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OD FOR CALCULATING PORESURES FROM WELL LOGS

R. c. RANSOMUnocal CorporationBrea, California

ABSTRACTThis paper describes a simplified method involving well-log measurements for the pu rpose of estimating both thepore pressu res in overpressured formations and the mudweight necessary to balance such pressures.The method d escribed herein permits he calculation ofpore pressures where abnormal pressures exist withoutadvance knowledge of formation pressure or mud weightinformation.This method has been employed successfully by theauthor for many years throughout most parts of the worldin rock formations which show different geologic histories.In the au thors experience, it has been found that not manypeople actually involved with field operations are ac-quainted with this m ethod; and fewer are acquainted withits derivation, or conditions for its use. This paper hasbeen written primarily as an educational piece suitable foruse in both academia and industry. The derivation of themethod is shown for the first time.

BACKGROUNDA number of investigators have pursued stu dies of se di-ment compaction, compressed clays, and pore pressureprediction methods.- Of these , Ham3 in particular,helped pioneer the method generally referred to as theequivalent depth method. I have used such a methodsince the late 1960s with extraordinary success.Rubey and Hubberts (1959) showed that the net-overburden pressure, c which is that Overburden supported

by grain-to-grain framework is equal to the differencebetween the geostatic load, S, and the pore pressure, P.c = s P

When th e clay minerals were originally dep osited, theassociated water constituted perha ps 65 to 80 of thetotal bulk volume. W hile undergoing compaction, a por-tion of this volume of water is squeezed out of the claysediments leaving a pore volume which is related to thecompressive stress on the clay mineral framework. Intheory, similar clay minerals when subjected to equal net-overburden pressures compress to equal bulk volumes con-taining equa l total pore volumes.0 Conversely, under thestress of overburden, two like samples of compressed clayor sh ale, in-situ, having equal porosities must be suppo rt-ing the same net-overburden pressure, regardless of their

respective depths of burial. T his is the observation I wishto em phasize. It is this feature which allows us to makepore pressure predictions in a drilled well when no pressuredata or mud weight data are available for establishmentof an emp irical relationship.CERTAIN WELL LOGS ARE REQUIRED

The method ou tlined requires that certain well-loggingmeasurements be available. ny well-logging measurementcan be used which is related to sediment porosity. Thedensity log or othe r suitable substitution) for the pred ic-tion of the weight of sediments is a requirement over atleast part of the overpressured formation to be evaluated.At present, electrical resistivity and thus, conductivity)is almost always available from to p to bottom in a well.Acoustic measurements, such as interval transit time At),are routinely recorded in most w ells, particularly wildcats.Other measurements such as density and neutron responsesoften are recorded over formations of interest. Of thesemeasurements, I find that At is the easiest to work with.As a result, m ost examples which are shown below utilizeAt.

MAKE A P m F DEPTH VERSUSHE POROSITY-RELATED PARAMETER

First, a depth-porosity plot must be made similar to thatdescribed by Hottman and Johnson4 or Matthews andKelly? This plot can be made by plotting any param eterwhich is directly related to porosity on a logarithmic scaleversus depth on a linear scale. S uch parameters might beAt, e b , C, onductivity from the d eep resistivity curve,or any porosity m easurement. A plot of At from an acousticlog is easy to work with and has fewer variable influencesthan conductivity. Plot only those data from clay shalesdisplaying similar quality. For example, plot data w hichrepresent clay shales of 80 or m ore clayiness. Stronglycoherent arrays of data will appear on the plot if suchdiscriminator is used. See Figures 1 and 3, in particular,where minimal scatter can be observed.Nex t, draw a trend biased somewhat toward lowerporosity) through those points which are believed to repre-sent normal-pressured clay-shales. This trend, represent-ing normal pressure w ill be nearly a straight line only overshort intervals of several thousand feet. At depth s greaterthan ten to twenty thousand feet, the line will be seen toTHE LOG ANALYST 72

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s

LINEARDEPTHSCALE

s =u1 + P1 (1s2 =u + P2 (2)3)= s2 P2 =u 1 = S l - P IPi = D i x 0.433 x SGf average (psi) (4)(S2-s i) = h X 0.433 X SGb average (psi) (5)

when @ is constant, u =ff2:

pore pressure(6)(7)

at DEPTH 2: P2 = (S2-S1) + P1 (psi)p2mud weight = 19.27 1bslU.S.galD2

Derivationof Mud Weight CalculationFIGURE 1

Pore Pressure at D2 is Greater than at D2FIGURE 2

approach the matrix value zero porosity) of the x-axisparameter asymptotically. At shallow depths where clayshales have been buried less than 3000 to40oO feet) valuesfrom the acoustic log At) will be observed to bend towardhigher apparent porosity because of lack of compaction.Over the interval of interest, departure s from the norm al-pressure trend toward higher poro sities usually delineateoverpressured sedim ents. Overpressure in reservo ir for-mations can be deduced from the pressure in the closelyassociated clay shales. In some instance s, the presence oforganic matter in clay shales will produce much the sam eeffect as overpressure. Organic matter will produce anapparent increase in porosity in source rocks measuredby most porosity logging tools.

