The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics's Paper

8/13/2019 The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics's Paper

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The Electrical Resistivity Log as an Aid in Determining SomeReservoir CharacteristicsBy G. E. ARCHIE*

(Dallas Meeting, October 1941)THE usefulness of the electrical resistivity login determining reservoir characteristics isgoverned largely by: (I) the accuracy withwhich the true resistivity of the formation canbe determined; 2) the scope of detailed dataconcerning the relation of resistivity measure-ments to formation characteristics; 3) theavailable information concerning the conduc-tivity of connate or formation waters; 4) theextent of geologic knowledge regarding proba-ble changes in facies within given horizons, bot hvertically and laterally, particularly in relationto the resultant effect on the electrical proper-ties of the reservoir. Simple examples are givenin the following pages to illustrate the use ofresistivi ty logs in the solution of some problemsdealing with oil and gas reservoirs. From theavailable information, it is apparent that muchcare must be exercised in applying to morecomplicated cases the methods suggested. t

should be remembered that the equations givenare not precise and represent only approximaterelationships. I t is believed, however, thatunder favorable conditions their applicationfalls within useful limits of accuracy.INTRODUCTION

The electrical log has been used exten-sively in a qualitative way to correlateformations penetrated by the drill in theexploitation of oil and gas reservoirs andto provide some indication of reservoircontent. However, its use in a quantitativeway has been limited because of variousfactors that tend to obscure the significanceof the electrical readings obtained. Someof these factors are the borehole size,

Manuscript received at the office of the InstituteSept. 27; revised Dec. 8, 1941. Issued as T.P. 1422 inPETROLEUM TECHNOLOGY, January 1942.Shell Oil Co., Houston, Texas.

the resistivity of the mud in the borehole,the effect of invasion of the mud filtrateinto the formation, the relation of therecorded thickness of beds to electrodespacing, the heterogeneity of geologicformations, the salinity or conductivityof connate water, and, perhaps of greatestimportance, the lack of data indicating therelationship of the resistivity of a formationn s tu to its character and fluid content.On the Gulf Coast it is found that theeffects of the size of the borehole and themud resistivity are generally of little

importance, except when dealing withhigh formational resistivities or extremelylow mud resistivities. Fortunately, littlepractical significance need be attached tothe exact values of the higher resistivitiesrecorded. Low mud resistivities are notcommon, but when this condition isencountered it may be corrected byreplacing the mud column. With thepresent advanced knowledge of mudcontrol, invasion of mud filtrate intosands can be minimized, t hereby increasingthe dependability of the electrical log.The effect of electrode spacing on therecorded thickness of a bed is often subjectto compensation or can be sufficientlyaccounted for to provide an acceptableapproximation of the true resistivity ofthe formation. As development of a fieldor area progressively enhances the knowl-edge of the lithologic section, the resistivityvalues of the electrical log take on greatersignificance, ultimately affording accept-able interpretations. The salinity, and

54


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G. K. ARCHIEtherefore the conductivity, of the connatewater associated with the various producing horizons may be determined withsufficient accuracy by the usual samplingprocedure.Determination of the significance ofthe resistivity of a producing formationas recorded by the electrical log appears,for the present at least, to rest largelywith the application of empirical relationships established in the laboratory betweencertain of the physical properties of areservoir rock and what may be termeda formation factor. t should be stressedat this point that numerous detailedlaboratory studies of the physical properties of the formations in relation to theelectrical measurements in question areessential to a reliable solution of theproblems dealing with reservoir content.The purpose of this paper is to presentsome of these laboratory data and tosuggest their application to quantitativestudies of the electrical log. t is not in[ended to attempt to discuss individualresistivity curves and their application.The disturbing factors (borehole, bedthickness, and invasion) are discussedbriefly only to indicate instances whenthey are not likely to affect the usefulnessof the observed resistivity.RESISTIVITY OF SANDS WHEN PORES ARE

