en t i a l ac ro ss a p e r f ec t l j ^ ca t i o n se l ec t i v e m em
b r a n e w h i c h s e p a r a t e s t w o m o n o v a l e n t i o n s o l u t i o n s , f o r
e x a m p l e N a C l a n d K C l , m a y t h e n b e c o n s i d e r e d a s t h e
s u m o f t w o D o n n a n p o t e n t i a l s a t t h e f a c e s o f t h e m e m
b r a n e i n c o n t a c t w i t h t h e s o l u ti o n s a n d a l i q u i d j u n c t i o n
p o t e n t i a l f o r m e d i n s i d e th e m e m b r a n e . T h i s l i q u i d j u n c
t i o n p o t e n t i a l i s a f u n c t i o n o f t h e r e l a t i v e m o b i l i t i e so f t h e i o n s N a + a n d K * w i t h i n t h e m e m b r a n e . T h i s c o n cep t di f f e r s f ro m th a t of So l ln e r , s i n ce t h e d i s t r i b u t i o n
o f i o n s i n a m e m b r a n e w h e n a B . I . P . i s m e a s u r e d i s n o tco n s id ered t o b e u n i f o rm . In f ac t i t i s co n s id ered t h a tt h e m e m b r a n e g r a d e s f r o m a c o n d i t i o n i n w h i c h a l l i t s
ex ch ang e posi t ion s are f il led by K̂ " ions at i t s in t er fac e
wi th t h e KC l so lu t i o n t o a co n d i t i o n w h ere a l l i t s ex ch a n g e p o s i t i o n s a r e o ccu p ied b y Na+ io n s . Th e l a t t e rc o n d i t i o n e x i s t s a t t h e i n t e r f a c e o f t h e m e m b r a n e w i t h
t h e N a C l s o l u t i o n . M o r e g e n e r a l l y f or m i x e d s o l u t i o n so f two io n s of w h a t ev er v a l en c j^ , t h e d i s t r i b u t i o n o fio n s o n each m e m b ran e f ace i s ca l cu l ab l e i f t h e d i s t r i b u
t i o n co ef f i c i en t s o f t h e ca t i o n ex ch an g e m ate r i a l o f t h em e m b r a n e i s k n o w n f o r t h e i o n s c o n s i d e r e d . T h e l i q u i dj u n c t i o n p o t e n t i a l is f o r m e d w i t h i n t h e m e m b r a n e b e tween th e i o n s o n each f ace o f t h e m em b ran e .
T h e s e c o n s i d e r a t i o n s g i v e r i s e t o e q u a t i o n s a n a l a g o u sto t h o se o f t h e M.S .T . t h eo ry i f t h e m em b ran e i s n o t
co n s id ered t o b e p er f ec t l y se l ec t i v e t o o n e t y p e o f i o n ,e .g . , ca t i o n s . Ho wev er , fo r i d ea l l y ca t i o n se l ec t i v e m em b r a n e s t h e e q u a t i o n s s i m p l i f y , s i n c e t h e a n i o n s t h e n p l a y
n o p ar t ex cep t fo r t h e i r e f f ec t o n t h e ac t i v i t i e s o f t h ec a t i o n s i n t h e s o l u t i o n s . T h e f o l l o w i n g e q u a t i o n s m a y b ed e r i v e d ( s e e W v l l i e , 1 9 5 4, a n d W v l l i e a n d K a n a a n ,1 9 5 4 ) .
I . Monovalent — Monovalent
e . g. N a C l v e r s u s K C l
RT ttK VK
E = In •
F aifa TJ-Ka
H e r e ttK, f f.va a re t h e i o n i c ac t i v i t i e s o f t h e so d iu m an dp o t a s s i u m i o n s s e p a r a t e d b y t h e m e m b r a n e , UK/TISG is
t h e i r io n i c m o b i l i t y r a t i o w i t h i n t h e m e m b r a n e ( e q u a lt o t h e r a t i o of t h e i r t r a n s f e r e n c e n u m b e r s ) .
I I . Monovalent — Monovalent - j - Monovalente . g. N a C l v e r s u s N a C l + K C l
BT a'na+aKiUK/UNa)
E = In
F a"-sa
H er e aVo i s t h e ac t i v i t y o f t h e so d iu m io n i n t h e m i x eds o d i u m a n d p o t a s s i u m s o l u t i o n , a "y a i s t h e s o d i u m i o n
a c t i v i t y i n t h e p u r e s o d i u m c h l o r i d e s o l u t i o n .
P ar t VI I ] CLAY TECHNOLOGY IN THE PETKO LEUM INDUSTRY 297
Here the symbols are as before with the addition that Aca is the activity of calcium ions within the membranewhen the membrane is wholly in the calcium form, and^A'a the corresponding sodium activity when the membr an e is wholl j' in the sodium form. The assum ptio n tha t Aca = 2'-'i-Va imp lie s tha t th e act iv it y coefficients of thecalcium ions in the calcium form of the membrane is
identical with the activity coefficient of sodium ions inthe sodium form of the membrane. While quantitativeinformation concerning such activity coefficients is lacking, this assumption may be in considerable error. Nevertheless the activity ratio, A^a/Aca, is constant and theapproximate relationship given above based on a ratio of uni ty maj- be useful for certain qualitat ive applicat ionsof the relationship. The ratio Aya''2Aca is probablygreater than unity.
IV. Monovalent -\- Divalent — Monovalent
e.g. N aCl + CaCla vers us NaCl
RT aVa AKa BT E = I n • \
F a"^a aysji
ajiji [ t/.v«
If̂ c
F
- 4 A - .
t Sa
(l-NaR
UNa
[TJca]
(2(axaB)--aca^
I
(Ui,
-•i.Va
a.r,B •
TJsa 2(a.vaB)2 • aca.
Uc OJ ^a
In-
Aua
Vca
Here the symbols are as before. In addition a\-aR is theactivity of the sodium ions on the membrane when itis in contact with a mixed solution of NaCl and CaCl2which has a sodium ion activity in the mixed solution of aVa and a calcium ion activity of aca-
This complex equation may also be written in terms of the exchange coefficient of the sodium-calcium exchange.A similar but not identical equation pertains to thesystem mon oval ent -f- diva lent v ersus monov alen t.
V. Monovalent + Bivalent — Monovalent -{- Divalent
e.g. NaC l + CaCla ver sus Na Cl + CaClo
This may conveniently be written as
BT a'iia RT x"yaB RT E = In \ Iw 1
F a"Na F x\aB F
Vca
yca
y.Va
2YCa
y.Va,
x'Ka
In
L' Xa
Vca
2yca
jKa.
