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The S.P. Log: Theoretical Analysis and Principles of InterpretationBy H. G. DOLL,* MEMBER AIME

(New York Meeting. February 1948)ABSTRACT

THE S.P. log is shown to be a measurementof the potential drop along the drill hole,caused by ohmic effect in the mud. The notionof static S.P. is brought forward, and itsrelation to the S.P. log is discussed. Otherfactors influencing the shape and amplitudeof the log are considered; attention is givento conditions encountered in practice. Numerous figures are given illustrating graphicallythe results; these figures are of particularinterest for comparison with field examples.The S.P. log, although indicating permeability, is not an absolute measurement ofpermeability, nor of porosity, of the formationstraversed by a drill hole. I t is affected byseveral parameters, such as resistivity offormations and mud, thickness of formations,and others, which should be appraised carefully. Simple rules have been established for abetter distinction of the boundaries of permeabl" sections, particularly in difficult cases,such as those encountered in highly resistiveformations. A systematic application of theestablished principles will assist in obtainingmore information from the S.P. log than waspossible thus far; for instance, under favorableconditions, presence of oil may be detected, oramount of shale in sands may be estimated.

INTRODUCTIONTh e S.P. log, or spontaneous potential

log, has been known and widely used dur-ing the last IS years for the location ofpermeablet beds traversed by drill holes. 12

Manuscript received at the office of theInstitute Feb. 14. 1948. Issued as TP 2463 inPETROLEU:VI TECHNOLOGY. September 1948.* Director of Research, Schlumberger WellSurveying Corp., Houston, Texas.t Throughout the paper, the term permeable is used in a broad sense to qualifyall media which may pass fluid, even thoughtheir permeability might be too low for production requirements.1 References are at the end of the paper.

In electrical logging practice, the S.P.log is shown on the left hand side track ofthe record (as ma y be seen in later exam-ples) where it can be easily correlated an dinterpreted with the resistivity curveslocated to the right. Usually, the S.P. logconsists of a base line, more or less straight,having excursions or "peaks" to the left.Th e base line frequently has been found tocorrespond to impervious beds, while thepeaks are usually found opposite permeablestrata.

Measurements which will indicate positively the presence of permeability in theformations, and which will give accuratelythe boundaries of the permeable zones, areof great importance in oil-field practice.Thus far, the S.P, log is the best approachto such determinations; unfortunately, itsinterpretation is no t always evident.

With respect to the base line of th e S.P.log, it ma y be noticed that this line is no talways at a definite location on the chart.Sometimes it may shift abruptly, whileother times a gradual drift is apparent.

As far as the peaks are concerned, theirshape is no t uniform; some are roundedwhile others are sharp. Also, from otherdata, it may be found that occasionally th epeaks extend appreciably beyond theboundaries of permeable zones into zoneswhich are no t everywhere permeable.

A comparison with permeability measure-ments made on cores has often confirmedthat there was no definite correspondencebetween th e magnitudes of the peaks andthe permeability values. In the same geological horizon, it generally will be foundthat most of the thick and permeable for-

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H. G. DOLL I47mations exhibit peaks on the S.P. log thathave about the same magnitude, althoughthe permeability is variable. On the otherhand, thin formations of comparablepermeability may show peaks having different magnitudes.

There has been a desire to derive fromthe S.P. log information such as quantita-tive permeability or porosity. Since the logis unable to supply this quantitative information, a certain confusion has beencreated about the real meaning of the S.P.log. As a result, it is no t always interpretedwith complete efficiency, particularly whenholes are drilled through hard formations.

There is no doubt that the shape of theS.P. log, as well as the magnitude of itsdeflections, are affected by conditionsother than the permeability of the formations. In order to improve the interpreta-tion of the log, an attempt will be made inthis paper to explain the conditions responsible for its shape. I t will be shownthat, among other things, the thickness ofbeds, as well as their resistivity, have animportant bearing on the S.P. log. A discussion concerning the emf (electromotiveforce or forces), which produce the poten-tial differences measured on the log, will begiven. In addition, numerous examples oftypical cases, 11).0st of them computed withgood accuracy, will be shown, thus constituting a sort of catalogue which shouldenable the reader to make a better use ofthe S.P. logs recorded in actual field practice. A few simple rules will also be given toimprove further the interpretation, especially for determining the boundaries ofpermeable beds.

TECHNIQUE OF S.P. LOGGINGThe recording of S.P.logs is made accord

ing to a simple technique. As illustrated inFig I , an electrode M, located at the end ofan insulated cable C, is moved up or downin the mud filling the drill hole. The cablepasses over a calibrated sheave S, and iswound on a winch W. Contact with the

insulated conductor is established througha slip-ring collector SR, which is connectedto one terminal of a recording galvanometerRj the other terminal of the galvanometeris connected to a potentiometric circuit P,and then to an electrode N, usually placedin the mud pit or attached to the casing ofthe hole.

Th e movement of the sensitive paper orfilm in the recorder R is synchronized withthe movement of the electrode M along thedrill hole. Th e depth scales used in recording are I in., 2 in., and 5 in. per IO O ft ofelectrode motion. The recorder registers alog on which the abscissas are proportionalto the depth of electrode M, and the ordinates represent the potential of electrodeM with reference to electrode N.

The drill holes in which the S.P. logs arerecorded are usually filled with mud havinga water base. The mud density is such thatat each depth the hydrostatic pressure inthe hole is greater than in the formations;as a result, the fluid contained in the permeable beds cannot contaminate the mud.Also, the mud is in constant circulationduring the drilling operation, prior to thelogging, and therefore it is homogeneous.

According to the circuit shown on Fig I ,it can be seen that the recording galvanometer R measures all the differences of potential appearing between electrodes M andN. However, provided some proper precautions are taken, experience has shown thatunder usual conditions the deflections onthe S.P. log correspond to phenomena occurring at the contacts between the mudand the different beds, and also at the contacts between the beds themselves. Thesephenomena produce an electric current,called "S.P. current,"* which uses themud as its return path. In so doing, itcreates in the mud by ohmic effect, potential differences which can be measured and

Th e expression ., S.P. current" may seemrather illogical as S.P. stands fo r " spontaneouspotential"; however, as it ha s definitely passedin common use, th e author thought it preferableto keep it.

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148 TH E S.P. LOG: THEORETICAL ANALYSIS AND PRINCIPLES OF INTERPRETATIONplotted versus corresponding depths, toconstitute the S.P. log.

Other sources of potential, which are notrelated to the formations, do not usually

potential may normally appear betweenthese two electrodes in the absence of anyS.P. current. This difference of potential isnot recorded on the S.P. log; it is counter-

~ ~ : I ~ ~ ~ - - - - - - - - - - - - - - - -

~ " ' : : = - - = - f i : E ~ = - : = - = - = - = - : = - : : - = : : - = - : : - : : - = - = - = - = - : : : :

------------------------------=-:.

FIG I-SCHEMATIC CIRCUIT FOR RECORDING S.P. LOGS.cause any deflection on the S.P. log; ifpresent and bothersome, proper steps aretaken to overcome them. Particularly,electrodes M and N are chosen to be stableinsofar as their contact potential with themud is concerned; in practice, M and N arelead electrodes. A constant difference of

balanced by means of the potentiometriccircuit P.Accordingly, the potential of electrodeM is measured on the S.P. log with reference to an arbitrary constant. However,the variations of the potential, that is, the

d e f l e ~ t i o n s on the S.P. log, do not depend

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H. G. DOLL 149on the arbitrary constant, and they measurethe potential differences as created in themud by the S.P. current. These deflectionsmake it possible to characterize the formations. Under normal conditions, the excursions toward the negative characterizepermeable beds, while excursions towardthe positive characterize impervious beds.*

ELECTROMOTIVE FORCES-THE STATICS .P . DIAGRAM AND IT S RELATION TO

TH E S.P. LOGThe emf generating the S.P. current,

which affects the S.P. log, arise from twotypes of phenomena. The first one is ofelectrokinetic nature, producing an emfof filtration' at the contact drilling mudpermeable bed. Since the hydrostatic pressure of the mud in the drill hole is greaterthan the pressure in the permeable formation, some mud fluid filtrates slowlythrough the mud cake into the permeahlebed. This causes an emf to appear, primarily where the pressure difference ismaximum, that is, across the mud cake.The emf depends on the nature of thefiltrate and of the filter (mud fluid and mudcake), and on the pressure difference. As aresult, for a given formation, the emf willbe uniform all along the contact mudpermeable bed. I f the difference in pressureis about the' same for various permeableformations traversed by a drill hole, theemf of filtration will also be the same.

Th e second phenomenon is an electrochemical one. I t occurs at the contact ofmedia of different nature, and creates anemf at each such contact. t For instance,

Th e polarity of th e excursions might bereversed in certain cases, and in particularwhen th e salinity of the mud is higher thanthe salinity of th e water in the permeable beds.t It should be remarked tha t th e presenceof a clay or shale be d adjacent to a permeableformation has a definite bearing on th e valueof th e electrochemical emf. This wa s noticedby Conrad Schlumberger an d reported in apaper ' in 1933. Later on , Mounce and Rustelaborated on this matter and discussed theirfindings.' Also, Dickey' investigated th equestion of potentials appearing in drill holesan d open shaft.

referring to Fig 2a and b, there are threecontacts or boundaries shown at A, BandC as follows:

A boundary between mud and saltwater sand,*

B = boundary between salt-water sandane! clay,

C = boundary I;>etween clay and mud.An emf of an electrochemical origin exists at each of the boundaries, A, B, C. As

each medium is fairly homogeneous, eachemf is uniform along the correspondingboundary.

A the boundary A, an electrokineticphenomenon as well as an electrochemicalone is present; thus, there is an emf corresponding to the algebraic sum of two forcesof different origin.

In order to get a better understanding ofthe effect of the emf, it is convenient toconsider first an idealized case where theS.P. currents are prevented from flowing.In this connection, Fig 2a represents a drillhole section that traverses two identicalthick beds of clay separated by a ratherthin salt-water sand. Although this wouldno t be easily feasible in practice, it may beconceived that two insulating plugs areplaced in the hole to interrupt the electricalcontinuity of the mud column at the twoboundaries between sand and clay.

