OTC-13042-MS

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Copyright 2001, Offshore Technology Conference

This paper was prepared for presentation at the 2001 Offshore Technology Conference held inHouston, Texas, 30 April–3 May 2001.

This paper was selected for presentation by the OTC Program Committee following review of

information contained in an abstract submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the Offshore Technology Conference and are subject tocorrection by the author(s). The material, as presented, does not necessarily reflect anyposition of the Offshore Technology Conference or its officers. Electronic reproduction,distribution, or storage of any part of this paper for commercial purposes without the writtenconsent of the Offshore Technology Conference is prohibited. Permission to reproduce in print

is restricted to an abstract of not more than 300 words; illustrations may not be copied. Theabstract must contain conspicuous acknowledgment of where and by whom the paper waspresented.

AbstractA procedure is presented for using wireline or MWD data toidentify when high pressure techniques are necessary to predict pore pressures inside velocity reversals. Shale sonicvelocity and density data are smoothed and cross-plotted. If the reversal data lie on the same trend as points from lower pressure intervals, shale pore pressures can be computed withan Equivalent Depth approach. A high pressure technique isnecessary when the reversal velocities track a slower trend.

IntroductionAn indicator of possibly high overpressure is a velocityreversal, i.e., a zone in which the velocities all drop below thevalue at some shallower depth. When velocity-effective stressdata from a reversal diverge from the compaction trenddefined by shallower formations, the Equivalent Depthmethod can significantly underestimate pore pressures (Fig.1). The same will hold true for any pore pressure estimationmethod that relies upon a single velocity-effective stressrelation.

Bowers (1995) discussed ways to account for high pressure situations. For instance, a second velocity-effective

stress relation can be introduced, the exponent in Eaton’s pore pressure equation (1975) can be increased, or the standardEaton equation can be combined with an exponential normaltrend (Fig. 2). Wilhelm (1998) employs velocity effectivestress relations that steepen with decreasing cation exchangecapacity (CEC) and, to a lesser degree, increasing temperature(Fig. 3). Temperature defines the shape of the shallow normaltrend curve. High pore pressures are matched by reducing theCEC values for an interval.

Not all velocity reversals warrant high pressure techniques(Bowers, 1995). In cases where the Equivalent Depthapproach is appropriate, high pressure methods can cause pore pressures to be significantly overestimated. Therefore, it isimportant to have some systematic way to determine whichtype of pore pressure approach is required within a velocityreversal.

Until recently, the best criterion for determining anappropriate pore pressure method was thought to be a directcomparison between computed and measured pore pressures.However, with dipping sands having good hydrauliccontinuity and significant vertical structure (Fig. 4), so-called“centroid” effects can cause mismatches between the pore pressure measured in a sand and those calculated in nearbyshales (Traugott, 1997; Stump, et. al., 1998). Calibrating a pore pressure estimation method to match crestal or basal sand pressure measurements can lead to erroneous results at other depths. Therefore, it is also important to know when a pore pressure estimation method should not match observed pressures.

This paper presents a procedure for using a crossplot of shale sonic velocity vs. density data to identify when high pressure techniques are required inside velocity reversals, andwhen the Equivalent Depth method is appropriate even whenit fails to match measured pressures. The paper begins with areview of the theory the procedure is based upon. The procedure is then presented, followed by a discussion on howvelocity-density crossplots can be used to refine the Bowers(1995) pore pressure estimation method. An example fromEugene Island 330 is then presented and discussed.

Theory

Compaction Trend Departures. There are two factors thatcould cause velocity reversal data to diverge from the maincompaction trend. One is a change in rock properties. Theformations in the velocity reversal may simply be differentfrom the shallower rocks, and so they follow a differentcompaction trend. Dutta (1987) and Lahann (1998) attributecompaction trend changes to clay diagenesis.

Another possibility is the cause of overpressure (Bowers,1995). When excess pressure results from undercompaction(trapped pore fluid being squeezed by the weight of morerecently deposited sediments), overpressured and normally

OTC 13042

Determining an Appropriate Pore-Pressure Estimation StrategyGlenn L. Bowers, Applied Mechanics Technologies, Houston, Texas

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2 GLENN L. BOWERS OTC 13042

pressured formations with similar lithologies should follow thesame compaction relation. Overpressure just prevents thevelocity and effective stress from increasing as quickly as theywould for normal pressure.