2yca
+• yA'a
Vca
yca
y.Va
2YCa
y.Va,
3:"Ka Vsa
Vca
2yc-(i
y.vii_
2y(7a
+ — yNa
Here a'sa and a".Ya are the activities of the sodium ionsin the mixed sodium and calcium chloride solutions separated by the membrane; x'^aR is the fraction of the exchange sites occupied by sodium ions on the membraneface in contact with the solution i-ontaining sodium ionsof activity a-i, and x'\iji is the corres pondin g fraction onthe other membrane face. The ratio yca ' V-Va is the ratio
of the activity coefficients of the calcium and sodiumions when the membrane is in the calcium or sodiumform respectively.
Although still a simplification, the only cations ininterstitial waters in permeable formations may be considered to be sodium and calcium. In general this is true,but occasionally the magnesium ion content is not negligible. As a divalent ion, however, magnesium can probablybe lumped with calcium without the introduction of anyserious error. In most, but not all, interstitial waters,the number of equivalents of sodium ion greatly exceedsthe member of equivalents of calcium ion.
In the mud fluid the principal soluble cations are alsosodium and calcium, with again the sodium ion predominating. Nevertheless, in modern lime-base muds the
amount of soluble calcium can be appreciable. This hasbeen shown by Bergma n (1952).
A shale in situ may tlms be considered to separate twosolutions which differ in ionic strength but both of whichcontain sodium and calcium ions. The equation derivedas case V above should then be applicable.
Before the equation may be used it is necessary toconsider what values x'^aR, X/'NOR are likely to have innatural shales. Should these be identical it is clear thatthe equation of case V reduces to
BT a Na
E = InF a"y„
Thus if the fraction of exchange sites occupied by
sodium ions on the shales in the borehole is identical withthe fraction of exchange sites occupied by sodium on theshale face in contact with the interstitial water in thepermeable formation, the shale will obey the Nernstequation for the sodium ions in the interstitial waterand the mud. In this case the only effect of the divalentcalcium ion will be to increase the ionic strengths of thesolutions and otherwise to affect the sodium ion activities.
Now the magnitude of x'^aR, fl^e fraction of exchangesites occupied by sodium on the shale face in equilibriumwith the interstitial water, undoubtedly varies both Aviththe ratio of sodium to calcium ions in the interstitialwater and with the absolute concentrations of these ionsin the wat er. Wo rk by Case (1933) and Taylor (19 29) ,
shown in tabl es 4 and 5. suggest th at alt houg h t hisfraction is variable it has an average of something over0.7 in marine shales. Limited data obtained by thewriter's colleagues tend to confirm this figure. By andlarge the ratio will tend to be highest, for any Na/Ca
ratio in an interstitial water, if the interstitial water ishighly saline, and lowest in waters which are comparatively fresh. In the extreme case of shales in the zoneof surface waters, it appears from table V that x'x„Bapproximates zero.
In the borehole the situation is more difficult to assess.Although the usual Na/Ca ratio in the mud will be
much higher than in the interstitial water, the equilibrium calcium fraction of the clays on the faces of shaleformations in the borehole may not grea tly differ fromthe fraction on the faces of the same shales in contactwith interstitial water. This would be the case becausethe low ionic strength of the usual drilling mud wouldlead to preferential divalent ion absorbtion. Hence inmost cases the difference between x\^aR and x"}faR maybe extremely small. The ratio of x't^aB to a;",voi? wouldthen approximate unity.
For a baseline shift to occur in crossing a permeablebed in which the interstitial water is uniform, the ratio
X SaR
of for the upp er shale bed would have to be X Satl
different from that for the lower shale bed. If the typeof clay in these beds is similar, as seems to be the case,it seems possible that the exchange constants of the two
X iVd '^
beds are similar and therefore the ratio for the
X Ha^
two beds are virtually identical. Thus no baseline shift
Uifa JCa
would occur unless the ratios and differedUca jNa
greatly. This would fit observations on logs.
If, however, two shales dift'ered in their exchange X Nati
constan ts thev could give rise to different ratios X"N,B
when separating tlie same two solutions containingVxa
sodium and calcium ions. Probably in such easesUca
JCa
and would also differ. Such an effect may be pos-
sible. Further work on the properties of clays in shalesand their variation from shale bed to shale bed in ageologic column is necessary before the probability canbe assessed. If, however, as sta ted by Millot (1952)kaoliniti c minerals are character istic of fluviolacustrinecontinental facies and illite of saline lagoonal and basiccontinental facies, it is not unreasonable to expect abaseline shift when a borehole passes from a non-marineto a marine sequence. Within each facies the baselineshould be essentially constant.
As previously noted, if
BT (I Na
x'xaB = x'\aB, E = In .F a"ya
In this event, the potent ial across the shale and thereforethe entire S.P. measured will be less than that given byequation (3), which assumes that the total salt contentof the interstitial water behaves as NaCl, not merely theactual NaCl content of the interstitial water. If, however, x"NaR is not equal to x'l/aR the potential is givenby the equation of case V.
Assuming x'^aR = 0.7 and that when using highsodium/calcium ion ratio drilling muds the clays of theshale face in the borehole will be enriched with respectto sodium ions, the potential change may be calculatedif certain assumptions are made. It will be assumed that x"saB = 1-0, i.e. all divalent ions on the shale in theborehole are replaced by sodium, the worst possible case.
Experi ments with shales indicate that may be about
Uca
5, although other experiments with synthetic membranesnow in progress indicate that pressure may increase this
ycarat io considerably. The rat io is difficult to estimate
and for convenience will be considered to be unity.
Tonkawa seriesLower Permian red shaleLower part of shale
2 0 ' above Gilcrease sandAbove shaly sand—^Woodford, just above Hunton l imestoneIn contact with oil sandBetween two streaks of Cromwell sand
Tulsa outcrop, 6 ' below base of Checkerboard l imestoneTulsa outcrop sample, 25' below Checkerboard l imestone-.Tulsa outcrop, underclay of coal 12' below Checkerboard
2 - 6 " below coal ^Tulsa outcrop, as above but 0-2" below coalOther Tulsa outcrop samples-
N a
15.6
0.00050.0013
0.0064
0.0059
0.0046
0.0079
.\verage
5. 68 .1
12 .310 .86 .85 .12
( \ ; i u i u l C a i n n i f . / l O O « . )
PercentN a
547273
7679727481
73
< 0 . 1< 0 . 1
< 0 . 1< 0 . 1< 0 . 1< 0 . 1
PercentCa
4628272421282619
> 9 9 . 9> 9 9 . »
> 9 9 . 9> 9 9 . 9> 9 9 . 9> 9 9 . 9
BT x'\JtT h e n In = - | -9 .2 l u v an d t h e e x p ress io n ,F x'i,aB
RT r VyJUca year yxa
F Uhui/Vca — 2 y c a / y A ' o _
I' Xii yca yCa
2 H2.f 'xiiR V Ca JNa y.Va
l!( = : — 6 . 8 m v .