The presence of the plugs does not affectthe emf; at the boundaries A, B, and Cthere are emf designated respectively by a,b, and c. Since the plugs prevent any currentflow, the potential within each singlemedium, enclosed by boundaries or plugs, isthen constant. However, the potentialvaries from medium to medium, the difference of potential between two adjacentmedia being equal to the emf existing attheir common boundary.

Considering that the emf, a, b, and c, arepositive in the direction shown by thesmall arrows, and designating by Vo the po-

Fo r simplification, it is assumed thntthere is no appreciable invasion in th e permeable formation. Th e effect of invasion willbe examined in a later section.

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IS O THE S.P. LOG: THEORETICAL ANALYSIS AND PRINCIPLES OF INTERPRETATION

tential of the mud in the section above theupper plug, the potential in each mediumis as indicated in the corresponding boxeson Fig 2a. These potentials are. determined

In the salt-water sand: V. - c - b.In the mud section comprised between

the plugs: V. - c - b - a.In the lower clay bed: V. - c.

.Yo-(O+b+l:)

---:-------- - - -MUD--=-

- = = = - = = = ~ ~ - = = = - ~ : = = ~ E f l ---1------ - - , - - - - - - --------=-- = - - - ~ . : : : _ _ f ~ _ - _ - . : . : _ _ - ___ _- = - - : : - = - { ~ - --=- ~ ~ ~ ~ ~ ~ ~ .--==::::1 =-b =-:: B =-_-X -=----..:...: : . ) 5 ~ : : 3 : ~ ~ { 1 : ~ ~ ~ r : ~ ~ ~ ~ # ~ ,___ ___ B_--.:t ____ __B_ b ___-- _/_----- - =-----=- -1 - - - - - - - .--1---------- I ------

(A)-1- - - - - - - - -- - - --------_ ~ - - - - - - - - _____ -===_-___~ - ~ ~ ~ ~ ; ~ ~ - - - - - - - = - ~ = - -------=..:::::.-.....::::::.- ---::..- - --------

J - o -L AND ~ : ELECTROMonVE FORCEI ACIIOS. IOUNDARtfl A ,8 AND O.~ : - : POTENTIAL IN CORRESPONDING MEDIUM.

-- --- STATIC S.P. DIAGRAM- POTENTIAL IN MUD WHEN S.P. CuJUllNTS AlII! PREVENTID ntOII n o .. ._____ S. P. LOG - POTENTIAL IN MUD WHEN S. Po CURReNTS 'R ' FLOWINe.FIG 2-SCHEMATIC REPRESENTATION OF POTENTIAL AND CURRENT DISTRIBUTION IN AND AROUND

A PERMEABLE BED.by algebraic addition of the potentials encountered when going from one medium tothe next. The values of the potentials are asfol.lows:

In the upper section of the mud: Vo.In the upper clay bed: Vo - c.

In the lower section of the mud: Vo.From the point of view of the S.P. log, it

is, of course, essentially the potentials inthe different sections of the mud which areof interest. In that respect, it is very important to remark that the potential of the

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H. G. DOLL

mud section in front of the lower clay is thesame as in the upper section. I t is alsofundamental to observe that the potentialof the mud in front of the sand differs fromthe potential Vo in front of the clays by thequantity (a + b+ c), which is the sum ofthe emf of the 3 boundarys, a, b, and c.

At this point it is pertinent to remarkthat the boundary emf show their effectthrough a combination of 3 values. Furthermore, the existence of 3 boundaries havinga common junction is quite fundamentalin the analysis of S.P. logs; they constitutea triad which will appear in further discussions. The combination of 3 emf at theboundaries, along any closed path traversing all three media, establishes what isconveniently called a "3-link chain emf."

The left part of Fig 2a represents a diagram which can be considered as the S.P.log for this idealized case. On this diagramthe potential in the mud is plotted versusdepth. As it corresponds to the case whereno current is flowing, or in other words to astatic case, it will be designated hereafteras the "static S.P. diagram."*

Although a purely theoretical concept,the static S.P. diagram is of great interest.I t represents, in a convenient manner, thevalues of the emf which produce the S.P.currents, and which therefore determin e theS.P.log.

Going over to Fig 2b, it will be seen thatthe figure represents the same schematicalexample as Fig 2a, except that the insulating plugs have been removed to re-establishthe continuity of the mud column. In theseconditions, there is no longer a static equilibrium, bu t rather a dynamic state. TheS.P. current can flow in the drill hole throughthe mud, as well as in the formations.

The 3 emf, a, b. and c, add their effects togenerate the S.P. current which follows thepaths represented on Fig 2b by solid lines.Each line corresponds to a line of flow, the

Th e word diagram, rather than log, isused here to insist on th e fact that this curveis of hypothetical nature and is no t actuallylogged.

current circulating in the direction of thearrows.

Each current line must necessarily crossthe three boundaries A, E, and C. Furthermore, that part of the current generated byeach of the 3 emf, a, b, and c, follows thesame path; the current lines are independent of the repartition of the emfbetween the 3 boundaries. In other words,the intensity of the current circulating inthe mud of the drill hole depends onlyupon the algebraic sum of all the partialemf in the circuit, and does not dependupon the allocation of these partial emf toeach boundary, provided that each emf isuniform everywhere on its correspondingboundary.

Along its path, the S.P. current has toforce its way through a series of resistances,both in the ground and in the mud. In sodoing, it produces potential differencesaccording to Ohm's law. Along a given lineof flow, the potential falls down continuously in the direction of the current, asindicated by arrows, bu t at each boundarywhere an emf occurs, the potential israised by an amount corresponding to thevalue of the emf. Along a closed line ofcurrent flow, the total drop of potential isnecessarily equal to the sum of the emfencountered.

Also, the intensity of the current beingconstant along its path, the potential dropvaries according to the resistance of thesection through which it flows. This meansthat the total potential drop (which isequal to the sum of the emf), is dividedbetween the different formations and themud in proportion to the resistances respectively encountered by the current ineach medium. Accordingly, the potentialdrop in the mud of the drill hole measuresonly part of the total emf, unless the electrical resistance offered by the mud is vlrylarge compared to the one in the formations.

The S.P. log records the potential dropoccurring in the mud. I t follows that theamplitude of the peak of the S.P. log ap-

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152 TH E S.P. LOG: THEORETICAL ANALYSIS AND PRINCIPLES OF INTERPRETATION

proaches the amplitude of the static S.P.,which is the sum of the partial emf, onlyin favorable cases. When the resistance ofthe mud to the flow of S.P. current is notlarge compared to the resistance in theformations, then the S.P. log will show apeak of lesser amplitude than the staticS.P. diagram.

I t may also be seen on Fig 2b that thecurrent circulates in the mud, not onlyopposite the permeable formation (saltwater sand), bu t also part way beyond theboundaries of the formation. As a result,though the static S.P. diagram indicates asharp break corresponding to the boundaries of the permeable bed, the S.P. logexhibits a more progressive change inpotential, extending along the drill holebeyond the boundaries of that bed.

In the case illustrated by Fig 2b, thepermeable bed is thin, so the resistance inthat bed is appreciable compared to thetotal resistance in the S.P. current path.This is why, in that case, the deflection ofthe S.P. log, which measures the potentialdrop in the mud, is only a fraction of thetotal emf. To make that point clearer, theS.P. log has been represented in solid line,together with the static S.P. diagram whosedeflection characterizes the total emfinvolved.

As shown by the figure, the deflectionof the S.P. log is not only smaller than theone of the static S.P. diagram, but it is alsomuch more progressive. I t is interesting tonote that the slope of the S.P. log measuresthe potential drop per unit length in thehole, which is proportional to the intensityof the S.P. current in the mud at the corresponding level. Starting from the top partof the log and going down, the slope increases progressively because the currentin the hole increases progressively, untilthe level X (contact clay-sand) is reached.At that level, the intensity of the current inthe hole maximum, and this correspondson the S.P. log to a maximum slope, or inother words, to an inflection point. Below

that level, the current progressively decreases until it becomes nil in the middle ofthe sand; this corresponds to the point ofmaximum deflection. Farther down, thecurrent flows in the opposite direction, sothat the slope of the S.P. log is reversed.That slope increases progressively, until anew maximum is reached at the level Y(lower sand-clay contact), which corresponds to another inflection point on theS.P. log; and still farther down, the slopeprogressively decreases again because thecurren itself decreases.

The above remark about the inflectionpoints of the S.P. log is important for theirinterpretation. There has sometimes beena tendency to place the boundary betweena permeable and an impervious bed at thepoint which corresponds to half deflectionon the S.P. log. This can be substantiallywrong in certain cases. The contact levelshould be taken as corresponding to theinflection point on the S.P. log.

THE SHAPE AND AMPLITUDE OF THES.P. LOG-INFLUENCE OF VARIOUS

FACTORS

The shape and amplitude of the peak onthe log opposite a given bed may be influenced by the following factors: (1) thetotal emf involved; (2) the thickness ofthe bed; (3) the resistivity of the bed, of thesurrounding formations, and of the mud;(4) the diameter of the drill hole; and (5)the depth of penetration of the mud filtratein the permeable beds.Where the permeable beds contain someimpervious and conductive material, suchas shale, the S.P. log may also be affectedby the presence of that material. This subject will be discussed in the section onshaly sands.

The S.P. log would be influenced additionally by a lack of homogeneity in themud; a change in salinity of the mud at acertain level would result in a base-lineshift at that level. However, it has been

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H. G. DOLL 153found in practice that such change insalinity is very seldom encountered.

In the text, the expression "imperviousbed" or "impervious formation" is alwaysused to designate formations like, for ex-ample, shale or clay, which are at the sametime impervious and porous. As they containwater, they are also conductive. On the fig-ures such beds are identified by the letter Cfollowed by an index number which refersto the particular bed concerned. Compactor hard formations which contain extremelylittle water, and have no permeability, aredesignated by the expression"hard forma-tion" and are identified on the figures bythe letter I I with corresponding index num-ber. Finally, formations like sands, porouslimestone and the Jike, which are permeable-even though the permeability might bevery low-are designated by the expression"permeable bed," or "permeable forma-tion," and they are identified on the figuresby the letter P followed by the correspond-ing index number.