THE CALCULATIONS ARE EXPLAINEDFirst of all, it is assumed that the borehole is verticalfrom top to bottom. All calcu lations in the equation sbeloware based on true vertical depths or m easured depths con-

verted to true vertical depths.Rubey and H ubberts postulated that the total overburdenstress (S) was supported by stress a) on the matrixframework and pore pressure (P). Figure 1 shows theillustrative equations. See Nomenclature for the defini-tions of all symbols.)Observing Figure 1 again, if we can write the Rubey-Hubbert equation for one depth DEPTH I) we can alsowrite it for any other depth DE PT W ), and all parameterswould be app ropriately subscripted. However, if we wishto estimate maximum pore pressure and maximum mudweight in an overpressured zone, we must locate DEPTH2at the depth of maximum departure of plotted data) fromthe previously located normal pressure trend norma l com-paction trend).Clay shales which have the sam e mineral compositionand elastic properties and w hich are subjected to the sam ecompactive stresses produce equivalent porosities andporosity-related parameters) to a high degree. The clayshales under these co nditions will display the equivalen tporosities even though they may be buried to differentdepths. By plotting data from clay shales, the problemsof packing, so rting, secondary porosity, etc. are minimized.The deriviation of the method is shown on Figure 1;anexplana tion follows. T he depth of the normal pressure trendwhere the porosity is the sam e as that at the overpressuredzone of interest is referred to as th e equivalent compac-tion depth, DEPTH1, and grain-to-grain stress ul atDEPTH1 must be equal to u2 at DEPTH2.Under such conditions, u1of equation (1)canbe set equalto u2of equation 2) and S,-PI)equals S2-P,) as in equa-tion (3). Abnormal pore pressure P2 of equation (6) canbe solved by the app ropriate substitutions of equations (4)and 5) . Appropriate conversions can be applied to equa-tions (6)and (7) to produceresults n specificunits desiredSee Figure 4 where sample calculations are illustrated.

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4000 I

4000

5 0 0 0 .

6000

EQUIVALENT COMPACTION ___EPTH

5000

6000

7000

tWY 8000W

9000

10000

11000-

10750' MEASURED DEPTH = 8000TRUE VERTICAL DEPTH _ _were used to des ign the drilling program for the secondwell. No drilling problems were experienced with the sec- ,ooo 1 I l l I I

DEPTH OF INTERESl

I

remain equal, the difference in pore pressures between D2and D is equal to the difference in normal pore p ressures 8000between D , and D;.Figure 3 shows a plot of data from a portion of a wellwhich was drilled with a drillin g mud that was about threepounds per gallon lower than the density required tobalance predicted pressures. This well was eventually lostbecause of drillingaproblems. A second well was drilled. looooTh e mud weigh ts predicted from th e plot of the first well

9ooo

20013000 50 100At

Depth Versus Log At for Straight HoleFIGURE 3

-

--

The value of D, in equation 4) hould be corrected whenthe distance between the depth datum and the water tableor sea level) is significant.Figure 2 illustrates that lines d rawn parallel to the normalpressure or normal com paction trend do not represent thesame pore pressure. Here, the pore pressure at D2 s greaterthan at D;. Such parallel lines sometimes do representthe sa me amou nt of overpressure when average bulk den-

weight necessary to balance the expected pore pressurewas 0.1 pound per U.S. allon lower than the m ud weightactually used to kill the well.WHAT IS QVEWRESSURE?

In the second edition of the SPWLA Glossa ry12, ver-pressure is described as follows:Overpressure is an expression which has beenused c ommonly to refer to high pressure foundin som e form ations; supernormal pressure or sur-pressure. Techn icallj it should be said that over-pressure is that amount o f pore pressure whichis in excess of normal pore pressure in over-pressured formations.