ENTIRELY FILLED WITH BRINEA study of the resistivity of formationswhen all the pores are filled with water

is of basic importance in the detection ofoil or gas by the use of an electrical log.Unless this value is known, the addedresistivity due to oil or gas in a formationcannot be determined.The resistivities of a large number ofbrine-saturated cores from various sandformations were determined in the laboratory; the porosity of the samples rangedfrom 10 to 4 0 per cent. The salinity of theelectrolyte filling the pores ranged from2 0 0 0 0 to 100 000 milligrams of NaCI

per liter. The following simple relationwas found to exist for that range ofporosities and salinities:R = FR , [I]

where R = resistivity of the sand whenall the pores were filled with brine, R ,resistivity of the brine, and a for-mation resistivity factor.In Figs. I and 2, is plotted againstthe permeabilities and porosities, respectively, of the samples investigated. Thedata presented in Fig. I were obtainedfrom consolidated sandstone cores inwhich the cementing medium consistedof various amounts of calcareous as wellas siliceous materials. The cores hadessentially the same permeability, parallelto and perpendicular to the bedding ofthe layers. All of the cores were fromproducing zones in the Gulf Coast region.Cores from the following fields were used:Southeast Premont, Tom Graham, BigDome-Hardin, Magnet-Withers, and Sheridan, Texas; also La Pice, and Happy own,La. Fig. 2 presents similar data obtainedfrom cores of a widely different sandstone;that is, one that had extremely low permeability values compared with thoseshown in Fig. I for corresponding porosities.These cores were from the Nacatochsand in the Bellevue area, Louisiana.From Figs. I and 2 it appears that theformation resistivity factor is a functionof the type and character of the formation,and varies, among other properties, withthe porosity and permeability of the reservoir rock; many points depart from theaverage line shown, which represents areasonable relationship. Therefore, individual determinations from any particularcore sample may deviate considerablyfrom the average. This is particularlytrue for the indicated relationship topermeability. Further, although the variation of with porosity for the two groupsof data taken from sands of widely differentcharacter is quite consistent, the effect


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56 ELECTRICAL RESISTIVITY LOG AND RESERVOIR CHARACTERISTICSof variations in permeability on thisfactor is not so evident. Naturally thetwo relationships could not be held toapply with equal rigor because of the well

100I 50.guIS

'+- - x xity. Thus knowing the porosity of thesand in question a fair estima te may bemade of the proper value to be assignedto F based upon the indicated empirical

,

:;;t; 10;;;

x x ~ \5 5EL-oLL.

I I 5

x ~ K

10 50 100 500 1000 5000 0 10 0 30 1 00PermeOibility milliolarcys PorosityFIG. I . -RELATION OF POROSITY AND PERMEABILITY TO FORMATION RESISTIVITY FACTOR FOR CON

SOLIDATED SANDSTONE CORES OF THE GULF COAST.

500

I0.1

0 .o 00 0 0 .. 0. 0 . 00.5 1 0 5 10Permeability. millidClrcys

\0\0 - 0 f\J ... 0 ,

50 100 0 10 0 30 1 00PorosityFIG. 2.-RELATION OF POROSlTY AND PERMEABILITY TO FORMATION RESISTIVITY FACTOR, NACATOCH

SAND, BELLEVUE, LA.Permeabil ities below o. mill idarcynot recorded.established fact that permeability does notbear the same relation to porosity in allsands. From close inspection of these data,and at the present stage of the investigation it would appear reasonably accurate toaccept the indicated relationship betweenthe formation resistivity factor and poros-

relationship F = 8-or from Eq. I

R = R .fJ-mwhere 8 is the porosity fraction of thesand and is the slope of the line representing the relationship under discussion.


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G. E. ARCHIE 57From a study of many groups of data, mhas been found to range between 1.8

and 2.0 for consolidated sandstones. Forclean unconsolidated sands packed inthe laboratory, the value of m appearsto be about 1.3. t may be expected,then, that the loosely or par tly consolidatedsands of the Gulf Coast might have avalue of m anywhere between 1.3 and 2.RESISTIVITY OF FORMATIONS WHEN PORESARE PARTLY FILLED WITH BRINE, THEREMAINING VOIDS BEING FILLED WITH

OIL OR GASVarious investigators-Martin,1 Jakosky,2 Wyckoff,3 and Leverett 4-have studied the variation in the resistivity of sandsdue to the percentage of water containedin the pores. This was done by displacingvarying amounts of conducting waterfrom the water-saturated sand with nonconducting fluid. Fig. 3 shows the relation

which the various investigators found toexist between S fraction of the voidsfilled with water) and R the resultingresistivity of the sand) plotted on logarithmic coordinates. For water saturationsdown to about 0.15 or 0.20 , the followingapproximate equation applies:1