Th e theoretical figures, which illustratethe effect of the various factors on the S.P.log, have been drawn to correspo;d to fieldconditions as closely as possible. Eachfigure shows the geological cross section, thedrill hole, the S.P. log and the static S.P.diagram. H.esistivity values are indicatedby numbers in circles, in units of mud re-sistivity. To facilitate a comparison be-tween the examples and field logs, thethickness of formations, size of drill hole,and depth of mud invasion have beenrepresented at the same dimension scale foreach figure. Furthermore, the amplitudeof the deflection on the static S.P. diagramand on the S.P. log has been plotted tohave the same ratio to the dimension scaleas the ratio used for logs recorded in thefield at 5 in. per lO O ft. The maximum po-tential deflection has been indicated ascorresponding to 100 mv for convenientcomparison.

Unless otherwise specified, all the exam-ples given in the following paragraphs have

been computed mathematically. In thisconnection, each medium is consideredhomogeneous and isotropic. When anaccurate computation was not possible,approximations were made, and this fact ismentioned on the corresponding figures bythe word" schematic" in the caption.

11lfluence of the Electromotive ForcesAll other factors remaining the same, achange of the total emf affects the ampli-tude but does not otherwise modify theshape of the S.P. log. A change 'of the emfat the different levels in a drill hole, by thesame proportion, is equivalent, as far asthe S.P. log is concerned, to a change in themillivolt scale, or, in other words, in thesensitivity of the recording galvanometer.

In practice, the emf involved may varyfrom one hole to another, either because thesalinity of the mud, or of the formations, isquite different, or, to a smaller extent, be-cause the differential pressure between themud and the formations is different. In agiven hole, however, and for the same typeof formations and depth, there is a definitetendency for the total emf to be the samefor all beds of the same type. This is clearlyshown by logs taken in formations consist-ing of thick and conductive imperviousbeds, and thick permeable beds. In front ofthe former, the S.P. log gives a good,straight base line, while the peaks corre-sponding to the latter have generally thesame value, which implies that the emf arethe same for all of them. True enough, theremay also be a certain number of thin per-meable beds which give on the S.P. logpeaks of smaller amplitude. Conversely,there might be, within thick permeableformations, thin impervious beds for whichthe S.P. log does no t come back to the baseline. Bu t this effect of the thin beds can beexplained by other causes, as will be shownhereafter, and there is therefore no reasonto assume that they produce smaller emf.On the contrary, the fact that there is agood base line shows that all conductive

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154 TH E S.P. LOG: THEORETICAL ANALYSIS AND PRINCIPLES OF INTERPRETATIONimpervious beds are of much the samenature, while the fact that all large peaksare of the same amplitude shows thatsalinity and differential pressure are thesame for all thick permeable beds. Then, inall probability, these conditions should bethe same for the thinner beds in between,and it is quite logical to look for otherfactors, and in particular for the thickness,to explain the smaller deflections observed.

Permeable beds of different porosity, orwith different dimension of grains, give thesame emf, if other factors are unchanged.The emf are also independent of the per-meability value, even down to fractions ofone millidarcy.The electrochemical emf depend only onthe salinity of the permeable beds, on thenature of the impervious formation withwhich they are in contact, and on thenature of the mud, while the electrofiltra-tion emf depends only on the differentialpressure and on the nature of the mud,which itself determines the mud cake wherethat emf is generated.

I t has been observed that the salinityand the differential pressure are not alwaysconstant for all permeable beds, especiallyat widely different depths or in very dif-ferent formations. Fresh water sands orvery salty sands will show respectivelyabnormally low or large amplitude ofpeaks. The polarity of the peak even re-verses if the sand is less salt y than the mud.Depleted sands, where the pressure is verylow, give peaks of large amplitude, espe-cially with muds of very low salinity whichfavor the electrofiltration emf. Suchchanges in salinity and pressure producechanges of the emf. Generally these can bedetected without too much difficulty in thethick permeable beds because the ampli-tude of the peaks on the S.P. log for thethick beds is equal to the total emf. In thethin beds, for which the peak amplitudeon the S.P. log depends, as will be shownlater, on the thickness and the resistivity,it is practically impossible to separate the

effect of the different factors on the S.P.log, and, therefore, to evaluate the emf.Certain muds of special chemical compo-sition have the property of reversing thepolarity of the emf. In such cases, the S.P.log excursions will be reversed and the per-meable sections will correspond to positiveexcursions.In the remainder of the paper, the totalemf, which is responsible for the differentpeaks on the S.P. log, is assumed to be ofequal value. This assumption is representedon the figures by the fact that all deflectionsare of the same amplitude on the staticS.P. diagram. Consequently, the amplitudeof all peaks on the S.P. logs should be thesame, were it not for other factors whoseeffects appear as differences between theS.P. logs and the corresponding static S.P.diagrams.The above hypothesis of a constant totalemf for the static S.P. diagram, although

apparently made only to assist in the de-scription of the figures, is in fact, very oftenconformed to by the ac tual field conditions.This is particularly true, as already men-tioned, in the case of a long section of sandand shale formations, when the followingrequirements are satisfied: (I ) all shales areof similar nature; (2) the salinity of theconnate water in all sands is nearly thesame and; (3) the differential pressureacross the mud cake is the same for allsands.These conditions, for example, are quitewell satisfied in the Gulf Coast area in theFrio formations, which are many thou-sands of feet thick-the shales give avery good base line, while the salinity ofthe sands varies only from 35,000 to65,000 ppm.

Influence of the Thickness of BedsIn this section the resistivity of all beds

is chosen to be the same and is equal to theresistivity of the mud. This case is not astheoretical as it may appear to be; it occursrather frequently, in the Gulf Coast area

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H. G. DOLL

DRILL HO

- - -c5--------

--Pa---- - - - = - ~ -=-=----

PERMEABLE CONDUCTIVE S1R AlA PIMPERVI OUS CONDUCTIVE STRATA C

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I56 TH E S.P. LOG: THEORETICAL ANALYSIS AND PRINCIPLES OF INTERPRETATION

. . . . . . . ........................... ... ', .::::::::>:: -:.: -: .:.:' :.:. :- :. :- :- : : . - :- " : . . . . .. . . . .. . . . . . . "

.. . . . .. ' . . . ,. . . . . . . . . . . . . 6,-=,:;"';";,,"=

. : :. :-."::. . ',:',. . . . . .. . . . . . . .. . . " . ' ..........:'.: : ::.-: :':."::: : . ~ { ....: ....>.:.... : : ~ ~ ~ : > : . > : . : ':'::':'.::.:'

'. ' . . ' . . . ' ......... ~ . ~ . : : : : : : ..: .... . : .... .....:

.. .. PERMEABLE CONDUCTIVE STRATA P-=----_=_ _=_ IMPERVIOUS CONDUCTIVE STRATA C

(j) RESISTIVITY VALUES. WITH THE MUD RESISTIVITYBEING USED AS A UNIT

_____ STATIC S.P. DIAGRAM_ _ _ _ S.P. LOGFIG 4-S.P. LOG FOR DIFFERENT THICKNESSES OF IMPERVIOUS BEDS IN A THICK PERMEABLE STRA

TUM (Rt = R",).

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H. G. DOLL

DRILL HOLE

__ _ - - - = - - - I ~ _ - _ - _ - - - - - - - - ~ ~ I - . : . . . . . . - _ - - - - -

= - ~ - _ - ~ c . - _ - _ - _

~ _ - _ - ~ c . - ____ _ -

PERMEABLE CONDUCTIVE STRATA PIMPERVIOUS CONDUCTIVE STRATA C

o RESISTIVITY VAWES, WITH THE MUD RESISTIVITYBEING USED AS A UNITSTATIC S.P. DIAGRA.Ms.P. LOG

157

--0----=-=

FIG 5-S.P. LOG FOR VARIOUS COMBINATIONS OF PERMEABLE AND IMPERVIOUS BEDS (R, R",)

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158 THE S.P. LOG: THEORETICAL ANALYSIS AND PRINCIPLES OF INTERPRETATIONfor example, when formations of shales andsalt-water sands are traversed by drillholes containing natural mud. Figs 3, 4, and5 illustrat e the effect of bed thickness on theS.P. log.

Fig 3 represents a succession of saltwater sands separated by thick layers ofshales. In this figure, the S.P. log, whichhas been computed mathematically, issomewhat rounded at the level of eachboundary, bu t its peaks are practicallyequal to those of the static S.P. diagram,whenever the thickness of the sand is morethan twice the hole diameter. Fo r smallerthicknesses, the maximum value given bythe peaks is definitely reduced, and theS.P. log no longer reaches the static S.P.diagram. For sands having a thicknesssmaller than one-half of the diameter of thehole, the amplitude of the peak is approximately proportional to the thickness. Withthe assumption that all resistivities areequal, the proportionality factor is suchthat a thin bed, whose thickness is x pctof the drill-hole diameter, shows a deflection on the S.P. log which is about xpct of the maximum possible deflection,represented on the static S.P. diagram.This point is shown more clearly on Fig 7and 8, discussed later.

Fig 4 represents an inverse case of theone illustrated on Fig 3, with shale beds ofvarying thicknesses, separated by thicksalt-water sands. As can be seen, the log issimply the symmetrical image of the onerepresented on Fig 3. For thin shales, thedeflection is approximately proportional tothe thickness, with the same proportionality factor as for thin sands in thick shales.

Fig 5 is a composite log, illustrating theS.P. log in the case of various bed thicknesses. Th e bottom part of the figure is ofparticular interest, as it shows a successionof thin beds of sand and shale, hereafterreferred to as a "sandwich." Comparingthe S.P. log of the sandwich with the oneof the homogeneous sand P2, it can be seenthat the sandwich is characterized by: (1) a

smaller average deflection of the S.P. log;and (2) ripples about the average deflection.