x"siiR '̂-Vi/ yca yca
Vca yNa yNa
T h e i n c r e a s e i n t h e S . P . ( a c t u a l l y a n i n c r e a s e i n t h e
n eg -a t iv e S .P . r eco r d ed ) wo u ld b e 2 .4 m v o v er t h a t o b t a in ing? i f on ly the so diu m ion ac t iv i t ies in the tw o so lut i o n s w e r e a f f e c t i n g t h e s h a l e p o t e n t i a l . F o r x'xaB = 0.5a s i m i l a r c a l c u l a t i o n g i v e s t h e i n c r e a s e i n n e g a t i v e S . P .as 5 .6 m v . I t i s seen t h a t t h ese e f f ec t s a r e n o t l a rg e u n l ess; r ' y aS i s v e ry sm al l b y co m p ar i s o n w i th x"f,,iR. I n m u d sw h i c h d e c r e a s e x'\aB b e lo w x'saB ( a s m a y o c c u r w i t hs o m e l i m e - b a s e m u d s ) t h e n e g a t i v e S . P . w i l l b e s o m e w h a t
• BT a'i,ar e d u c ed b e lo w th e 1 M f ig ure. I t m a .y b e n o t e d
F a"i,a
t h a t t h e s e p o t e n t i a l s a r e n o t d e p e n d e n t u p o n t h e a c t u a li n t e r s t i t i a l w a t e r s a l i n i t y e x c e p t i n a s m u c h a s t h i s s a l i n i t yaffects the value of X ' N ^ B . T h u s t h e i r e ff ec ts a r e g r e a t e r
p e r c e n t a g e w i s e w h e n t h e r a t i od Na
i s s m a l l t h a n w h e n
tt Na
i t i s l a rg e , an d m ay b e ex p ec t ed t o b e a t a m ax im u m in
t h e c a s e o f r e l a t i v e l y f r e s h i n t e r s t i t i a l w a t e r s .
I n g e n e r a l t h i s a n a l y s i s i n d i c a t e s t h a t t h e e l e c t r o
ch em ica l S .P . i s l i k e ly t o b e m o re a fu n c t i o n o f t h es o d i u m i o n c o n t e n t of t h e d r i l l i n g m u d a n d i n t e r s t i t i a lw a t e r t h a n o f t h e t o t a l s a l i n e c o n t e n t s . T h u s e q u a t i o n
( 3 ) m a y b e e x p e c t e d t o g i v e v a l u e s f o r c o n n a t e w a t e r
s a l i n i t y w h i c h a r e s o m e w h a t t o o s m a l l . I t w i l l s e r v e b e s tw h e n a p p l i e d t o w a t e r s h a v i n g a h i g h p r i m a r y s a l i n i t y . *
The Electrochemistry of Shaly Sands. The effects o fa l a m i n a t e d s e q u e n c e o f t h i n s h a l e a n d c l e a n s a n d b e d so n t h e s h a p e a n d m a g n i t u d e o f a S . P . c u r v e h a v e b e e na d e q u a t e l y d i s c u ss e d b y D o l l ( 1 9 5 0 a ) . I n t h e t r e a t m e n t
u sed b y Do l l i t i s a s su m ed th a t t h e t h i n sh a l e l a m in at i o n s a r e e l e c t r o c h e m i c a l l y p e r f e c t , i .e . a r e p e r f e c t l yca t i o n se l ec t i v e . S in ce t h ese sh a l es a r e su b j ec t t o t h e
f u l l p r e s s u r e o f t h e i r o v e r b u r d e n t h e w r i t e r b e l i e v e s t h i sa s s u m p t i o n t o b e j u s t if i e d . A n e x p e r i m e n t a l v e r i f i c a ti o no f D o l l ' s e q u a t i o n s u s i n g l o g d a t a f r o m t h e C o r p u sC h r i s t i a r e a of T e x a s h a s r e c e n t l y b e e n m a d e b y P o u p o i i
( 1 9 5 1 ) . T h e a g r e e m e n t c a l c u l a t i o n s b a s e d o n l o g d a t aa n d o n D o l l ' s e q u a t i o n s w a s g o o d a n d l e a d t o t h e c o n -
2t BT
e lu s io n t h a t t h e v a lu e o fF
i n e q u a t i o n ( 3 ) w a s
a b o u t 8 0 m v . T h i s v a l u e s e e m s t o i n d i c a t e t h a t t h e t h i ns h a l e l a m i n a e w e r e c a t i o n s e l ec t iv e . W h e t h e r P o u p o n ' si s o l a t e d d a t a a r e i n d i c a t i v e of t h e g e n e r a l t r u t h o f D o l l ' sa s s u m p t i o n s is n o t c e r t a i n .
Th e i n f lu en ce o f i n t e r s t i t i a l sh a l e o r c l ay i n a p e r
m ea b le b ed i s m o re di f fi cu lt t o as sess q u an t i t a t i v e ly . On
t h e a s s u m p t i o n t h a t e a c h i n d i v i d u a l s h a l e o r c l a y p a r t i c l e
a c t s a s a n i n d i v i d u a l s h a l e c el l w h e n i t s e p a r a t e s m u d
f lu id f r o m i n t e r s t i t i a l w a t e r , D o l l m a d e a p p r o x i m a t e
ca l c u l a t i o n s t o sh o w th a t t h e S .P . o p p o s i t e a sh a ly san d
wo u ld b e l es s t h an t h e v a lu e i t wo u ld h a v e o p p o s i t e a
c l e a n s a n d c o n t a i n i n g i d e n t i c a l i n t e r s t i t i a l w a t e r . D o l l
I t ha . s r e c e n t l y b e e n f o u n d ( W y l l i e , 1 9 5 2 ) t h a t w i t h m a n y a r t i f i c i a l m e m b r a n e s Ca ++ i o n a p p e a r . ? t o b e h a v e a s a m o n o v a l e n t i o n ,p o s s i b l y a s C a ( O H ) + . T h e d a t a of M c L e a n , B a r b e r a n d M a r s h a l l ( 1 9 5 1 ) g- iv en i n T a b l e I o f t h e i r p ap e r f o r p o t a s s i u ma g - a i n s t m i x e d s o l u t i o n s of p o t a s s i u m a n d c a l c i u m i o n s a r e a l s oe x p l i c a b l e i f t h e c a l c i u m i o n b e h a v e s a s a m o n o v a l e n t i o n w i t ha c o n s t a n t m ' o b il i ty w i t h r e s p e c t t o p o t a s s i u m o f a b o u t 1.9(). T h em e m b r a n e u s e d b y t h e s e w o r k e r s w a s a 60 0 " C P u t n a m c l a ym e m b r a n e . H o w e v e r , s h a l e s p e c i m e n s so f a r t e s t e d g i v e a n o r m a l d i v a l e n t r e a c t i o n w i t h c a l c i u m i o n s . W ^e re c a l c i u m t o b e h a v eas a m o n o v a l en t i o n i n t h e ea r t h , t h e a rg -u m en t s g -i ven ab o v e fo rb a s e l i n e s h i f t s w o u l d r e m a i n s u b s t a n t i a l l y s i m i l a r . H o w e v e r t h ep o t en t i a l a c ro s s t h e s h a l e w o u l d t h en t en d t o ex ceed t h a t g - i v enb y ea u a t i o n (,*?) p a r t i cu l a r l y fo r i n t e r s t i t i a l w a t e r r i ch i n ca l c i u m i o n . T h e e q u a t i o n s o f c a s e TI a r e a p p l i c a b l e .