S ~ y or R = R.s- [ ]For clean unconsolidated sand and forconsolidated sands, the value of n appearsto be close to 2, so an approximate relationcan be written:

S ~ [51or from Eq. I , S ~ F ; w [61

Since in the laboratory extremely shortintervals of time were allowed for theestablishment of the equilibrium conditionscompared with underground reservoirs,there is a possibility that the manner in

I References are at the end of the paper.

which the oil or gas is distributed in thepores may be so different that theserelations derived in the laboratory mightnot apply underground.


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58 ELECTRICAL RESISTIVITY LOG AND RESERVOIR CHARACTERISTICSground R), and 2) the resistivity of thesame sand when its pores are entirelyfilled with connate water R.).The first value can be obtained from theelectrical log when all factors can beproperly weighed. The latter may also beobtained from the log when a log is available on the same horizon where it is entirelywater-bearing. Of course, this is true onlywhen the sand conditions, particularly porosity, are the same as at the point in question and when the salinity of the connateor formation water throughout the horizonis the same.

In a water-drive reservoir, or anyreservoir where the connate water is indirect contact with the bottom or edgewater, there should be no appreciabledifference in the salinities through thehorizon, at least within the limits set forthfor the operation of Eqs. 1 and 4; that is,when the salinity of the connate wateris over 20,000 mg. NaCl per liter and theconnate water is over 0 15 In depletiontype reservoirs, or when connate wateris not in direct contact with bottom oredge water, special means may have tobe devised to ascertain the salinity of theconnate water.When it is not possible to obtain R.in the manner described above, the valuecan be approximated from Eq. 3 ) and mhaving been determined by core analysesand R by regular analyses.CALCULATION OF CONNATE WATER, POROSlTY AND SALINITY OF FORMATION WATER

FROM THE ELECTRICAL LOGThe resistivity scale used by the electricallogging companies is calculated assumingthe electrodes to be points in a homogeneous bed. 5 Therefore, the values recorded must be corrected for the presence

of the borehole, thickness of the layersin relation to the electrode spacing, andany other condition different from theideal assumptions used in calculating thescale.

Consider a borehole penetrating alarge homogeneous layer, in which casethe electrode spacing is small in comparisonwith the thickness of the layer. If theresistivity of the mud in the hole is thesame as the resistivity of the layer, therewill be, of course, no correction for theeffect of the borehole. If the resistivityof the mud differs from the resistivity ofthe layer, there will be a correction.Table 1 shows approximately how thepresence of the borehole changes theobserved resistivity for various conditions.The third curve, or long normal, of theGulf Coast is considered because thisarrangement of electrodes gives verynearly a symmetrical picture on passinga resistive layer and has sufficient penetration in most instances to be littleaffected by invasion when the filtrateproperties of the mud are suitable.T BLE I. E.ffect of orehole on InfinitelyLarge Homogeneous Formation

Observed Resisttvity on fiectric LogIn an 8 in. In a Is in.Borehole BoreholeTrue Resisti vity of ~ ~ ~ t f i i l o l ;esistivity Mud in Holeof Formation (at Bottom-hole (at Bottom-holeMeter-ohms Temperature) of Temperature) of

05 1.5 05 1.5M eter- M eter- Meter- Meter-ohms ohms ohms ohms0.5 05 05 05 055 6 5 5 510 I II II II50 65 65 50 55

The values in Table have been calculated assuming a point potential pickup electrode 3 ft. away from a pointsource of current, other electrodes assumedto be at infinity, and it has been foundthat the table checks reasonably wellwith field observations. Checks weremade by: (I) measuring the resistivity ofshale and other cores whose fluid contentdoes not change during the coring operationand extract ion from the well; 2) measuringthe resistivity of porous cores from waterbearing formations after these cores were


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G. E. ARCHIE 59resaturated with the original formationwater. Adjustment due to temperaturedifference, of course, is necessary beforethe laboratory measurement is comparedwith the field measurement.T BLE 2. EiJect of Formation Thickness