When all resistivities are the same, as inthe present case under discussion, theaverage deflection represents a percentageof the total emf, approximately equal tothe percentage of sand in the sandwich. Theripple is a function of the thickness of theindividual beds and decreases very quicklywhen the individual thickness falls belowone-half the diameter of the hole. Th e discussion of thin interbedded layers in connection with the S.P. log is of particularimportance when analyzing the problem ofinterpretation of shaly sands. This subjectwill be considered in more detail later on.Influence of Resistivities of Formations and

MudThe effect of the resistivities of the

media on the S.P. log is better consideredas a function, not of their absolute values,bu t rather of the ratio between the resistivity of the formations R, and the resistivity of the mud Ron. In the text, theRvalue R: is called" resistivity ratio." Fig 6illustrates the influence of the resistivityratio on the S.P. log.

In order to permit an accurate computation, in each of the examples, the resistivityis chosen uniform for all beds, bu t nowgreater than the mud resistivity.

Th e S.P. log is similar in character tothat where the formation resistivity is thesame as the mud resistivity, except that:(1) the S.P. log is more rounded at theboundaries; an d (2) the peaks in corresponding thin beds are reduced in amplitude.

These two effects are more pronouncedas the resistivity ratio becomes greater.This is illustrated by Fig 6, which corresponds to the same formation arrangementas Fig 5, except where the resistivity ratiois 1, 6, 21 , and 101 . Fig 6 illustrates veryclearly that, when the resistivity ratio increases, the S.P.log becomes more rounded,the peaks for thin beds are reduced in

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H. G. DOLL 159amplitude, and, more generally, all detailsbecome less apparent; this is particularlynoticeable in the progressive decrease ofthe ripples for the sandwich P10C ll , and the

.J.J

almost imperceptible indication of theshale C7 in the case R, = IOIRm

The effects of bed thickness and of resistivity ratio on the amplitude of S.P. logpeaks are vividly illustrated on Fig 7 and 8.On Fig 7, the ordinates correspond to the

amplitude of the S.P. log peaks in percentage of the static S.P. deflections. Th eabscissas represent the thickness of the permeable strata, in units of drill-hole diam-

EII::5..Ii"

EII::CIJIIr

EII::(j')IIri"

EII::"eter. Several curves have been plotted.each corresponding to a different value ofthe resistivity ratio.Fig 8 has the same ordinates as Fig 7,but the abscissas represent differ.ent valuesof the resistivity ratio. The chart consists

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Q;en(,)

t;u. 8, ,E T 1/1 j::7"""1

001 I ~ L 1, :%ot J..- "" IQ;enu.oI&J::>..J:!

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a.:vi 10

4

3

-I 2

:.::UJa...

THICKNESSES OF jPERMEABLE STRATA0 I- V--- -----.. --r-- ---r--.. - - - - - ~ - - -O ~ -... -...... ~ ~ ................ ~ ~I'... r-.....0 ~ .......... ~ , ~'- l'-.o ...............

r-..... '" '.... ~ I ~ ' B C ~ ~ ........1.0 ~ "'- ~ 4 l"- I'.......... .......J'o,. ~ ........0 r---..... '" ~ ,2d ~ ~ '" ..............~ .......... ~ d ~ , r....... ~ ..................0 ............ ! ............ "-.... ~ '-......--. ~ ...........0- - - ~ I".:::.... I'-. r-... ------ ---- ~ I--- ------ '--.. r------ ............I ~ r-...,-- --- = DRILL HOLE 0 AMET ER -' I 4 8 10 20 40 60 8o 100 ZOO 400 6( 0 8~ ..,Rm

FIG 8-S.P. PEAK VALUE AS A FUNCTION OF Rt fRm FOR DIFFERENT THICKNESSES OF PERMEABLE STRATA.

..........

b-I'----

r--00

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162 TH E S.P. LOG: THEORETICAL ANALYSIS AN D PRINCIPLES OF INTERPRETATION

of several curves, each one corresponding toa given thickness of permeable stratameasured in units of the drill-hole diameter .

I t is apparent from these charts that over90 pct of the maximum amplitude of theS.P. deflection at the center of a permeablestratum is reached for low resistivity ratioswhere the thickness of the stratum isover 6 times the diameter of the drill hole.Thus, thick permeable salt-water sands oflow resistivity show S.P. values close to thestatic S.P. and the maxima on the S.P.logs do not vary appreciably for changes inthickness. For highly resistive media theS.P. deflection at the center of permeablestrata tends to increase linearly with theirthickness.Remarks

In practice, the resistivities of the successive beds are not always the same; theymay even differ widely, as when shales orsalt-water sands are interbedded in compact sandstone or limestone. Then accurate

m a t h ~ m a t i c a l computation of the S.P. logbecomes very complicated and laborious.

Ne'ertheless, t he preceding discussion ishelpful in interpreting the S.P. log, as itsshape remains generally the same. I tshould be noted particularly that, except inextremo cases, the boundaries betweenpermeable and impervious beds still correspond to points of inflection on the log.

In the case of very thin beds, having athickness of less than one-half of the diameter of the drill hole, the inflection pointsare s l i g h ~ l y outside of the boundaries. This ,however, does not appreciably affect theinterpretation rule given in the previousparagraph, since the beds whose boundarieshave to be determined in practice are generally of s'lbstan tially larger thickness.

When the resistivities are different in apermeable bed and in the adjacent impervious stratum, the shape of the S.P. log \\illlack symmetry when it crosses the boundary. I t will be more rounded in the moreresistive formation than in the other one.

Accordingly, the point of inflection will bedisplaced toward the top of the peak if thepeak corresponds to the less resistive formation, and vice versa.

I f both beds are thick, the poin t of inflection on the S.P. log may be determinedwith good approximation. The ratio of thenumber of millivolts between the base lineof the impervious bed and the point ofinflection, to the number of millivolts between that point and the maximum amplitude opposite the permeable bed, is approximately equal to the square root of the ratioof the resistivity of the impervious bed tothe resistivity of the permeable bed.

I njluence of Hole DiameterAn increase in hole diameter acts

approximately like an increase in the resistivity ratio: it tends more to round the deflections on the S.P. log, and to reduce theamplitude of the peaks opposite thin beds.

Referring to previous figures, and particularly to Fig 7, it will be recalled that adecrease in bed thickness will affect theS.P. log. I t should be kept in mind, however, that this effect is not a function of theabsolute value of bed thickness, but ratherof the ratio bed thickness to drill-holediameter. Accordingly, an increase in holediameter will decrease the ratio bed thickness-hole diameter. This will tend to decrease the amplitude of the peaks and toround the S.P. log near the boundaries.

IlIjluellce of Invasioll by Mud FiltrateIn this section, it will be assumed at firstthat all the emf which generate the S.P.

current at the level of permeable beds, areof electrochemical nature.

In this condition, penetration of mudfiltrate into the permeable formation has aneffect on the maximum of the S.P. deflection similar to an increase in the holediameter. The equivalent hole diameter,however, becomes appreciably smaller thanthe diameter of the invaded zone, as theresistivity ratio increases.

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H. G. DOLL

In order to give an illustration of thiseffect, several conditions of invasion areshown schematically in Fig 9, where theresistivity ratio of the permeable stratum is

the undisturbed formation is illustrated atP, Q. and R for diameter of invasion of2d, 4d. and Sd, respectively. The emf corresponding to the boundary betll'een mud and11------------------------ , r---------------------------- - - - - - - - - - - ~ ~ ~ - - - - - - - - - - ------------ - - ~ - - - - - -----.___________ -- - - ______________ _------------ - _--=f--- - - - . - .--------

------------ ~ Q D _ _ = _ f - - - - - - - - - - - - - -_-_---=91-_-_-_-_-_-_-_-_ - _ -_-_-_-_-_-_---=--_-_-_-_...:::_------------- =-_-_f_------------- - - - - - - - - - - - - - =-_---=f--------------

- - - f_- -----------.111I

- -d - - ! I ' .ID j- 2d - I 1:-:-:I,....1: t : - I

'.' I P2Rj Rj Rj =-Rm--: Rj Rj Rj 1?:Rt">.

'.' , .1 i D j- 4d f:'-:'-:! Dj= 8d i 1:.:-:,," : . ~ I - - ___ _ - ~ - ~ ~ ~ ~ ~ - - - + - - - - - - - ~: ~ : ~ _ _ _ _ _ _____ --=-t : __ ___ - - - - - ~ . ~ ~ ~- - - ~ - - - - - - - - - - ~ ~ - - - - - - - - - - - - -

- - - - - - - - - - - - - - - - ~ - - - - - - - ~ - - - -- - - - - - - - - - - - -- --------------------------=-==-- ------------------------ -- - - ' : ' -d=DIAMETEROFDRILLHOLE- - -C:3 - - - - - - - --=-,.1UE,- -- -- - - - - - - - - - - -- - Dj=DIAMETER OF INVADED ZONE

~ _ - _ - _ - _ - - - = - - _ - _ - - - = - _ - _ - - - - Rj = RESISTIVITY OF INVADED ZONE-=-----_-_---=-_-_-_ -=---_-_-= - . _ t = RESISTIVITY OF UNDISTURBED_-_-_ -_ -_ _ - _ - _ - _ -_ ____=_ _ - = 1-_- FORMATION- - - - - -- -- - - -OR I LL - - R =RESISTIVITY OF MUD IN DRILL_ - _ - _ - _ ~ _ _ = _ _ - _ - _ - _ -_- - =-HOLE- - m- - - - - - - - - - - ~ ~ - - ~ ~ - - - - - - - -

FI G 9-SCHE, lATIC DIAGRA11 FO R Il'.'VADED Z O ~ E S OF DIFFERENT DIA1lETER WITH Ri = R,.

assumed to be the same as the resistivityratio of the adjacent formations. To allowexact computation, the invaded zone isconsidered completely invaded to a uniformdistance, and the resistivity, K, of thatzone is taken to be the same as the resistivity, R" of the undisturbed formation. Theboundary between the invaded zone and

permeable formation, which was at thewall of the drill hole, has now been displaced to the cylindrical surfaces shown atP, Q, or R.