Any pore pressure greater than normal pore pressure canresult from number o f conditions some of which arelisted below:1. Abn orm ally high pore pressure related to geostaticload. A s geostatic load increases porous clay rockcompresses with the resulting expulsion o f associated

water. Fractures and porous and permeable reservoirbeds serve as conduits to carry off he expelled waterI f the water in the pore spaces of the reservoir rockcannot be expelled the water will be trapped. Underthese conditions as overburden is increased the clayrock is prevented from further compaction and the in-creased compressive stress is transmitted to the in-terstitial water. Pore pressure in isolated reservoir beds

4250' MEASURED DEPTH= 3500 TRUE VERTICAL DEPTH

3500 x 0.433 x 1.01= 1530.6(8000-3500) x 0.433 x 2.27 = 4423.1PORE PRESSURE ESTIMATED AT DZ= 5953.7 psi

5 19.27= 14.3 1bdU.S. galsity of rock over distan ceh is the sam e as that over distanceh In the case shown in this figure, if all other variables 7000 MUDI- D

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will increase along with the pore pressures in theoverlying clay rock shale).

2. Abnormally high pore pressure related to the densitycontrast between reservoir fluid if oil or gas) and in-terstitial water.Some reservoirs which, when filled with wateG ex-hibit normal pore pressures) exhibit abnormal pressureat the crest of the structure when containing a columnof oil or gas. For example, in a gas-filled reservoir,the normal pore pressure at the level of the gas-watercontact may be transmitted through the gas columnto the crest of the structure with only a small reduc-tion since the pressure exerted by the weight of asubstantial column of gas is low compared to that ofthe same height of interstitial water). This results inhigher than normal pore pressure at the crest of thestructure.3. Abnormally highpore pressure related to causes otherthan those found in 1) or 2).For example, high pressure may result h m he charg-ing ofone bed in communication with another at higherpressure.A FURTHER DISCUSSION ON FACTORSINFLUENCING THE COMPACTION PROCESS

In order for overpressureto be preserved, an imperviousseal must occur which prevents the upward extrusion ofwater from the compacting sediments below. Throughoutthe seal-interval, density of shale may be normal; or, itmay be greater than normal. The seal interval usually isan impervious shale, but it does not have to be shale. Forexample, in someinstances t mightbe an evaporite, a densecarbonate layer, or even a halite. Below the seal depth,the water found in the shales might be prevented from fur-ther expulsion. If no communicating permeable stratumis available for relief, the pressures within the pores willcontinueto increase along with continued geostatic loading.The result is that overpressured intervals demonstrate lowerbulk densities and higher porosities where water has notbeen expelled from pore volumes.Sediments probably break contact in a porosity rangesomewhere between 45 and 50 percent depending on theshape, size, packing, and distribution of the particles. Whenparticles are separated or are nearly separated, a plasticstate results in which little or no net-overburden can besupported by structure and most or all the geostatic loadis supported by the pore pressure. An aggravated situa-tion such as this can be predicted for overpressured shaleswhere the equivalent compaction depth D,) is discoveredto be close to the ground surface. Under this circumstanceit is reasonable to expect that the clay shale is approachinga plastic state and might flow. Under actual drilling con-ditions such as this, drill pipe is likely to become stuck.Further, the density or porosity displayed by a forma-tion is that produced by the maximum geostatic load theformation has ever been subjected to. Subsequent uplift

and erosion may have occurred bringing nearer to the sur-face a formation which previously was found at a deeperdepth. Deposition might occur on top of the previouslycompacted formation, but further compaction will not takeplace until geostatic loading exceeds the former maximumload. A discontinuity in the sedimentary process such asthis will cause at least two different normal compactioncurves to be evident. If the overpressured zone of interestappears at a depth range corresponding to a deeper butseparate normal-compaction curve, the equivalent com-paction depth must be located on the same compactioncurve. It might be necessary to extrapolate the compac-tion curve to much shallower depths in order to accomplishthis. The vertical distance separating the normal compac-tion curve of the rock below a discontinuity from the nor-mal compaction curve of the rock above the discontinuityis directly related to the height of rock eroded away beforethe sedimentary process was resumed.Because regional and local variations can and do exist,then, a different depth-porosity curve can be drawn to fitthe various prevailing conditions. Different normal pressurecurves might apply for different combinations of the follow-ing factors:1. Uplift and erosion2. Geostatic loading3. Diagenetic porosity4. Occurrence of organic matter5 . Borehole departures from vertical6. Logging tool calibrations

CONCLUSIONSThe method described is a simple and practical methodthat can be applied by either computer or manual means.

Most of the logs routinely run in wells can be adapted foruse in this kind of work. The main requirements are thatclay shales be present and the log or logs used should ade-quately cover the shale formations drilled by the well, alongwith the nonshale formations of interest.Inasmuch as the well must be drilled to some depth andlogged before this method can provide any information,the user can determine only in retrospect how the drillingpractices can be improved. A number of questions can beanswered, such as:1 .What depth is overpressure first encountered?2. Where and how rapidly must the drilling mud weightbe increased as drilling progresses?3. What minimum mud weight is necessary to overcomemaximum pore pressure?4. Where does formation pressure return to normal?5 . To what depth should an intermediate casing string

The answers to these questions are extremely helpfulin planning drilling operations for deeper drilling in thecurrent well and for drilling all subsequent wells throughthe same formations. These answers often can be learnedfrom this method.

be set?