On the other hand, overpressure generated internally by

fluid expansion mechanisms such as heating, hydrocarbonmaturation, and up-dip transfer of reservoir pressures, affectthe rock differently. Here, overpressure results from the rock matrix constraining the pore fluid as the fluid tries to increasein volume. Unlike undercompaction, this can cause the pore pressure to increase at a faster rate than the overburden stress,which forces the effective stress to decrease as burialcontinues (Fig. 5). It should be noted that both the Dutta(1987) and Lahann (1998) clay diagenesis models also produce effective stress reductions during burial. In effect,unloading in their models results from the transfer of stressfrom smectite “grains” to pore water as illitization occurs.

Since compaction is predominately an inelastic process,only a small amount of elastic rebound occurs when theeffective stress is reduced (unloading ). Consequently, elasticrebound occurs along a flatter effective stress path than theinitial compaction curve. During reloading, the rebound curveis re-traced until the past maximum effective stress is reached,and inelastic deformation resumes. Figure 6 illustrate thiswith laboratory data for Cotton Valley shale (Tosaya, 1982).The solid lines are estimates of the original compactioncurves, while the laboratory data define the rebound curves.

Regardless of why reversal data diverge from the maincompaction trend, the bottom line is that when they do, theEquivalent Depth method will fail.

Detecting Unloading. The Equivalent Depth method will failwhenever unloading has occurred. Therefore, the criterion for determining when a high pressure pore pressure estimationmethod is required in a velocity reversal is actually a criterionfor determining when unloading has occurred.

It is impossible to determine from velocity data alonewhether or not unloading has occurred. For example, thevelocity at Point C in Fig. 7 could have evolved along either Path AC, or Path ABC. The first path does not involveunloading, while the second one does. This apparent dilemmacan be resolved by incorporating the response of the density

log.

As demonstrated by the laboratory compaction data inFig. 6 (Tosaya, 1982) and Fig. 8 (Bowers & Katsube, in press), transport properties such as sonic velocity, permeability, and resistivity generally undergo more elasticrebound than bulk properties (porosity and density). Amongthe porosity data in Fig. 8-a, only a sample of seafloor mud(VSF-1) undergoes any significant porosity change duringloading. And yet, all of the permeability and resistivity data inFigs. 8b & 8c exhibit comparable sensitivities to increases ineffective pressure.

The key difference between bulk and transport properties isthat bulk properties only depend upon net pore volume, whiletransport properties are sensitive to pore sizes, shapes, andhow the pores are interconnected. Bowers & Katsube (in press) proposed that a rock’s pore space consists of acombination of relatively large, high aspect ratio storage pores

linked together by a network of smaller, lower aspect ratioconnecting pores (Fig. 9).

Storage pores undergo primarily inelastic deformation, whilethe more flexible connecting pores are capable of elasticrebound. According to the pore structure model of Toksoz(1976) and Cheng and Toksoz (1979), connecting pores withaspect ratios in the 0.1 to 0.001 range should undergo the mostwidening during effective stress reductions. Larger aspectratio storage pores are too rigid. And crack-like pores withaspect ratios less than .001 are too flexible; they close at lowstress levels, and require near zero effect stresses before theyare able to re-open.

Since elastic deformation is, by definition, a reversible process, we can use the elastic reloading data in Figs. 6 and 8to infer how these formations would respond during elasticrebound. As the connecting pore widths vary, they alter theflow path sizes available for electrical current and fluid, andchange the number of intergranular contacts for transmittingsound. The data in Figs. 6 and 8 indicate that elastic reboundshould have a much greater impact on sonic velocity,resistivity, and permeability than porosity and bulk density.This, in turn, suggests that a velocity reversal in which thewireline sonic and resistivity data drop without a comparablechange in bulk density is an indicator of elastic rebound, andtherefore, unloading.

Pore Pressure Estimation Method CriteriaThe procedure for determining whether or not a high pressuremethod is required within a velocity reversal is as follows:

• Pick the cleanest available shale data from inside andoutside the reversal;

• Smooth the data by passing them through a boxcar filter.Since only general trends are of interest, filter sizes on theorder of 300’ to 500’ are typically used.;

• Crossplot the data;• If the reversal data lie on the same trend as points from

lower pressure intervals, the Equivalent Depth method, or any approach that uses a single velocity-effective stressrelation will work;

• If the reversal data track a slower velocity trend, a high pressure technique is required.

For the two examples shown in Figure 7, a high pressuretechnique is indicated for Case C’, but not Case C.

A simple quick-look evaluation can also be performed bydirectly comparing the sonic, resistivity, and density logs. Aclear indicator of the need for a high pressure technique is

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OTC 13042 DETERMINING AN APPROPRIATE PORE-PRESSURE ESTIMATION STRATEGY 3

when the sonic and resistivity logs undergo reversals, but thedensity log does not, as in Fig. 10.