demonstrated also that the S.P. would be furtherdiminished if the shaly sand contained hydrocarbons.
The correct interpretation of beds containing interstitial shale particles is peculiarly difficult since the S.P.is diminished but not necessarily altered in shape. Ashape effect is often observed in the S.P. opposite inter-laminated shale and sand sequences unless the laminae
are extremely thin. "When the S.P. curve indicates laminations the log interpreter is at least aware of a probablediminution in the S.P. deflection. The effect of shalysands on the S.P. is more insidious and this is the moreunfortunate since such sands are frequently of economicimportance.!
A mathematical approach to the problem of a shalysand containing interstitial clay material may be basedon the M.S.T. theory. In this analysis the structure of a shaly sand will be analagous to that shown on figure9 for a shale.* However, in a shaly sand not all conducting passages may be considered to be blocked bythe effects of electrostatic repulsion. Rather the claysmay be considered to exist in the pores and on the grainsurfaces in the manner suggested by Grim and Cuthbert
(1945). Their effect will be to introduce in the poresa charge as defined in the M.S.T. theory. If this averageeffective charge is fairly large the shaly sands will behave as inefficient membrane electrodes. The potentialthey give when separating two solutions will lie somewhere between that for a perfectly anion-impermeablemembrane and the ordinary liquid junction potentialbetween the two solutions.
The term average effective charge, A, is used becauseof the steric hindrance effects which must always be considered in membrane phenomena. Thus a clay particlelocated in a pore constriction in the permeable bed willhave a rather large effective value of A, since the effective volume in which the negative charges on the clayare disposed will be the volume of the pore neck rather
than the entire pore volume. Conversely the same clayparticle located in the pore itself would have a relativelysmall effective charge A. Thus the amount of clay in apermeable bed in a shaly sand is far less imp ort ant froman electrochemical standpoint than is its disposition. Inall cases, however, if the amount of water in the poresis diminished the effective charge A will be increased,since A is expressed as a molality and is dependent tosome extent on the water content of the permeable bed.Thus the addition of oil to the pores will serve to increase the effective value of A and thus to increase theefficiency of the shaly sand as a membrane. Since thetotal electrochemical S.P. is the algebraic sum of theshale potential and the potential between the mud andinterstitial water in a permeable bed, an increase in
the membrane efficiency of a shaly sand implies a decrease in the total S.P. In the earth the sign of the ordinary liquid junction potential is such that this potentialincreases the S.P. If, however, the efficiency of the shalysand as a membrane becomes sufficient to reverse the
t Note added in proof: An investisation of the S.P. and resistivityphenomena sliown by dirty sands has recently been published byWyllie and Southwick, 1954. This investigation obtained datathat provide answers to many of the problems that were unanswer ed in 1952. •
* This appro ach will be found similar to tha t used bv deWitt e(1950), who apparently was unaware of the M.S.T. theory or thework of Sollner. However, deWitte found no concentration dependence of the potential of the type shown in figure 11. Thisis not in accord with all other work on membrane electrodes.
ou
90
40
30
•>
^ e o
d
NERNST POTENTIAL
90
40
30
•>
^ e o
d
90
40
30
•>
^ e o
d
/ ACTIVITY RATIO " / - K )
90
40
30
•>
^ e o
d
90
40
30
•>
^ e o
d
-1 0 LIQUID JUNCTION POTENTIAL
0.8 lao 18.0
02
FiGUKE 11 . Th e form of the varia ti on of pot ent ial with ab solute concen tra t i ons for an imperfee t l.y se lec t ive negative ly chargedm e m bra ne s e pa ra t ing Xa Cl so lu t ions of c ons ta n t a c t iv i ty r a t io .
liquid junction potential, this potential will actuallyoppose the shale potential. The decrease in the totalS.P. maj' thus be very great.
Figure 11 shows a tj-pical curve for a shaly sandseparating XaCl solutions having an activity ratio of 10 : 1. The two limiting potentials are the Nernst poten
tial of about 58.5 mv at the temperature considered,and the liquid junction potential of —11.5 mv. Herethe positive sign is applied to the solution of lesseractivitJ^ When both solutions are very dilute, i.e. a2 issmall, the potential developed approximates to 58.5 mv.When both concentrations are large, the curve is asymptotic to —11.5 mv.
For the optimum application of equation (3) the potential should be —11.5 mv. Figure 11 suggests thatshaly sands will involve least error in the use of equation (3) when interstitial water salinities are high, andthat in all cases the error will be decreased if the mudsalinity is maintained at a high figure. In the case of very shaly sands allied to very low interstitial salinitiesit would appear desirable to increase the mud activity to
a figure greater than the interstitial water activity andto record positive S.P. deflections.
Low mud resistivities, that is high mud activities,seem extremely desirable. They should improve the accuracy with which the electrochemical S.P. approximates to equation (3), they serve to diminish the elec-trokinetie potential correction, and they assist in theinterpretation of focussed current resistivity logs. Whenrunning conventional S.P. logs these advantages may bepartly offset by the short-circuiting effect of the conductive mud, which serves to reduce the S.P. This may be
Part VII] CLAY TECHNOLOGY IN THE PETROLEUM INDUSTRY 301
overcome by using a Static S.P. log, and the ease for the•wider use of this device seems strong.
If nearly all permeable formation contain some interstitial clay and have in consequence an appreciablecharge A, as is suggested by deWit te (195 0), a previoussuggestion by the writ er (1951) tha t the electrokineticpotential in many cases now serves to counterbalance
the reduced S.P. receives support. Against deWitte'sview is the fact that on many logs a consistent maximum S.P. extending over many formations may bedrawn. This implies that all such formations containclay dispersed so as to give rise to identical electrochemical properties. This seems improbable. It seemsmore probable that a consistent S.P. of this type, corrected for electrokinetic effects, will yield on calculationa salinity which closely approximates that of the NaClcontent of the interstitial waters in the formations.