The effect of invasion is shown by theS.P. log in Fig IO for resistivity ratios I , 6,21 , and 101 , and for permeable beds withthicknesses d, 4d, and 16d. The maximum

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164 TH E S.P. LOG: THEORETICAL ANALYSIS AND PRINCIPLES OF INTERPRETATION

deflection of the S.P. log for case ofR, = Rm varies as if the hole diameter weresimply increased to a diameter D. in a caseof no invasion. For a larger resistivity

'1,;--~ , ~ : - : : - - - -

same absolute thickness without invasion,but with a hole diameter of 2d. This alsocorresponds to a bed of thickness 2d in ahole of diameter d (see Fig 7).

::r

/---"

Rt = 6R m . . '. ' . PERMEAB!.E STRATA P =--_-_-_ =_ IMPERVIOUS STRATA C

d- DIAMETER IN DRI!.!. HO!.E I o = DIAMETER OF INVADED ZONES.P. !.OGS: -NO INVASION; . .. . . Dr=2d , _ _ . D j = 4d ; ----Dj=BdRESISTIVITY OF: MUD - Rm ; INVADED ZONE = Rj ; UNDISTURBED FORMATION-Rt

FI G I e -EFFECT OF INVASION ON S.P. LOG WITH R. = Rt ratio, however, the maximum is affected asif the equivalent hole diameter were some-what greater than the actual hole diameter,but appreciably less than the diameter ofinvasion. For example, where R t = IOIR m ,a permeable bed of thickness 4d, invaded toa diameter of 8d, gives a peak of approxi-mately the same amplitude as a bed of

The shape of the S.P. log, though, is alsoaffected by invasion. The dashed lines onFig 10 , illustrating the case for D, = 8d,show that the S.P. peak is wider than forthe case of no invasion.

The S.P. logs for the other two cases, forinvasion to a distance of 2d and 4d, whoseexcursions outside the permeable strata are

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H. G. DOLL

omitted from the figure, fall between thedashed line for maximum invasion of 8dand the full line for no invasion.

This spreading of the S.P. log beyond theboundaries of the permeable strata issimilar to that caused by an increase inresistivity ratio, since the effective resistance within the cylinder determined bythe invasion diameter, is less than thedrill-hole resistance corresponding to thecase where no invasion occurs.

The behavior of the S.P. peak forinvasion in a given permeable stratum isqualitatively that to be expected for an increased effective hole diameter with noinvasion.

Invasion not only reduces the amplitudeof peaks corresponding to thin permeablebeds, bu t it also has the same influence onthe appearance of those inverse peakscorresponding to thin impervious bedslocated in invaded permeable formations(acting similarly, for example, to the casein Fig 4 for thin shale stre,lks in thicksands). This is another consequence of thecorrespondence which exists between thecase of sands in shales, and the case ofshales in sands.

I t sometimes happens that a hole is firstdrilled with a given mud, so that the permeable beds are penetrated by the corresponding mud filtrate, and that afterwardsthe salinity of the mud is changed. Thisdoes not affect the analysis given, exceptinsofar as the process of fIltration may havecreated a zone of appreciably different resistivity in the permeable formations.

Such part of the S.P. jlotential differencesin the mud, which is due to electrofiltrationemf, is practically unaffected by invasion,except by resistivity change in the invadedzone, since the electro filtration emf remains across the mud cake. For that reason,and when the clectrofiltration emf is responsible for a substantial part of the S.P.,the overall invasion effect is generally lesspronounced than represented by Fig 10 .

SPECIAL TOPICSCertain selected topics of particular

interest will be considered, based on anextension of the preceding discussion.

Interbedded Permeable and ImperviousLayers -S andwiches

The strata under consideration havethus far been bounded usually by comparatively thick beds. I t is desirable, however,to examine the effect of interbedded layersof permeable and impervious strata. Whenthere are thin layers of sand in shale, or thinlayers of shale in sand, their combinationconstitutes what has been called a "sand-wich," which can be considered as a moreor less shaly sand. *

The effect of sandwiches has already beenbriefly mentioned in connection with Figs. I t is further illustrated by Fig I I , I2 , and13 which are believed to be self-explanatory. These figures show the followingpoints, with respect to the S.P. log:

I. On thick sandwiches the average deflection is approximately proportional tothe percentage of permeable beds.

2. The average contour corresponding toa sandwich of finite thickness is the samefor a homogeneous permeable bed of thesame thickness and resistivity, bu t forwhich the total emf involved would appar-ently be smalIl'f.

3. The amplitude of the ripples aroundthe average curve decreases very quickly

Th e expression "sandy shale" will no tbe used here, though th e proportion of shalestreaks is such that there is more shale thansand. Sandy shale will be considered as shalecontaining sand grains entirely encased inshaly material, th e whole be d being com-pletely impervious. From the point of viewof the S.P. log, such sandy shales behaveexactly like shales. On the contrary, bedscontaining sand and shaly material, includingclay or other colloids, will be called shalysands, whatever th e proportion of sh,,;le, aslong as they are permeable. In particular.sands that contain only a few pe r cent of shalymaterial, which would usually he consideredas clean. will be placed in this paper in th ecategory of "shaly sands." The term "cleansand" is reserved for sands containing no shalyor colloidal material. 'With that ciassification,most of th e sands met in practic:e are shaly.

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166 TH E S.P. LOG: THEORETICAL ANALYSIS AND PRINCIPLES OF INTERPRETATION

with decreasing thickness of the individualbeds, so that the ripples are hardly noticeable when the individual thickness of both

......J0:x:..J..J2i

the impervious and permeable beds is lessthan one-half the diameter of the hole.

The following properties, which are notillustrated by the figures, must also bementioned:1. The amplitude of the ripples decreaseswhen the permeable beds are invaded bythe mud filtrate.2. The average amplitude of the peaks

decreases when the resistivity of the permeable beds increases with respect to thatof the impervious beds.

Qr.l.... QQ0 r.lz.11. !:ld is.., 10 : ~IIIIIII*IIIIIIIIIIII:J:..

.. ...!;t 10 0":> "ZZ> :;; ... 1>:0: !-.., ~ >1.! " '

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H. G. DOLL

in other words, to stratified compounds ofsand and shale. There are, however, sandbeds with certain unstratified shaly mate-

tirely surrounded by mud filtrate, or by theoriginal interstitial water, generate no S.P.currents, because there is no chain emf.

DRILL HOLE

.' . '. '. ' . PERMEABLE CONDUCTIVE STRATA P--=---=---_- IMPERVIOUS CONDUCTIVE STRATA CCD, RESISTIVITY VALUES. WITM THE MUD RESISTIVITY

BEING USED AS A UNIT.- - - - STATIC S.P. DIAGRAM____ S.P. LOG

FIG I 2 - S . P . LOGS FO R INCREASING LAYERS OF THIN INTERBEDDED PERMEABLE AND IMPERVIOUSSTRATA (Rt = 6 Rm).

rial, and which must, therefore, also comeunder the category of shaly sands.

Whether the different shaly particlesenclosed in a shaly sand are stratified ornot, the compound behaves substantiallyin the same way from the point of view ofthe S.P. log, provided that the shaly sandremains permeable. In unstratified shalysands, the shale particles* which are en-

Th e word particle is to be interpreted asmeaning an agglomeration of minute solidparts together with their adsorbed water.

When, however, a shale particle is in contact on one side with the mud filtrate, andon the other side with the original interstitial water, the 3 media constitute a 3-linkchain and generate S.P. currents. The totalof the S.P. currents generated around eachparticle add their effects, and the corresponding S.P. log is identical to the onethat would have been obtained if the sameamount of shale contact had been present inthe form of thin interbedded shale streaks.

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168 TH E S.P. LOG: THEORETICAL ANALYSIS AND PRINCIPLES OF INTERPRETATIONIn other words, the amplitude of the S.P.log does not depend on the type of repartition of the shaly material in a permeableshaly sand, provided, of course, that the

a large number of shale particles, parts ofwhose surfaces are in contact with water ofvarying salinities. Each such particlegenerates a small emf, but, because there

---C 7 - - - - - -p.--------- -~ ___ -::: ~ t \ 8 \ C . ~ - ~ -::..:::.-=-_---:- -~ - - - - - - - - i i , A.89~ c r c r ~ ~ ~ ~ _ = ~ ~ ~ ~ ;tz....:r:z:..t: / .Z .c c7 . z : :7tz:.l72J7-2::T c;rcz::;i.

. . . .: - : - : . :- PERMEABLE STRATA P -=---=- IMPERVIOUS STRATA C

8 P + ~ C M 6 PERMEABLE + IMPERVIOUS STRATA, INTERBEODED.

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H. G. DOLL 169of the static S.P. diagram at the scale normally used, that is 5 in. per 1 00 ft. On theother hand, the S.P. log for a shaly sand, inwhich the average proportion of shalymaterial is the same at all levels, is identicalto the S.P. log for a clean sand giving anapparently lower emf (as if it were, for example, a clean sand of lower salinity), andmay be represented by a uniformly reducedstatic S.P.This lower emf, which would give thesame S.P. log in the case of a clean sand,will be called hereafter the "pseudo-staticS.P." In fact it is the S.P. that would bemeasured in front of the shaly sand if insulating plugs were set at its upper andlower boundaries, as in Fig 21, to interruptthe mud continuity at these levels. Thepseudo-static S.P. represents the maximumpossible average dellcction for such shalysand, which is reached only if the shalysand is thick enough.

Slzaly Sallds COlltaillillg OilThe presence of oil in a shaly sand IV ii i

increase the resistance of the permeablepart of the medium. I t can be shown thatthis increase will lower the pseudo-staticS.P. Accordingly, the amplitude of the deflection on the S.P. log can be expected tobe smaller opposite an oil-bearing sectionthan opposite a \yater-bearing section. Sucha change in the dellections of the log canonly be found for shaly sands or for thinsands; it will not occur for thick clean sands.