No Borehole PresentTrue Resistivity Observed Resistivity

Layer between Large Thickness of LayerShale Bodies HavingResistivity of 1 .0 24 Ft. 16 Ft. 8 Ft.eter-ohms --- --- ---1 1 I 15 5 5 310 10 9 6

20 20 19

The correction at the higher resistivitiesappears to be appreciable. However,in the Gulf Coast when the value of R.is low the correction is not so important.For example, assume a friable oil sandwhose true resistivity is 50 meter-ohmsand whose resistivity when entirely waterbearing is 0.50 meter-ohms; the connatewater would occupy about 0.10 of thepore volume CEq 5). However, if theobserved value on the log, 65 meterohms, were used without correcting forthe borehole, the connate water would becalculated to occupy 0.09 of the porevolume. Therefore, although the effectof the borehole size and mud resistivityon the observed resistivity readings maybe appreciable, the resultant effect onthe calculated connate-water content ofthe sand is not important.When the thickness of the formationis very large in comparison with theelectrode spacing, there will, of course, beno correction to make for the thicknessof the layer. However, when the thicknessof the formation approaches the electrodespacing, the observed resistivity may bevery different from the true value. Table 2shows approximately what the third curve(long normal) of the Gulf Coast wouldread for certain bed thicknesses and resis-

tivities. I(is assumed that large shale bodiesare present above and below the beds, atthe same time neglecting the presence ofthe borehole and again assuming pointelectrodes.

Resistivity meter ohmsO ~ ~ ~ I O ~ ; ; : ; ; ; ; ~ 2 0 0

- ~ ~ ~ - - - - ; - ~ - - , - - ~ 3 4 8 0- - ~ ~ - - - - - - Q - _ - - _ _ I 3 5 0 0

- - - r = - - - - - - - I - - - - . O ~ i = ' . . . . . . , . . . . . . d . 3520NormOiI curve- - - - - - - - - ~ _ . _ - _ _ I 3 5 4 0

~ i .

- ~ - ~ - - - - ~ _ + - ~ ~ m ~ ~ ' - - ~ 3 5 6 0Longnormal . t ~ )urve - - ~ ~ ~ : : ~ ~ ~ , ';- - - - - ( ; = - - - - - - - - - + - - ~ ~ = - - - I 3 5 8 0

= - - - - - - ; ; ; ~ = = l 3 6 0 0- ; - - - - - - -+7 -r '-=--t--------l36Z0-------- ----- ------- 3640FIG 4.-ELECTRICAL LOG OF AN EAST TEXAS

WELL.Diameter of hole, i in.; mud resistivity,3.4 at 85F.; bottom-hole temperature, approximately 13SoF.Tables I and 2 assume ideal conditions,so if the sand is not uniform, or if invasionaffects the third curve, the observed resistivity values may deviate farther from

the true value. The magnitude of theinfluencing factors, of course, willlim,it theusefulness of the observed resistivity valuerecorded on the log. Invasion of the mudfiltrate is probably the most serious factor;however, as previously mentioned, it canoften be controlled by conditioning themud flush for low filtrate loss.Fig. 4 shows a log of an East Texas well.The observed resistivity on the long normalcurve for the interval 3530 to 3560 ft. is62 meter-ohms, or, from Table I approximately 50 meter ohms a fter correcting forthe borehole. In this instance the mudresistivity at the bottom-hole temperatureof 135F. is approximately 2.2 meter-ohms.


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60 ELECTRICAL RESISTIVITY LOG AND RESERVOIR CHARACTERISTICSThe interval is thick enough so that thereshould be no appreciable effect due toelectrode spacing. The formation is more orless a clean friable sandstone, so Eq. 5 can

Resistivity.meter-ohmsSelf pofenf/al 0 5 1- - ' : - - : ; } - - - .+ - - r - - - , 4 0 4 0I 5 J+-tmv.

j jr 4li: t 4060

-*=------+- Zlrt---14080Normal urve --> I

FIG 5. -ELECTRICAL LOG OF A SAND IN EASTWHITE. POINT FIELD, TEXAS.Diameter of hole, 7 in.; mud resistivity,1.7 at 80F.; bottom-hole temperature, 138F.