The Effect of Clays on the Resistivity of Permeable Rocks. The formation factor concept, introduced byArchie (1942), is now an essential par t of any systemof electrical log interpretation. Its validity is implicitly
dependent upon the assumption that within a porousrock the conduction processes are all electrolytic andfurthermore that electrolytic conduction occurs onlythrough the network of saline solution filling the pores.It is also implied that the properties of the saline solution tilling the pores are uniform; that there are nosurface conductivity eifects. Provided the salinity ismaintained greater than about 0.1 molar this assumptionis justitied.
Patnode and Wyllie (1950) pointed out that in practice it appeared that these conditions were not alwaysfulfilled, and that in certain instances the matrix structure of porous rocks had an appreciable conductivity.This conductivity appeared to result from the presenceof clays in the rock. The clays could be disposed as thin
shale laminae or as interstitial clay.It was suggested that the resistivity of a saturated
rock containing clays (the so-called "conductive solids")was given by the expression
whereC, + C„ = C, + CJF (6)
apparent conductivity of the rock saturatedwith fluid of conductivity Cc
Cf = conductivity of the conductive solids as distributed in the rock
(7„ = conductivi ty of the saline tluid as di stribute din the rock
F = formation factor applicable to all the solids
both conductive and non-conductive.It may be noted that in equation (6) Cs/F' may besubstituted for C/. Here Cs is the actual conductivityof the conductive solids and F' their formation factor,i.e. F' = Gs/Cwa when C„ is zero. (This expressionassumes that in a dry rock Gf could be measured. Physically this would probably be impossible.)
Equation (6) implies that the conductivity of theconductive solids as distributed in the core is a constant,independent of the magnitude of Co, and that thesesolids may be treated as if they constituted a constant
resistance in parallel with the resistance offered by theliquid tilled pores. Typical data to test the validity of equation (6) are plotted in figure 12. In this figure coreconductivity is plotted as a function of the conductivityof the saline water used to saturate the cores. If equation (6) is followed, the data should plot as a straightline with slope equal to 1/F and intersect with the core
conductivity axis at zero if there are no conductivesolids present in the core and at Cf if conductive solidsare present. Figure 12 shows that these conditions areonly partially fulfilled. If the saturating water conductiv ity exceeds about 0.5 mho-meters (50 mho-cms) areasonably straight-line plot results, but for conductivities lower than this the points curve towards the waterconductivity axis. A satisfactory solids conductivity maybe obtained from the Cf derived by extrapolating thestraight line to cut the core conductivity axis.
The reason for th e observed cur va tur e is not yet clear.*It may represent experimental error, but the regularitywith which the phenomenon has been observed seems topreclude this as a sole explanation. The observed dataindicate that the conductivity of the conductive solids
appears to decrease when the saturating water conductivity becomes less than about 0.5 mho-meters.
Now the data shown in figure 12 were obtained atroom temperature using solutions of sodium chloride asthe saturating fluids. Tables 4 and 5 indicate that theclays in a core, which probably constitute the conductive solids, are almost certainly not in equilibrium witha pure sodium chloride solution. AVhen the core is removed from the ground the mere act of saturating thecore must al ter -the ions on the clay from a mix ture of calcium and sodium to wholly sodium if flushing of theoriginal fluids is prolonged and complete. Thus no valueof Cf obtained in laboratory experiments can be correctsince the conductivity of a clay in the calcium form isless than its conductivity in sodium form. By and large
then, any value of Cf found in conventional experimentswill be too large.
It is customary to saturate clay-containing cores firstwith concentrated sodium chloride solutions. The formation factor of the core containing the highly saline fluidis then determined. Later measurements are made withsolutions whose ionic strength is progressively reduced.The object of this procedure is to main tain sufficientpermeability to permit the core to be flushed with different solutions. Were the operation commenced withthe most highly dilute sodium chloride solution usedthe core would be plugged and rendered impermeable.
These physical difficulties show that the solutions usedalter the physical form in which the clays are disposedwithin the cores. The clays swell and disperse, particularly in dilute solutions, thus leading to plugging of the pores of the core. If clays change in volume in dilutesaline solutions and if the clays move from their initialpositions, then the assumption that C; = Cs/F' is constant and independent of the salinity of the saturatingfluid is untenable. If the clays expand Cs, since it is aconduction per unit volume, will decrease. Similarly F',which reflects the initial configuration of the clay in therock, will alter if this configuration alters. WhetherF' will increase or decrease is less easy to predict, but the
• The explanation is given hy Wyllie and Southwick, 1954.
Part VII] CLAY TECHNOLOGY IN THE PETROLEUM INDUSTRY 303
probability that Cg/F' will alter as the clays swell anddisperse certainly seems great. That Cg/F' should showan overall decrease along the lines indicated on tigure 12is quite possible. Clearly these considerations requiremore detailed investigation.
It may be noted that the determination of C; withoutaltering the ions on the clays is a matter of considerablepractical difficulty unless the Ca/Na exchange constantfor the clay present is known. Possibly this constant isthe one applicable to illite, but this is, of course, purespeculation. If the exchange constant were known itwould be theoretically possible to adjust the Na/Ca ionratio in the saturating solutions at values appropriateto their ionic strengths. From the standpoint of utilizingthe method of Figure 12 in routine operations such aprocedure appears inherently undesirable. The writerwould recommend that the magnitude of the error resulting from ion-exchange effects be investigated. Conceivably this error will be found too small to be of practical signiflcance. It may be noted that if the erroris not negligible it will effect also the accuracy of calculations which are based on the resistivity of the mud-
filtrate invaded zone sur rou ndi ng the borehole. In thiszone cation exchange may take place as previously discussed for the case of the S.P. curve.
Equation (6) applies to formations containing onlyconductive solids and saline water. If it may be considered reasonably valid when the ionic balance on theshales is not upset and the clays are not dispersed, itimplies that if the net water conductivity were alteredCf would not alter. Thus
C„.a=-Cj + Sw''-Cc/F (7 )
In Equation (7) Sw represents the fraction of voidvolume between the solids, both conductive and non-conductive, occupied by water, the fraction (l-Sw) beingoccupied by oil or gas. The exponent, n, is the resistivity
index exponent having a value dependent upon rock texture but averaging about 2.0. Equation (7) impliesthat a plot of F (C„a-Cf)/Co against Sw on double logarithmic paper would have a slope n. Data reported (14)have verified this in some cases.