As many sands are shaly, it is not surprising that a change in the S.P. log deflection has been found when passing theoil-water contact in a sand. I t is to be noted,however, that the change in the S.P. logdeflection is not a positive diagnostic forthe detection of oil, since the same effectwould be obtained if the salinity of theinterstitial water were reduced, or if thepercentage of shale were increased. I f thereare good reasons to believe that the salinityof the water remains substantially constantin the interval being studied, and that the

shale content within the sand is approximately the same, then the level at which theS.P. deflection is less is a good indication ofoil content. Such a possibility is at least tobe considered, if concurrently the resistivity is higher, indicating that an increase inshale percentage is no t the probable explanation for the lower deflection.

The presence of gas in shaly sands mayaffect the S.P. log in the same manner as thepresence of oil. I t seems, however, thatthere is a tendency for such shaly sands toshow a little less S.P., and a slightly higherresistivity when they contain gas than whenthey contain oil. This may be due to lessconnate water being left in the reservoir inthe case of gas.

Transition ZoneBetween a substantially clean sand and a

shale, there may be a transition zone ofmore or less shaly sand. In such a case thepseudo-static S.P. for the shaly sand part isintermediate between the respective staticS.P. for the shale and for the sand, asrepresented on Fig 14C.

I f the transition zone is not very thick, orif, as has been assumed on Fig 14C, the resistivity of the formation is much higherthan that of the mud, the S.P. log is toorounded to show a plateau at the level ofthe transition zone. Instead, there simplyis an inflection point, corresponding to aminimum slope, at the level where theactual S.P. potential in the mud is equal tothe pseudo-static S.P. In addition there are,of course, inflection points corresponding tomaximum slopes, at the boundaries of thetransition zone.

This particular case is brought up here toshow that, in special cases, there could beinflection points which do not characterizea boundary between an impervious and apermeable bed. I t is important to note,however, that the special inflection pointmentioned here corresponds to a minimumslope, while inflection points at boundaries

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dSTATIC S.P. I ~ D R I L L HOLE100 MILLIVOLTS I' - - - --

11- - - __---r.--=---- ~ @ - - - = - - : :

::::: :::p . :::.:.:-.:-:.:-:@.:.:-:-............................ .... '. '

II .. .... .. . . . . . . . .

A.-S.P. LOG FOR BROKEN LAYERS OF P AND CPERMEABLE STRATA P

I 100 M I L ~ I V O L TS I100 50 0

B. - S.P. LOGS OF (A) AND(e) SUPERPOSED

IMPERVIOUS STRATA C

I . STATIC S.P. 1!=5DRILL HOLE100 MILLIVOLTS "I ..-----

--c,

- = - - - ~ ----- - - - -- - - , .__ ..--"'--_p c. - ...-

~ = ~ ~ ~ ~ = ~

. -:.'.':p .

-:-::-

. . . . . . . .. .'. . . . . . . . . .c.- S P. LOG FOR INTIMATE MIXTURE OF P AND C

INTERBEOOED STRATA pteSTATIC S.P. DIAGRAM ---- S.P. LOG (LAYERS) --- S.P. LOG (MIXTURE I

FIG 14-SHAPE OF S.P. LOGS FOR DIFFERENT TRANSITION ZONES AT BOUNDARY OF PERMEABLE BED.

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II . G. DOLL 17 1

correspond, in practically all cases, tomaximum slopes.Fig 14a shows a particular case, on the

other hand, where the transition zone ismade of two thin beds, one permeable andthe other impervious, whose contact, orboundary, is characterized on the S.P. logby an inflection point corresponding,though, to a minimum slope. Th e purposeof this figure is to show that, in certainspecial cases, there could be an inflectionpoint coinciding with a minimum slope, andwhich nevertheless characterizes a boundary. In such a case, however, there wouldgenerally be sharper curvatures on bothsides of the inflection point, as is illustratedby Fig 14b, when the logs of Fig 14a and14C are superposed.

There migh t be cases where, in the transition zones, the percentage of shale contentincreases continuously toward the shale. Insuch instances the pseudo-static S.P. itselfwould vary continuously from the sand tothe shale. The S.P. log would show an almost constant slope, with no definiteinflection points, and this would bein accordance with the fact that there isno definite boundary in the formationsthemselves.

Area under the S.P. LogThe expression" area under the S.P log,"for a given interval, designates the area

between the S.P. log and its base line, forthat interval. I t will be assumed in thissection that the permeable formations aresands and the impervious formations areshales; the shale line, which corresponds tothe S.P. in front of thick shales, is takenas the base line. In that case, the area underthe S.P. log is the area between the log andthe shale line (or its continuation) for thegiven interval.

The reason for considering this area isthat, under favorable circumstances, and inparticular when the resistivities of sandsand shales are approximately equal, itgives a u ~ e f u l indication of the respective

proportions of sands and shales. When, in agiven interval, there are only thick sandsand thick shales, the boundaries betweenthem are easily determined and correspondto the inflection points on the S.P. log,which shows quite sharp deflections in thatcase. When, however, some of the successive sands and shales are rather thin, theS.P. log shows ripples which are difficultto distinguish, and it is practically impossible to determine the boundaries of eachindividual sand bed. In such a case the areaunder the S.P. log may be of great help, ifused with care.

In the ideal case, where the sands andshales have the same resistivity, and eventhough that resistivity is quite differentfrom that of the mud, the area under theS.P. log is the same as the area under thestatic S.P. diagram. For a given geologicalhorizon the shale line is usually approximately straight, and it can generally beassumed that the static S.P. is the same forall sands. Furthermore, the value of thetotal emf, or static S.P. difference betweenshales and sands, can generally be determined from the log. This will be done in aregion of thick sands that can be considered reasonably clean, containing the

~ a m e interstitial water as the other sands,and having approximately the same differential pressure.

Having determined the static S.P., it isan easy matter to evaluate the sand thickness in interbedded sections of sands andshales belonging to the same general horizon. The sand thickness will be obtainedfrom the following relation:total thickness of sand

area under the S.P. logtotal emf

in which both quantities in the secondmember are derived from the S.P. log.

Consistent units must be used for thearea, for the total emf, and for the totalthickness. If, for example, the total area is

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17 2 TH E S.P. LOG: THEORETICAL ANALYSIS AND PRINCIPLES OF INTERPRETATION

expressed in ft-mv, the total emf must bemeasured on the S.P. log in millivolts; thetotal thickness is then expressed in feet.

When the resistivity of the sands is notequal to that of the shales, the quantitativerule given above becomes less precise. Inthat case, however, it is still useful, becauseit gives a rough approximation of the proportion of sands. This approximation constitutes a lower limit to the equivalentthickness of the sands, when the sandsare more resistive than the shales. Similarly it constitutes an upper limit, when theshales are more resistive than the sands.

I f the method is applied to unstratifiedshaly sands, it will give an equivalent sandthickness which is less than the actual distance between boundaries, bu t this isprobably a better estimate. Since both theporosity and permeability of such shalysands are generally less than that of cleansands, they behave like reservoirs of reduced thickness. The estimate of equivalentsand thickness tends to correspond to thereduced reservoir.

In the case of intervals which are primarily made of sands, with a smaller proportion of shale streaks, the same reasoningcan be applied to the determination of thetotal thickness of shale in any given interval. In that case, it is more practical tomeasure the area between the S.P. log anda base line determined by the maximumdeflections opposite the sands. As in theother case, the rule is quantitative if theresistivities are equal. Otherwise, it givesonly an approximation, which is an upperlimit for the proportion of shales if they areless resistive than the sands.

The rule concerning the area under theS.P. log is not affected by a change in thediameter of the hole. Invasion of the permeable beds by the mud filtrate does notaffect it either, except for the influence of achange in ,the resistivity of the invadedzone.

An examination of the examples of S.P.logs, iHustrated in previous figures, par-

ticularly Fig 6 and II , shows the applicability of the rule for various cases.

For an evaluation of reservoirs, the discussion on the area under the S.P. log givesa new approach to an important problem.A word of caution should be given: theestablished rule can only be applied withassurance when the resistivities of thepermeable bed and adjacent beds are verynearly the same. When these resistivitiesdiffer, the area under the S.P. log is modified to an extent difficult to evaluatemathematically.

Base Line ShiftsI t has been assumed throughout the

paper that the S.P. was the same in front ofall thick shale beds, or, in other words, thatthere was a straight" shale line" or "baseline" on the S.P. log. Field experienceshows, however, that, in certain fields,there is a systematic shift of this shale linewhich occurs always at the same locationin the geological column. In fact, in certaincases, such base line shifts constitute excellent markers.

The shift is generally caused by a difference in the nature of the shales above andbelow the shift level. There can, however,be a shift in the base line, even thoughthe shales above and below the shift levelare of the same nature. This occurs whenthere is, in the ground, a dissymetricalsequence of formations constituting one ormore 3-link chain emf which do not cancelout.

S.P. LOG IN LIMESTONE FIELDSThe case of limestone fields, and moregenerally of permeable beds in compact and

highly resistive formations, deserves aspecial study.The permeable zones, whether oil bearing

or water bearing, are somewhat conductivebecause of the capillary water of generallyhigh salinity which is present in the pores.The other conductive beds, like shales forexample, are of impervious nature. When

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H. G. DOLL I73the permeable and impervious beds arethick and sufficiently conductive, the S.P.log approaches the static S.P. diagram, sothat the number of millivolts recorded in

front of a permeable zone differs from theone recorded in front of an impervious bedby an amount approximately equal to theemf involved, as in the general case.

When, however, the conductive beds arenot very thick, and are separated by thickhard formations of high resistivity, the S.P.

log has a shape which is difficult to understand at first glance. This comes from thefact that the very resistive formations tendto prevent the S.P. currents from leaving or

entering the hole opposite their level. TheS.P. currents thus have to fiow)nto the holealmost entirely by way of the permeablebeds and of the nearest conductive impervious beds. In so doing, the S.P. currentsproduce potential differences by ohmiceffect in the mud in front of the hard re-

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I74 THE S.P. LOG: THEORETICAL ANALYSIS AND PRINCIPLES OF INTERPRETATION

sistive formation. The result is that thepeaks corresponding to the permeable zonesspread above and beloll' these zones in anapparently abnormal manner.

I t will be shown here, with the help of atheoretical example, that the curiousbehavior of the S.P. log is more easilyexplained, and that the interpretation be-comes less diilicult, once the principles havebeen established.