If all three logs go through reversals, then pick a point atthe same depth in each reversal, and project it verticallyupwards until it crosses the log again. If all three logs are

crossed at similar depths, the Equivalent Depth method shouldwork. If the density log is intersected at a deeper depth thanthe other two logs, a high pressure technique is necessary.

Velocity-Density CrossplotsWhen interpreting velocity-density cross-plots, it is helpful tohave some bounds on the expected range of values for shales.For densities greater than 2.1 g/cc, Gardner’s relation:

V (ft/s) = (ρ/.23)4 (1)

has been found to serve as an approximate upper bound for shale velocity as a function of density. For a lower bound, thefollowing equation is used:

V (ft/s) = 4790 + 2953 (ρ-1.3)3.57 (2)

Fig. 11 compares Eqs. 1 and 2 with published velocity-density data for sands and shales. Note that Gardner’sequation can significantly overestimate near seafloor densities.

Revised Bowers MethodBowers (1995) proposed a “modified” Equivalent Depthmethod for dealing with velocity reversals when unloading isexpected. The vertical effective stress at Point B in Fig. 12would be computed from the equation:

σB = σMax σEDσMaxU

(3)

where σB is the effective stress at Point B, σED is theEquivalent Depth solution for the effective stress at B (σA inFig. 12), σMax is the Equivalent Depth solution for theeffective stress at the start of the velocity reversal (VMax), andU is a parameter calibrated with local data.

In reality, σMax and VMax are supposed to equal themaximum effective stress and velocity reached by a formation before unloading began. However, at the time, Bowers (1995)did not have a means for determining these values at each

point along the reversal.An approach has now been developed for estimating the

maximum velocity VMax and density ρMax at each point along areversal from a cross-plot of sonic velocity vs. density (seeFig. 13). After smoothing the data, points from outside thereversal are fit with a compaction trend of the form:

V = V0 + A(ρ-ρ0)B (4)

where V0, ρ0, A, and B are curve fitting parameters. Theunloading path between the curve defined by Eq. 4 and the

current velocity and density is then assumed to be of the form:

ρ-ρ0 = (ρMax −ρ0)

ρv-ρ0

ρMax-ρ0

µ (5)

where ρ is the current density, ρ0 is the parameter from Eq. 4,

ρMax is the density at which the unloading curve intersects Eq.4, µ is a parameter, and ρv is the density obtained bysubstituting the current velocity “V” into Eq. 4. As shown inFig. 13, µ=0 implies no elastic rebound for density, while µ=1aligns Eq. 5 with Eq. 4. As a default, µ=1/U can be used,where U is the unloading parameter in Eq. 3. For Gulf of Mexico and Gulf Coast areas, U=3.13 has been found to work well.

Eq. 5 can be inverted to yield the following relation for ρMax:

ρMax = ρ0 + ρ−ρ0

(ρv-ρ0)µ1/(1-µ)

(6)

V Max is then obtained by substituting ρMax into Eq. 4.

Figs. 14-16 illustrate how local values for Vmax and ρMaxcan change along a velocity reversal.

EI 330-A20S/T (Pathfinder )Figures 17-a,b plot shale sonic velocity and density data fromthe Eugene Island 330-A20S/T well. The data have been passed through a 300 ft. boxcar filter. Regional experienceindicates that compaction trends fit through the velocity anddensity peaks near 5800 ft would cause shallower pore

pressures to be overestimated. On the other hand, compactionrelations that honor the velocity and density data near 4900 ftwould make the top of overpressure appear erroneously deep.

The velocity-density cross-plot (Fig. 17-c) suggests thisdifficulty in picking compaction trends may be due tolithology changes. The shallowest data lie near the Gardner curve, while deeper points migrate towards the right, looparound, and eventually end up along the estimated compactiontrend drawn through the points from 5840 to 6365 km. Thecorresponding normal trends for velocity and density are plotted in Figures 17-a and 17-b. These compaction trendswere assumed to apply for all shales below 5840 ft.

Starting at 6400 ft, the velocities and densities both gothrough large reversals. Between A and B, the velocity dropsfaster than the density (see Fig. 17-c), similar to the unloadingcurves in Figures 6-c and 7-c. From B to C, the velocity-density data are nearly parallel to the lower bound curve, withPoint C ending back on the compaction trend. Oneinterpretation is that the data below 6400 ft are in variousstages of unloading. The amount of unloading (difference between the current velocity and Vmax) increases from A to B,and decreases from B to C, with no unloading at A or C. The

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estimated Vmax and ρmax values along the reversal are shownin Figures 17-a and 17-b.