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NOMENCLATUREInterval transit time, from sonic log. Modem symbolis t (psec/ft)Compactive stress resulting from overburden. (psi)Net overburden stress concentrated at the grain-to-grain contacts and supported by the rock framework.Pore pressure. Also supporting part of the over-burden. (psi)Depth of the equivalent compactive stress. That is,where the net compactive stress concentrated at thegrain-to-grain contacts is equal to that at depth D2.ft) Here, u1 = u2.Depth of that part of the formation of interest wherepore pressure is not normal. ft)Specific gravity of the formation fluids in direct com-munication with the surface. All formation fluidsalong the normal compaction trend are said to bein communication with the surface. In equation (4)it represents the average fluid specific gravity fromD1 to the surface. Numerically equal to the averagedensity of the formation fluids.Specific gravity of the interstitial-fluid-bearingrock.In equation (5) it is numerically equal to the averagebulk density over the formation found between DIand D2.Difference between D1 and D2. ft)Macroscopic neutron capture cross section obtainedfrom pulsed neutron type logs. (in C.U.or s.u.)Bulk density of the formation as measured by com-pensated density type tools. (gm/cm3)

(Psi)

ACKNOWLEDGMENTI wish to thank the management of the Science and

Technology Division of Unocal for permission to publishthis paper.

REFERENCES:1. Athy, L. F., Density, Porosity, and Compaction of Sedi-mentary Rocks, Bull. Amer. Assoc. Pet. Geol., v. 14, no.1, January, 1930.2. Fertl, W. H., Abnormal Formation Pressure, ElsevierScientific Publ. Co. 1976.3. Ham, H. H., 7 Method of Estimating FormationPressures from Gulf Coast Well Logs, TRANS., GulfCoast Assoc. of Geological Societies, v. XVI, 1966.4. Hottman, C. E. and R. K. Johnson, Estimation of For-mation Pressures from Log Derived Shale Properties,J. Pet. Technol., June, 1965.5. Magara, K., Compaction and Fluid Migration, ElsevierScientific Publ. Co., 1978.6. Matthews, W. R. and J. Kelly, How to Predict FormationPressure and Fracture Gradient, The Oil and Gas Jour-nal, February 20, 1967.7. Reynolds, E. B., D. . Timko and A. M. Zanier, Potential

Hazards of Acoustic Log hale Pressure Plots, AIME,paper SPE 4020, presented at 47th Annual Fall Mtg., SanAntonio, Texas, October 8-11, 1972.8. Rubey, William W. and M. King Hubbert, Role of FluidPressure in Mechanics of Overthrust Faulting, Bulletinof the Geological Society of America, v. 70, February,

1959.9. Serra,O., . Chiarelli, and C. Gras, Automatic Study ofClay Compaction: The Denson Program, SPWLA, TheLog Analyst, July-August, 1975.10. Terzaghi, K. and R. 6. Peck, Soil Mechanics n Engineer-ing Practice, John Wiley and Sons, Inc., New York, 1948.11. Wallace, W. E., Abnormal Subsurface Pressures Mea-sured from Conductivity or Resistivity Logs, SPWLA,The Log Analyst, February-March, 1965.12. SPWLA, GLOSSARY OF TERMS AND EXPRESSIONSUSED IN WELL LOGGING, Second Edition, edited byR. C. Ransom, October, 1984.

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PDl

hc

ABOUT HE AUTHORRobert C. Ransom is Senior Research Associate-

Formation Evaluation for Unocal Corporations Fred L.Hartley Research Center at Brea, California and anHonorary Member of SPWLA. He graduated in 1951fromYale University with a B.E. degree in Chemical Engineer-ing. Bob joined Schlumberger in 1951, left Schlumbergerin 1965, and consulted in Denver prior to joining Unionsresearch group early in 1969. He was General Chairmanfor the 1mOSPWLA Symposium in Los Angeles, has beena member of both SPWLAs Technological Committee andPublication Committee, and Chairman of the SPWLAGlossary subcommittee. Bob compiled and edited both the1st and 2nd editions of the SPWLA GLOSSARY. He alsoserved as a member of the Shaly Sand Reprint Volumesubcommittee, has served on two ERDA steering commit-tees for geothermal well logging interpretation and tooldevelopment, has taught formation evaluation at thegraduate level at the University of Southern California forthe past 7 years, and is a past contributor to THE LOGANALYST.

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