be used to approximate the connate-watercontent. The formation resistivity factorfor this sand is approximately IS, usingEq. 2 where 8 = 0.25 and m = 1.8. Theresistivity of the formation water by actualmeasurement is 0.075 meter-ohms at abottom-hole temperature of 135F. Therefore, from Eq. I , R for this sand isIS X 0.075 = 1.1 meter-ohms. This valuechecks reasonably well with the valuerecorded at 3623 to 3638 ft. on this log aswell as on the many logs from this poolwhere the Woodbine sand is water-bearing;i.e., 0.9 to 1.5 meter-ohms. The close checkobtained between the calculated and recorded resistivity of the water sand indicates that invasion is not seriously affectingthe third curve. Solving Eq. 5, the connatewater of the zone 3530 to 3560 ft. occupiesa.pproximately = 0.15 of the pore'\j50

volume. The accepted value assigned forthe connate-water content of the EastTexas reservoir is 17 per cent.An electrical log of a sand in the EastWhite Point field, Texas, is shown in Fig. 5.The observed resistivity at 4075 ft. isapproximately 5 meter-ohms. The value ofF for this sand by laboratory determinationis 6. The sand is loosely consolidated, having 32 per cent porosity average. Theresistivity of the formation water by directmeasurement is 0.063 meter-ohms at thebottom-hole temperature of 138F. Therefore, R = 6 X 0.063 or 0.38 meter-ohms.This checks well with the value obtainedby the electrical log between the depths of4 1 0 0 and 4120 ft. , which is 0.40 seeamplified third curve). Therefore, invasionprobably is not seriously affecting thethird curve. From Tables I and 2 it appearsthat the borehole and electrode spacing donot seriously a f f ~ c t the observed resistivityat 4075 ft. The connate water is approxi-

0 3 8mately --, or 0.27.5.0Other uses of the empirical relations mayhave occurred to the reader. One would bethe possibility of approximating the maximum resistivity that the invaded zonecould reach (wh n formation water has agreater salinity than borehole mud) byEq. I , where R , would now be the resistiv

ity of the mud filtrate at the temperature ofthe formation and F the resistivity factorof the formation near the borehole. Byknowing the maximum value of resistivitythat the invaded zone could reach, thelimits of usefulness of the log could bebetter judged. For example, assume that aporous sand having an F factor of less thanIS was under consideration. I f the mudfiltrate resistivity were 0.5 meter-ohms, theresistivity of the invaded zone, if completely flushed, would be IS X 05 = 7.5.Thus the observed resistivity values of thissand up to approximately 7.5 meter-ohmscould be due to invasion.


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DISCUSSION

ACKNOWLEDGMENTCooperation of the Shell Oil Co., Inc.,and permission to publish this paper aregratefully acknowledged. The resistivity

measurements on the numerous cores wereperformed under the supervision of S. HRockwood and J H McQuown, of theShell Production Laboratories.

REFERENCESI Martin, Murray and Gillingham: G.ophysics (July1938).2. Jakosky and Hopper: Geophysics {Jan. 1937).3. Wyckoff and Botset: Physics (Sept. 1936) 325.4. Leverett: Trans. A.I.M.E. (1938) J32 149.S. C. and M. Schlumberger and Leonardon: Trans.A.I.M.E. (1934) 110 237.

DISCUSSIONH. F. Beardmore presiding)

S. W. WILCOX, Tulsa, Okla.-This paperrecalls some of my own observations on thecorrelation of the electrical resistance of earthmaterials with their other physical properties.While Geophysical Engineer for the Department of Highways, of the State of Minnesota,from 1933 until 1936, I was primarily engagedin conducting earth-resistivity surveys prospecting for and exploring sand and graveldeposits. This work was done by two fieldparties using equipment of the Gish-Rooneytype, and was carried out in every part of thestate, both winter and summer.