DeWitte (1950a), however, disagrees with the formof equations (6) and (7), at least as general equations,and presents data to show that equation (7) can giverise to impossible results. In essence deWitte maintainsthat when oil is introduced into a core Cj is no longera constant, but is a function of the water saturation, Sw.The experimental evidence presented by deWitte is ingood accord with this view. Certainly the evidence doesnot support equation (7).
The fact that equation (7) has been confirmed by theuse of other data implies, since deWitte's data appearconvincing, that there are cases to which it applies.Tentative ly at least it may be said that equations (6)and (7) will apply to shaly sands in which the shale isdefinitely laminated and the sands between laminationsare shale-free, while deWitt's equations will apply betterto cases where the shale or clay is truly interstitial. Insuch cases deWitte's basic approach, that of considering the conductive solids to constitute a part of the conducting water system in the pores rather than a distinctand separate conducting solid network, may be the more
rewarding. This approach, which considers that the conductive solids and conducting water together constitute aconductive slurry, gives rise to a format ion fac tor fora rock containing conductive solids which is the quotientof the rock resistivity and the computed slurry resistivity. To the writer, however, this approach seems undesirable, since such a formation factor seems to be related
only to the texture of the non-conductive solids in therock. From the point of view of fluid flow it is the texture of the entire solid matrix, both conducting and nonconducting, which must be determined.
In fine the problem of shaly sands is far from beingsolved. This is the more true since both the equations of Wyllie and Patnode and deWitte are not well adaptedto practical computations based on log data only. Froma practical standpoint the final solution may be in theappropriate combination of electrical and radioactivitywell-logging data (Wyllie, 1952a).
The Radioactivity Log. The detailed study of radioactivity logs is still in its infancy, but the writer wouldpose at least two problems which urgently need elucida
tion. Is the generally higher gamma-ray activity of shalesvis-a-vis sands contingent upon the cation-exchange capaci ty of the clays in shales, or is the difference merelyan indirect measure of shale compaction? That is, wasthe initial deposition of radioactive material per unitvolume of mud and sand sensibly constant and are thepresent differences in radioactivity between shales andsandstones merely a reflection of the greater compactionthat shales have undergone by comparison with sandstones? What are the neutron interaction properties of clays and shales? Such knowledge would greatly assistin the interpretation of so-called "dirty" sands, sincein these it will be necessary to distinguish water held intrue rock pores from water constituting a part of hydrat-able clay minerals.
Summary. The electrochemistry of the shale cell inthe earth has been examined in the light of modern theories of charged membranes. The fundamental importance of a constant shale baseline has been stressed. Ithas been shown that the constancy of the shale baselineappears to indicate that shales, when subjected to pressure, tend to behave as anion-impermeable membranes. Atentative electrochemical shale structure has been presented.
The problem of the bi-ionie potential has been considered and new equations given for the bi-ionic potentialswhich may be involved in S.P. log data indicate that theexchange constants of clays in shales are either all verysimilar or only change slowly with depth in a particulargeological column. The problem of the shale baseline shifthas been examined.
If the calcium ion behaves in situ as a divalent ionthen the formula previously proposed by the writer tocompute interstitial water salinity from the electrochemical S.P. curve is likely to give a salinitj' more closelyrelated to the monovalent ion salt content of the interstitial water than to the total solids. Thus the methodshould probably be applied only to waters which have ahigh primary salinity.
The problem of shaly sands has been considered fromthe standpoint of the Meyer-Sievers-Teorell equation.For optimum practical results in log interpretation the
advantages of using saline muds when logging has beenstressed.
The effect of sliale content on the resistivity of rockshas been briefly examined. Equations that have been proposed to account for such shale effects have been discussed. It has been pointed out that the effects of cationexchange and clay dispersion have been ignored and that
the entire problem of shaly sands and their resistivityeffects deserves further study.
Acknowledgment. The writer's thanks are due toDr. Paul D. Poote, Executive Vice-President, Gulf Ke-search & Development Company, for permission to pu blish this paper. He would like to acknowledge also theassistance afforded by Miss Shirley L. Kanaan in carrying out the basic experimental work on which certain of the theoretical results have been based.
DISCUSSIONW. E. Bergman:
Wyllie has made reference to the theory of membrane electrodesto well-logging problems and he states that he has made measurements of ion activities in colloidal solutions. Since there is considerable doubt as to the significance of such measurements in colloidal systems, I would like to know his interpretation of thesignificance of the pH, Na±ion activity, and similar activities of drilling fluids.
M. R.J. Wyllie:
We have measured the activ ities of muds and of the filtrate fromthem and have found no appreciable difference between the twoactivities unless the tip of the calomel electrode becomes contaminated with clay. Indeed, this result might have been anticipated.Consider a case where a mud has overlying i t a layer of filtrate.Assume that the membrane electrode is in the mud and the calomelelectrode in the filtrate. Then the potential across the membraneis R T / F I n aMua/aHefemnec, while the phase bounda ry po ten ti al between the mud and filtrate is K T / F I n aFiitratc/aiiod. If thecalomel/filtrate junction potential is zero, what is measured is
RT /F InaMud a p i l t r a t e
: RT/F Ina F l l t r a f e
If the calomel electrode is actually pushed into the mud, exactlythe same potential as in the case above may be measured. Thisoccurs if the liquid junction between the saturated KCl and themud takes place in the electrode tip in the absence of clay particles. If the KCl leaking from the calomel electrode forms a
junc tion in the clay sus pen sio n itself, an indeterminate phaseboundary potential is added to the membrane potential. In thiscase the overall pot enti al measured may be appreci ably differentfrom the previous case. If this potential is interpreted as a mudactivity, the answer may be quite erroneous.
W.J . Weiss :
Wyllie stated that the resistivity of the drilling fluid should notbe more than two times the resistivity of the water in the formation for electric logging purposes. Since this is contrary to commonly accepted practices today, I would like to have Wyllie expandupon this point.
M. R. J. Wyllie:In the past, conductive muds have not been considered desirable
for two reasons. First, if the activity of the conductive mud is thesame or nearly the same as the activity of the connate water, littleor no S.P. curve is recorded. Second, extremely low apparentresistivities are recorded for low resistivity beds and the curve of resistivity is hardly distinguishable from the zero line on the resistivity log. This latter situation may be improved by the use of amplified resistivity scales.
Reference was made primarily to the use of conductive muds inconjunction with guard or focusing logging systems. In using thistype of logging system true resistivity is obtained directly, with areasonable degree of accuracy, if there is either no invasion of aformation or if the invading fluid is of nearly identical resistivity
to the fluid already in the formation. It may be argued that, by theuse of resistivity departure curves for such devices, reasonablyaccurate true resistivity may be obtained even when the mudresistivity is four or five times the resistivity of the interstitialwater. A reference to the appropriate departure curves will showthat while this is theoretically true if all the parameters are known,in practice a ratio of filtrate to interstitial water resistivity of twois necessary if true resistivity is to be found accurately and simply.