Fig I sa represents, in a schema icalway, the case of 4 thin permeable zonesP3, P 7, P 9, and P ll , and 3 thick shales C"C5, and C13 , separated from each other bythick, compact, and highly resistive bedsH2, II 4, II 6, II 8, II 10 , and II 12. In order tocharacterize the problem more explicitly, itis assumed, with the resistivity of the mudbeing taken as a unit, that the resistivityof the permeable zones, as well as that ofthe shales, is approximately 10 , while thehard formations have a resistivity of 500 ormore.

The S.P. log that corresponds approxi-mately to such a case is given in Fig I sa.The segments of that log Iyhich correspondto hard formations are represented bystraight lines (more precisely, they shouldhave slight curvatures as will be explainedlater, but the log would be similar inappearance).

The emf involved are, as usual, repre-sented by the static S.P. diagram on whichthe S.P. is superimposed. As can be seen,the departure of the S.P. log from thestatic S.P. diagram is remarkable in thiscase, and there is no wonder that this typeof log has sometimes been considered ab-normal. In Fig IS it is assumed that thestatic S.P. in front of the hard formationsis the same as that in front of the shales.In this schematical example, any otherreasonable value could have been assumedfor the static S.P. in front of the hard for-mations* without changing appreciably the

Needless to say. hard formations met inpractice are no t quite as sharply defined anddifferentiated as those represented on th efigures.

corresponding S.P. log. This is because thehard formations, as represented, are muchtoo resistive to allow any appreciable S.P.current to diverge into the mud, andthereby to influence the potential. Whathappens under other conditions will be discussed at the end of this section.

The shape of the S.P. log is easily under-stood if the circulation of the S.P. currentsis studied first. This circulation is repre-sented, in a quite schematical way, on Fig15c. The S.P. currents, which are generatedby the different emf, flow into the sands.

They cannot traverse the adjacent hardformations through sections located closeto the drill hole, because these sections aretoo small in area and, therefore, introduceinto the circuit large resistances whichwould practically prevent the current fromflowing. On the contrary, the S.P. currentpenetrates deeper than usual in the permeable beds and, consequently, enters thehard formations through larger cross sec-tions. From there on, it is easier for the S.P.currents to continue their path in the hardformations without appreciable reductionin their cross section, as would be requiredif they were to converge quickly toward thehole. The S.P. currents flow therefore to-ward conductive beds through which theycan return to the mud in the hole, andthen, through the mud, back to the per-meable beds to close their circuits. Theycannot come back to the mud throughother permeable beds, because they wouldencounte r emf which would oppose the flowof currents in that direction. When thefirst conductive beds they encounter are ofthe permeable type, they simply crossthem until they reach conductive andimpervious beds. This is the case for theS.P. currents which penetrate the permea-ble bed P 9; they have to cross the permea-ble bed P 7 in order to reach the imperviousbed C5, or have to cross the permeable bedP 11 in order to reach the impervious bedC,3 .

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H. G. DOLL 175The total potential drop along a current

path is equal to the total emf involved. Thecurrents divide between the different possible paths and produce in them potentialdifferences, according to Kirchhoff's !

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176 TH E S.P. LOG: THEORETICAL ANALYSIS AND PRINCIPLES OF INTERPRETATION

easy to detect on the S.P. log, even whenilard formations like I i and I i are present,because a very definite slope reversal occursopposite the permeable bed. In the case of

S.P. +..

case of beds P 7, P 9, and Pl!. Miscellaneousexamples corresponding to that case areshown by Fig 16 and I 7, on which thecorresponding S.P. logs and resistivityRESISTIVITY

- - - - - - - ~ - - - - - - t _ - f -- ~ _=_-_-_-_ _=_---=-___ _--=-----------------_ - r-C1 - =--=-----------=--=----=-----=------------, -- ------------

/

III H 4 ~ P 5 1 , - ~ ~ / ~ I ~ I - L , - ~ ~ . - ~. .----------}- - - ~ ~ - - - - - - - - ------------- ~ - - - - - - - - - - - ------------ .- -- ----------

L

. . . . . . .. . . . . . .' ,0

. . .. .. , '. . ... ..... .. . . . . . . . . .. . . . . .- r - L _ r ~ - r _ ~ _ r - L . _ ~ ~ ~ _ ~ ~ ~ r i r H 2 2 ~ - , ~ - . ~ ~ ~ ~ - , ~ - , ~ ~ - . - L - r....------------=t C 2 3 - ~ ~ - - - - - - - - - - -- - - - - - - - - - - -----------------------1--------------FIG 16-SCHEMATIC EXAMPLE OF S.P. LOG IN HIGHLY RESISTIVE FORMATIONS.

such an isolated permeable bed, a remainiilg difficulty is to determine exactly Itsboundaries.

Th e interpretation is less evident whenthere is a succession of permeable bedsseparated by hard formations, as in the

logs* have been represented schematicallyto illustrate the principles of interpretation.

Th e resistivity logs which are representedschematically on Figs 16 an d 17 correspondto a so-called "limestone device," or symmetrical sonde. This type of electrode combination is particularly useful when th e problem

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H. G. DOLL 177The large negative peaks from P s to Po

and from P g to PIS on Fig 16 are verysimilar, and do not show clearly what thereis in each interval. However, the resistivity

S f ' RESISTIVITY+ CORRESPONDINGSTRATA I

IP25 ,PII ,IP9 OR P, I,P, I

IP,s ,,1/H'6P" ,H6 IIIH26 II

ICs IIIIc, IIIC,' IC'9 I

Cn II

tion, as to what the conductive beds are, isresolved by the S.P. log, which shows without any doubt that bed CI9 is impervious,while beds P!7 and P 21 are permeable.

+ II

'>--::;--!IIIIIIIIIIIIIIII

}SLOPE CHANGE, WITH CONVEXITYOF LOG TOWARDS NEGATIVE S.P,INDICATES PERMEABLE BED.

PLATEAU ON NEGATIVE SIDEINDICATES THICK PERMEABLEBED OR HIGHLY RES IS T1VEFORMATION BETWEEN PERMEABLEBEDS.

CONSTANT SLOPE INDICATESHIGHLY RESISTIVE FORMATION.

PLATEAU ON POSITIVE SIDEINDICATES THICK IMPERVIOUSAND CONDUCTIVE BED, OR HIGHLYRESISTIVE FORMATION B E T W E ~ "IMPERVIOUS BEDS.

SLOPE CHANGE, WITH CONVEXITYOF LOG TOWARDS POSITIVE S.P,INDICATES IMPERVIOUS ANDCONDUCTIVE BED.

A. - SCHEMATIC E LECTRIC LOG. B - ANALYSIS OF CHARACTERISTIC SHAPES OF S. P. LOG.FIG 17-INTERPRETATION OF S.P. LOGS.

log gives additional information whichmakes the interpretation easy. Conversely,it can be observed that the resistivity logcorresponding to beds P g, P lI , and P I3 isvery similar to that corresponding to bedsP 17 , Cu , and P 21 But here the indetermina-consists primarily in locating th e conductivezones in hard formations. One of th e peculiarities of this device is to tend to give aconstant value when th e resistivity of th eformation becomes much higher than thatof th e mud. This explains why th e log ap proaches a constant limit in front of all hardformations. Th e principles given here, however, also apply to electrical logs recorded withth e standard electrode arrangements.

The characteristic shapes of the S.P. logwhich make it possible to determine thenature of beds, are summarized on Fig 17,which is self-explanatory.

In most of the schematic examples thepermeable beds considered were ratherthin. Nevertheless for thick beds the reasoning remains valid as illustrated for bedP s of Fig 17.Besides the zones which are definitelyporous and permeable, and might thereforebe of commercial interest if they containoil, hard formations, like limestones, may

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178 TH E S.P. LOG: THEORETICAL ANALYSIS AND PRINCIPLES OF INTERPRETATIONalso comprise zones which would be classified as compact, because their porosity andpermeability are too small to be of anypractical value. These formations desig-

/c. B.

S.P. is smaller than for highly permeablestrata, although likely higher than forshale beds. This, however, is difficult toprove, precisely for the reasons that these

A.FIG IS-SCHEMATIC REPRESENTATION OF S.P. LOGS SHOWING THE EFFECT OF SLIGHT CONDUCTIVITY

IN HARD FORMATIONS FOR DIFFERENT STATIC S.P.

nated as compact may, however, behavelike the more permeable zones, from thestandpoint of the boundary emf. When thepermeability becomes smaller and smaller,the static S.P. remains probably unaffecteddown to permeabilities of only a smallfraction of a millidarcy. Concurrently,though, the resistivity becomes so highthat the ability of the strata to conductcurrent from, or into, the mud becomesprogressively less as the permeabilitydecreases. This means that the drop ofpotential in the mud of the drill hole,caused by the current flow produced by thestatic S.P. in this type of formations, becomes negligible.

For zones of extremely low porosity andpermeability, it is probable that the static

zones have too high a resistivity to clearlyinfluence the S.P. log. Qualitative indications concerning the corresponding staticS.P. can, nevertheless, be obtained in favorable cases. For example, if such a substantially thick zone of extremely low permeability is between two shales, it tends toshow on the S.P.log by a small and roundedexcursion toward the negative, which indicates that its static S.P. is more negativethan that of the shales:

As long as the formations are somewhatconductive, current passes from the mudinto the formations at all levels where thestatic S.P. is more negative than the actualS.P. in the mud. The current loss per foot ofhole is proportional to the difference between the static S.P. and the actual S.P.,

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H. G. DOLL

and alse to the conductivity of the formations. This results in a progressive changein the slope of the S.P. log, or, in otherwords, in a slight bending of the curve withconvexity toward the negative. Inversely,wherever the static S.P. is more positivethan the actual S.P. in the mud, the currentflows from the formations into the mud,and the convexity is toward the positiveside of the curve.

To illustrate the above remark, theschematical example of Fig 15 has beenrepresented again on Fig 18, with the assumption that the hard formations H2, II"Hs, Ha, H10 , and H 12 , have enough conductivity to influence the S.P. log.