In brief, when a sand or gravel prospect wasdiscovered, in any way, it was detailed by theresistivity survey to outline its extent and tolocate test holes for field and laboratory sampleanalysis. This survey consisted of a grid ofsteptraverses of one or more electrode

separations, and for each an iso-ohm, orequal resistance contour plan map, was drawn.Several thousand earth-resistivity readingswere taken over more than one hundredprospects. In some instances the test pittingwas started before the completion of electricalsurvey and their findings were soon availablefor checking any suspected correlation theoryand confirming what subsurface factors werebeing measured and how effectively.From accepted earth-resistivity theory, itfollows that within a definite sphere surround-Seismograph Service Corporation.

ing tl,le electrodes the apparent resistancemeasurement is uniquely determined from thespecific resistance and position of each and allof the particles making up the sphere. Anyrational interpretation of these apparent resistance measurements is possible only for thesimplest combinations of particles and theirspecific resistances. Fortunately, soils, subsoils and subsurface rocks, with their embodiedfluids and gases, vary greatly in this propertyamong themselves. For example, clay appearsto have an average specific resistance ofapproximately 50 to. 150 foot-ohms, whereasfor sand and gravel the specific resistance isroughly from 2000 to 5000 foot-ohms. Theimportant feature is the great absolute differences in resistance, consequently a resistanceprofile across a buried lens of sand or gravel surrounded by clay produces a striking response.

In spite of the amount of control availableand the freedom for selecting various electrodeintervals, no reliable quantitative predictionscould be made that were not related to boundary surfaces. The probable depth to the firstdiscontinuity-namely, the clay-sand contact-could be determined fairly accurately if thethickness of the sand body was considerable.When the depth to the sand was known fromindependent data, or could be assumed to beconstant, it was possible to predict its thickness. f both were known, a good guess mightbe made regarding the depth to the watertable; and, i n addition, if all these were known,a surmise could be made about the quality ofthe sand; i.e., whether it contained organicmaterial or was weathered. Perhaps if thedegrees of control were sufficient the porosity ofthe sand, its grain size, or even its temperaturemight be predicted.I observed that few of these variables, eventhe ones that generally contribute to the bulkof the readings, could be quantitativelyseparated without additional independent data;therefore my interpretation was necessarilyempirical and based on experience. Fortunately, in sand and gravel prospecting theeconomically most important factors contribu tetheir effects in the same direction. A highapparent resistance indicates either a thin bodyof highly resistant gravel near the surface, or athicker one overlain with more clay stripping.Clean gravel is more resistant than weathered,and hard gravel more so than soft.


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62 ELECTRICAL RESISTIVITY LOG AND RESERVOIR CHARACTERISTICSn practical terms, I found that an apparentresistance reading of 500 foot-ohms for a20-ft. electrode separation recorded over

ground or glacial moraines of southern Minnesota reliably suggested a deposit of sand orgravel worth further investigation. As a matterof record, prospecting in the part of the statewhere these materials are very scarce, less than3 per cent of the test holes located on thegeophysical information failed to yield granula rmaterials of commercial quality and quantityfor at least highway subgrade treatment.Varying the electrode interval gave additionalconfirmation as to the thickness of the depositand very little else.

In connection with our field work, we madeextensive laboratory studies, attempting towork out the relation between the moisturecontent of sand and gravel and its specificresistance. These apparently simple eXlleriments were not of much help in clearing up myfield interpretations. Several variables werevery hard to control in the laboratory.

The analogy between this type of earthresistivity mapping and electrologging is close.The first measures electrical impedance along asurface generally parallel to the bedding planes;the latter, up a borehole more or less perpendicular to them. The same general limitationsand possibilities appear to be common to bothmethods. Obviously, controls for checking areeasier to obtain for plan mapping than forwell logging within the depth of effectivepenetration.

My interpretation problems appeared to beessentially similar to those of electrical welllogging where the operator, after observingthe character of the resistance and the selfpotential curves, tells his client whether pipeshould be set. The accuracy of his prediction isbased largely on experience and not on sliderule calculations.Mr. Archie s paper suggests an experimentalattack for expanding and improving theinterpretation technique of electrical wellJogging. Any contribution of this nature thatincreases its effectiveness is of great value tothe petroleum industry. I offer my own experiences and observations to emphasize that hehas tackled a difficult research problem andwish him luck.

Dr. A G LOOMIS Emeryville, Calif.-Inthe laboratory, we take into account the variations in measured resistivities of sands and tapwater by finding out the cause of the variationsin resistivity. That is, if the tap water itselfvaried from day to day, its electrolyte contentmust vary from day to day and chemicalanalysis would indicate the change. f sandsdid not give consistent resistivit y readings, thecharacter of the sands (in other words, theformation resistivity factor) probably changedor the kind and amount of water contained inthe sand must have varied.

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The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics's Paper