If formation factor is to be determined from devices with short
depths of investigation, the more conductive the fluid in the invadedzone, the less is the lowering effect of conducting solids on theformation factor calculated. In the case of the S.P. log, it is extremely desirable to minimize the influence of conductive solids bythe use of conductive muds.
M. P. Tixier:
Twenty years ago fresh mud was considered necessary to obtaingood definition on both S.P. and resisti vity curv es for c orrela tionpurposes. In recent years the use of salty muds has become desirable where logs are to be used to deduce reservoir characteristics. Thus it is generally necessary to achieve a compromise andalthough a value of two is desirable, a value as high as five timesmay be used except where a large amount of clay is known toexist in the formation . The Wilcox formation in the Gulf C oastregion is an example where the use of salty muds (or preferabl ytermed bra ckish mu ds) have overcome the difliculties of colloidalmaterial in the formation. Salty muds have not been used extensively in California because of the fresh waters encountered in
many formations.
W. C. Goins, Jr.:
Maintaining mud at resistivities desired by Wyllie for welllogging is not easy. Changing salinity of connate water with depthmakes it difficult to maintain resistivity ratios between 2 and 5over long drilling intervals. In deep wells several logs would haveto be run with different resistivity drilling fluids in each case.Instead of trying to control mud resistivities within the desiredlimits, has any consideration been given to the use of saturatedsalt water mud? This would give a very low resistivity fluid whichwould not be confused with high resistivity hydrocarbons and, although the S.P. curve would be reversed, it should still be subjectto interpretation.
M.J. R. Wyllie:
It is diificult to foresee the problems which might be encountered in the interpretation of resistivity curves when the ratio of interstitial water to mud resistivity is, say, ten to one. The meas
ured resistivity will then undoubtedly be too low in the case of both oil and water sands, but the error will be greater in the caseof oil sands. A positive S.P. kick will be obtained but it willbe necessary to resort to the "static" S.P. logging method to obtain a good curve because the shortcircuiting effect of the mudcolumn will be considerable in a saturated salt water mud.
M. P. Tixier:
Extensive use of saturated salt water mud would probably notbe desirable at the present time because the change would be toodrastic for those using present day logs. The reversed S.P. curveobtained would be of very low magnitude, the kicks seriouslyrounded and the definition very poor. It has been found throughout the country that connate water salinity does not continuallyincrease with depth but that it reaches a maximum at about 9000feet. Below this depth, the salinity actually decreases in manycases. Thus the use of extremely salty mt:ds is not necessary andthe range of connate water resistivities is not so great as to present und ue difficulties in mud resi stivi ty control. The use of bracki sh
muds should also be considered from the standpoint of well completion. Overcoming or minimizing the swelling of clays in reservoir sands by the use of brackish muds, may greatly improve wellperformance.
E. S. Mardock:
Wyllie posed two questions regarding the influence of clays onradioactivity logs. The first question concerns the mechanism bywhich clastic sediments acquire radioactive properties, and thesecond question concerns the mechanism of the effect of thesesediments on the neutron log. The correct answers to these questions should be of great value in the interpretation of radioactivity logs, but neither question can be answered at the presenttime.
Par t VI I ] CLAY TECHNOLOGY IN THE PETROLEUM INDUSTRY 305
It is my opinion that the distribution of radioactive materialin shales cannot be accounted for exclusively by either of the twohypotheses suggested by Wyllie, i.e. (1 ) a hypothesis based on aprimary deposition by which radioactive material is first uniformly distributed in the sediment and a subsequent compactionperiod which appare ntly induces a degree of non-un iformi ty withrespect to the distribut ion of the radioactive component; (2) ahypothesis of a primary deposition process based on a cation-exchange which accomplishes the deposition of radioactive material
in a manner dependent on the cation-e.xchange abilit.v of the clayminerals.
Each of these mechanisms may sometimes account for the differences observed in the ganima-ra.v activities of a particularshale. In addition, however, a third factor, the chemical composition of the minerals present, is thought to play an important rolein determining the gamma-ray activity of shale.
With regard to the effect of clay minerals on the neutron curve,it is our t)elief that this effect combines effects of the hydrogencontained in chemically bound liquids, e.g., oil and water, plus the"chemical effects" of certain of the elements mailing up the claymineral itself, such as iron and possibly some of the rare earthswhich have relativel.y large capture or scattering cross-sections forneutrons. These "chemical effects" sometimes intiuenee the login a much more decisive manner than a hydrogen-containingliquid.
An application of the work done on these problems is discussedby Bush & Mardock (19 51) .
SELECTED REFERENCES
Archie, G. E., 1942, The electrical resistivity log as an aid indetermining some reservoir characteristics: Am. Inst. Min. Met,Eng. Trans., v. 146, pp. 54-62,
Bergman, W. E., 1952, Effect of calcium sulfate on properties of a bontonite suspension. Part s I and I I : World Oil, v. 134, no. 5,pp . 170-178 . . . . V. 134, No. 6, pp. 122-1,33.
Bush, R. E., and Mardock, E. S., 1951, The quantitative application of radioactivity logs : Am. Inst. Min. Met. Eng. Trans ., v.192, pp. 194-198.
Case, L. C, 1933, Base replacement studies of Oklahoma shales•—critique of Taylor hy pot hes is: Am. Assoc. Petroleum GeologistsBull., V. 17, pp. 66-79.
Claudet, A. P., 1950, New methods of correlation by resistivityvalue of electrical logs; Am. Assoc, Petroleum Geologists Bull.,V. 34, pp. 2027-2060.
de Sitte r, L. U., 1947, Diagenesis of oil-field br ines : Am. Assoc.Petr oleum Geologis ts Bull. , v. 31, pp. 20,30-2046.
de Witte, L., 1950, Experimental studies of the characteristicsof the electrochemical potentials encountered in drill holes: Am.Inst. Min. Met. Eng., Paper 12G, Oct. 13, 19,50 meeting, Los Angeles, California [unpublished].
de Wit te, L., 1950a, Relations l)etween resis tiviti es and fluidcontents of porous rocks: Oil and Gas .Tour., v. 49, no. 16, pp.120-132.
Doll, H. G., 1949, The S.P. log—theoretical analysis and principles of inter pretat ions : Am. Inst . Min. Met. Eng. Tr ans. , v. 179,pp . 146-185.
Doll, H. G., 1950, Selective S.P. logging: Am. Inst. Min. Met.Eng. Trans., v. 189, pp. 129-142.