Fig 18c refers to the case where theirstatic S.P. is more negative than the actualS.P. logged in the mud, while Fig 18bshows the reversed case. The polarity of thedifference between the static S.P. and theactual S.P. in the mud was reversed in Fig18c with respect to Fig 18b, in choosing adifferent value for the static S.P. oppositethe hard impervious formations, as shownon the figure.

EXAMPLESIn this section, field examples are given

illustrating some features of the precedingdiscussion.

Application of the S.P. Computations toa Field Example

The example shown in Fig 19 comprisesseveral interesting features. I t illustratesthat base lines are relative, that imperviousmedia act as the inverse of permeablemedia for their effect on the S.P. log, andthat the mathematical ~ o m p u t a t i o n s havea wider range of practical application thanwould appear from their postulates (such asthe assumption of uniform resistivityratios).

A long section of an electrical log througha shale and a lime section is shown in Fig19d. I t is evident that where the shale ispredominant, in the upper section and at

the very bottom of the log, the base line istoward the positive S.P. In the lime section,known as such from other data, the S.P. logstays on another base line, displaced auniform amount toward the negative S.P.,for an interval of over a thousand feet.Thus, permeable beds in the upper sectionare indicated by excursions to the left of thebase line, while impervious beds in the limesection are indicated .by excursions to theright of another Lase line.

These relationships show that the baseline is an arbitrary choice. Thus, since theshales are conductive and generally moreabundant, they provide, in most cases, agood choice for a base line. When, however,as in the present example, there is a longinterval consisting of a permeable bed withonly a few impervious sections, the permeable bed line, which constitutes a negativelimit of the S.P. log, may give a more practical base line within that interval. This isone more illustration of the symmetricalnature of the S.P. log.

An enlarged section of the S.P. log isshown in Fig 19C. Th e principles given inthis paper were applied to the synthesis ofsuch a log. The results are shown in Fig 19b,while the resistivity ratios used and aschematic geological column are given inFig 19a. Th e resistivity values were takenfrom the electric log recorded in the field.

When computing the S.P. log for theimpervious beds shown at 2940, 2970, and3005 ft, the thickness of each bed, determined from the recorded log, was taken tobe respectively 4d, 14d, and Sd. The staticS.P., opposite the permeable section, wasconsidered to correspond to the permeablebed line, alrea dy mentioned. The static S.P.for the 3 impervious beds was assumed atfirst to correspond to the shale line. Todetermine the amplitude of the invertedpeaks on the computed log, it was considered that the resistivity for the formations bounding each impervious bed couldbe taken as the same as the resistivity ofeach bed. The shape of the curve was modi-

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180 THE S.P. LOG: THEORETICAL ANALYSIS AND PRINCIPLES OF INTERPRETATIONfred, however, to take into account thevariations in resistivity outside of the impervious beds.

... 'I '

....... . ... 0

A.-SCHEMATICGEOLOGICALCOLUMN .-COMPUTEDS.P. LOG

pseudo-static S.P. of half the maximumemf, such as might occur for a mixture ofshale and permeable lime.S.P. LOG

2800

2900

C.- RECORDEDS.P. LOG

S.P. ~ E S l S T J V l T Yf.1": . . .) noo}') ....,

~ 1000-< It.oo .T~ -; 11100,------ ~I ~tO o

) - ~'? 10 . ~/ " 2S.

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H . G. DOLL l S I

pected, because the shale is more conductive than the formation underneath. Acloser examination of the actual electric log,however, indicates that the assumption ofa sharp boundary is an oversimplification.A computed S.P. log was given for thisexample, in order to show one possiblesolution of a section of a particular S.P.log. Other reasonable assumptions couldalso be made, depending upon the judgment of the computer and information fromthe actual physical data on hand. The indications are that, even though the conditions of uniform resistivities postulated bythe mathematical computations are onlyapproximately met here (leave alone suchother phenomena, as the effect of invasion),it is nevertheless possible to construct anS.P. log giving close similitude in shapes andmaxima to a simple field example.

Shaly Oil SandAn instance of a shaly oil sand is givenin Fig 20 . A comparison of the field log withthe computed S.P. charts for clean sandsshows that the computed peaks are toosharp to match those of the field log, par

ticularly in the upper section (8930 to8955 ft and 8970 to 8990 ft), when using thethicknesses determined by the inflectionpoints and the resistivity ratios given bythe resistivity log. Assuming that the totalemf is given by the total deflection in thelower salt-water section, a pseudo-staticS.P. is required to explain the S.P. log forthe upper sands.Such a pseudo-static S.P. suggests thatthe sands are shaly, and in fact this isborne out by the core record. The requiredvalue for the pseudo-static S.P. can beexplained by two differen t sets of condi tions:

1. The sands are water bearing and theycontain a sufficient proportion of shalymaterial to explain the reduction of thestatic S.P. with respect to the total emf.

2. The sands are not only shaly bu t theyalso contain oil or gas, and, in that case the

proportion of shaly material required toexplain the reduction in the static S.P. isless than in case 1.

The resistivity of the sands, as given by$.p. RESISTIVITY

10Ohm-Meter.

FI G 2o-FIELD EXAMPLE OF S.P. LOG SHOWINGSHALY OIL SAND.

the resistivity log, is too high to be compatible with case I , and therefore the interpretation should be that the sands are oilor gas bearing. This is confirmed by theanalysis of the cores.

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18 2 TH E S.P. LOG: THEORETICAL ANALYSIS AND PRINCIPLES OF INTERPRETATIONBase Line Shifts

The examples of Figs 21 and 22 show baseline shifts. The shales in the upper parts ofthe log are known to be of different characte r from the shales present in the lowersections.

\RESISTIVITYOhm-Meters

1 - - - - : : ; > ~ ~ - - 1 2 4 0 0 ...t1-----. .1- ' ----12500

f - - - - - ~ - ~ 2 6 0 0--

f - - - - ~ - ~ 2 7 0 0

'::::P

Ir1--4.==,-L-i- - I2900~SrIf - - + - - - ~ ~ 2 0 0t

~ - - - ~ ~ ~ 4 0 0 i?It

FIG 21

cation of the geological section through theuse of the electric logs.Permeable Zones in Lime

An example illustrating the correspondence between the S.P. log recorded at anS.P. RESISTIVITY

m- eters~ - - - - - . r - ~ 4 3 0 0 1 - - . - - - - - 1

f - - - - - - . ~ - - - 1 4 4 0 0 ' ~ ~ - - - 1

FIG 22FIGS 21 AND 22 -F IELD EXAMPLES OF S.P. LOGS SHOWING BASE LINE SHIFT.

In these cases, the static S.P. for the different categories of shale are sufficientlydifferent to shift the base line. The levelwhere the shift occurs constitutes an horizon marker, and thus provides an identifi-

increased sensitivity (amplified S.P.) andthe core record for a section of lime is givenin Fig 23.

I t is seen that the zones otherwise knownas permeable, are indicated on the log by

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H. G. DOLL 183

S.P. RESISTIVITY- ~ - t -fiiiV1 Ohm-Meters

1 - - - - - : : : : ~ = - = = = ~ _ - - + I O O O O j . . . . , _ . . : : . . . . : + - - - - - - ~,,- :P3::

1 - - ~ ~ ~ - - - - - - - - - - - - ~ : ? 4 : :

~- - ~ ~ - - - - ~ ~ ~ - - - - - - - ~

: : : : : : P, PERMEABLE LIME,.. ' FROM CORES ~ NO RECOVERYFI G 23--FIELD EXAMPLE OF S.P. LOG IN LIMESTONE.

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184 TH E S.P. LOG: THEORETICAL ANALYSIS AND PRINCIPLES OF INTERPRETATIONcurved parts with convexity toward thenegative.

CONCLUSIONSTh e present paper presents a theory of

the S.P. log which might serve as a guidefor interpretation, and as a foundationfor further discussion on the subject.

The static S.P. diagram, which may seemtoo abstract at first, has been introducedbecause it is a convenient way to representthe emf involved. Some of these emf are ofelectrochemical nature, and occur at theboundaries between the mud and the formations, as well as at the boundaries between the formations themselves. Someothers are due to the electrofiltrationphenomena, and occur across the mud cake.Together they generate S.P. current s whichflow in the ground, and close their paththrough the mud in the drill hole. In sodoing they produce, in the mud, by ohmiceffect, potential differences which are recorded to obtain the S.P. log.

Some potent ial drops by ohmic effect alsooccur in the formations, especially when thebeds are thin and resistive; as a result thepotential differences recorded on the S.P.log are not always equal to the total emfinvolved. The amplitude of a deflection istherefore not a measure of the total emf,except in the case of thick and conductivebeds. In the general case, the amplitude isaffected by many other factors besides thevalue of the total emf; namely, the thickness of the beds, their resistivity and thatof the mud, colloidal content of the beds,the diameter of the hole, and the depth ofinvasion of the mud filtrate.

Extensive computations have been madeto analyze the behavior of the S.P. log inwell-determined and idealized conditions.When accurate computations were practically impossible schema ical equivalenceshave been used. In spite of the assumptionsand approximations made, the results obtained are of great value for the practicalanalysis of the S.P.logs, and should greatly

increase the amount of information thatcan be obtained from such logs.

In spite of the complexity of the problem,a number of simple conclusions can be derived and used as a practical guide for theinterpretation of the S.P. logs; namely:

1. The S.P. log is essentially a good detector of permeable beds, which, undernormal conditions, correspond to negativepeaks. I t does not, however, measure thevalue of the permeability or of the porosity,and in fact makes little differentiation between highly permeable beds and stratawhose permeability is too low to be of commercial value.

2. The boundary between a permeablebed and an impervious bed is characterizedby an inflection point on the S.P. log. Thisinflection point does not correspond to halfdeflection when the resistivities of the twobeds in contact are different, or when oneof the beds is thin. For the boundary of twothick beds the inflection point is nearer tothe plateau corresponding to the more conductive of the two beds.

3. When permeable beds are bounded byhighly resistive formations, as in limestonefields, the corresponding peaks spread appreciably beyond the boundaries.