Doll, H. G., 1950a, The S.P. log in shaly sands : Am. Inst. Min.Met. Eng. Trans., v. 189, pp. 205-214.
Grim, R. E., and Cuthbert, F. L., 1945, The bonding action of clays. Part 1—Clays in green molding sands : Illinois Geol., Survey Rept. Inv. 102, 55 pp.
Harned , H. S., and Owen, B. B., 1950, The physical chemist ryof electrolytic solutions. New York, Reinhold Publishing Corp.
Kressman, T. R. E., 1952, in Duncan, J. P., Theory and practice of ion exchange : Nature, v. 169, pp. 22-24.
Marshall, C. E., 1948, The electro-chemical properties of mineralmembranes. VII I. The theorv of selective membrane behavio r:Jour. Phys. Colloid Chemistry, v. 52, pp. 1284-3295.
Marshall, C. E., 1949, The colloid chemistry of the silicate minerals, 195 pp.. New York, Academic Press, Inc.
McLean, E. O., Barber, S. A., and Marshall, C. E., 1951, Ionization of soils and soil colloids. I. Methods for simultaneous determination of two cationie activities : Soil Sci., v. 72, p. 815
Meyer, K. H., and Sicvers, .T.-F., 1936, La permeability desmembranes. I. Theorie de la permeal)iIitS ionique: Helvetica Chi-mica Acta, v. 19, pp. 649-664 . . . . II . Essais avec des membranesseleclives artifieielles : Helvetica Chimica Acta, v. 19, pp. 665-667
. . . . I I I . La permeability ionique de couches liquides non-aqueuses: Helvetica Chimica Acta, v. 19, pp. 948-962.
Millot, G., 1952, in Mackenzie, R. C, Geological aspects of claymineralogy: Nature, v. 169, p. 656.
Mounce, W. D., and Rust, W. M., 1945, Natural potentials inwell logging: Am. Inst. Min. Met. Eng. Trans., v. 164, pp. 288-294.
Patnode, H. W., and Wyllie, M. R. J., 1950, The presence of conductive solids in reservoir rocks as a factor in electric loginterpretation: Am. Inst. Min. Met. Eng. Trans., v. 189. pp. 47-52.
Schlumberger, C, Schlumberger, M., and Leonardon, E. G., 1934,Electrical coring, a method of determining bottom-hole data by electrical measurements: Am. Inst. Min. Jlet. Eng. Trans., v. 130,pp. 237-272.
Schlumberger, C, Schlumberger, M., and Leonardon, E. G.,1934a, A new contribution to subsurface studies by means of electrical measurements in drill holes: Am. Inst. Min. Met. Eng.Trans., v. 110, pp. 273-289.
SoUner, Karl, 1945, The physical chemistry of membranes withparticular reference to the electrical behavior of membranes of porous character: Jour. Phys. Colloid Chemistry, v. 49, pp. 171-191.
Sollner, Karl, 1949, The origin of bi-ionic potentials across porous membranes of high ionic selectivity: .Tour. Phvs. ColloidChemistry, v. 53, pp. 1211-1239.
Sollner, Karl, 1950, Recent advances in the electrochemistry of membranes of high ionic selectivity: Elcctrochem. Soc. Jour., v.97, pp. 139C-151C.
Taylor, E. McK., 1929, The replaceable ba.ses in the clays and
shales overlying petroliferous stra ta : Ins t. Petroleum TechnologyJour.. V. 15, pp. 207-210.
Tajlor, E. McK., 1930, An examination of clays associated withoil-bearing strata in the United States: Inst. Petroleum Technology Jour., V. 16, pp. 681-683.
Teorell, T., 1935, An attempt to formulate a quantitat ive theoryof membrane permeability: Soc. Exper. Biol. Medicine Proc, v.33 , pp. 282-285.
Teorell, T., 1935a, Studies of the diffusion effect upon ionic distribution. I. Some theoretical considerations : Nat. Acad. Sci. Proc,v. 21, pp. 152-162.
Tixier, M. P., 1949, Electric-log analvsis: Oil and Gas Jour.,V. 48, no. 7, pp. 143-148, 217-219.
Wvllie, M. R . .T., 1948, Some electrochemical prope rties of shales :Science, v. 108, pp. 684-686.
Wyllie, M. R. J., 1949, A quantitative anal.vsis of the electrochemical component of the S.P. curve : Am. Ins t. Min. Met. Eng.Trans., v. 186, pp. 17-26.
Wyllie, M. R. J., 1949a, Statistical study of accuracy of some
connate-water res istivity determinatio ns made from self-potentiallog dat a : Am. Assoc. Petroleum Geologists Bull., v. 33, pp. 1892-1900.
W.vllie, M. R. J., 1953, An investigation of the electrokineticcomponent of the self potential curve: Am. Inst. Min. Met. Eng.Trans., v. 192, pp. 1-18.
Wyllie, M. R. J., 1953a, Theoretical considerations involved inthe determination of petroleum reservoir parameters from electriclog data: 3d World Petroleum Cong. Proc, sec. II, pp. 378-393,Leiden, the Netherlands, E. ,T. Brill.
Wyllie, M. R. J., 1951b, U. S. Patent No. 2,569,625, October 2,1951.
Wyllie, M. R. J., 19.52, Gordon research conference on ion exchange : Am. Assoc. Advancement of Sci., . Inly 1952.
Wyllie, M. R. .L, 1952a, Procedures for the direct employmentof neutron log dat a in electric log inter pre tat ion : Geophysics, v.17, p. 790.
Wyllie, M. R. J., and Morgan, F., 1951, Comparison of electriclog and core analysis data for Gulf's Prank No. 1, Velma pool,
Stephens County, Oklahoma, in Pifteenth technical conference onpetroleum production: Pennsylvania State College, Mineral Industries Exper. Sta., Bull. 59, pp. 111-127.
Wyllie, M. R. J., and Patnode, H. W., 19.50, The development of membranes prepared from artificial cation-exchange materials withpar ticula r reference to the determination of sodium-ion activiti es :Jour. Phys. Colloid Chemistry, v. 54, pp. 204-227.
Wyllie , M. R. .1., 19.54, Ion exchange membranes . I : J our. Phvs.Chem., V. 58, pp. 67-73.
Wyllie, M. R. J., and Kanaan, S. L., 1954, Ion exchange membran es. I I : .Tour. Pliys. Chem., v. 58, pp. 73-80.
Wyllie, M. R. J., and Southwick, P. P., 19.54, An experimentalinves tigation of the S.P. and resistivi ty phenomena in dirty sands :•Tour. Petrol eum Tech., v. 6, No. 2, pp. 44-57.