The velocity drop from A to B on the velocity-densitycross-plot could also be attributed to a lithology change, withsegment B-C defining a different compaction trend.

However, experience has shown that when reversal data drop below the compaction trend for lower pressure intervals, high pressure techniques are generally necessary.

Figures 18-a and 18-b compare the estimated pore pressures and effective stresses with measured data. Two setsof estimates are shown for each parameter: the current value,and the value at the onset of unloading.

The pore pressure and effective stress plots both indicatethat maximum unloading occurred at the point where the well penetrated the sand. Above and below this point, the currentand past profiles approach each other, and ultimately mergetogether. This effect is probably easiest to see in Fig. 18-c,which plots the ratio of the estimated past maximum effectivestress divided by the current effective stress.

Estimates of the maximum past effective stress at the point indicated by the triangle in Fig. 18-b were obtained byStump, et. al., (1998) through laboratory compaction tests. Itcan be seen that the lab-derived value is in good agreementwith the curve derived from the velocity-density data.

All-in-all, this well appears to be a textbook example of the centroid effect.

Summary

The velocity-density cross-plot can be a highly useful tool for pore pressure analysis. It can help: 1) identify where high pressure pore solutions are appropriate, 2) sort data intocommon compaction trend groups, and 3) for unloading zones,establish estimates of past maximum velocities.

Nomenclature

ρ = bulk density, g/ccρMax = maximum past bulk density, g/ccV = sonic velocity, ft/s, L/tVMax = maximum past sonic velocity, ft/s, L/tσ = vertical effective stress, psi, m/L2

σMax = maximum past vertical effective stress, psi, m/L2

V0,ρ0, A,B = parameters in the velocity-density relationµ = parameter in the velocity-density unloadingrelation

SI Metric Conversion Factorsft x 3.048 E-01 =mft2 x 9.290304 E-02 =m2

psi x 6.894757 E+0 = kPa

AcknowledgementsThe author thanks Beth Stump, Peter Flemings, and Penn Statefor generously allowing access to the EI 330-A20S/T welldata..

References

1. Bowers, G. L., “Pore Pressure Estimation from VelocityData; Accounting for Overpressure Mechanisms BesidesUndercompaction”, SPE Drilling and Completions, June,1995.

2. Bowers, G. L., and Katsube, T. J., “The Role of ShalePore Structure on the Sensitivity of Wireline Logs toOverpressure”, AAPG Special Volume on PressureRegimes in Sedimentary Basins and Their Prediction, in press.

3. Cheng, H. C., and Toksoz, M. N., Ïnversion of SeismicVelocities for the Pore Aspect Ratio of Rock”, JGR, v. 84,no. 813, 1987.

4. Domenico, S. N., Elastic Properties of UnconsolidatedPorous Sand Reservoirs”, Geophysics, v. 42, no. 7, 1977, p. 1339-1368.

5. Dutta, N. C., “Fluid Flow in Low Permeable, PorousMedia, 2nd IFP Exploration Research Conference on

Migration of Hydrocarbons in Sedimentary Basins,Caracans, June, 1987.

6. Eaton, B.A., “The Equation for Geopressure Predictionfrom Well Logs”, SPE 5544.

7. Gregory, A. R., “Aspects of Rock Physics fromLaboratory and Log Data that are Important to SeismicInterpretation”, in Seismic Stratigraphy – Applications to Hydrocarbon Exploration, AAPG Memoir 26, TheAmerican Association of Petroleum Geologists, Tulsa,1977.

8. Hamilton, E. L., “Variations of Density and Porosity withDepth in Deep-Sea Sediments”, Jr. of Sedimentary Petrology, v. 46, no 2., 1976, p 280-300.

9. Han, D., Nur, A., and Morgan, D., “Effects of Porosityand Clay Content on Wave Velocities in Sandstones”,Geophysics, v. 51, no. 11, 1986, p. 2093-2107

10. Issler, D. R., and Katsube, T. J., “Effective Porosity of Shale Samples from the Beaufort-Mackenzie Basin, Northern Canada”, in Current Research 1994-B;Geological Survey of Canada, 1994, p. 19-26.

11. Karig, D.E., and Hou, G., “High-Stress ConsolidationExperiments and Their Geologic Implications”, Journal of Geophysical Research, Vol. 97, No. B1, January 10,1992.

12. Karig, D.E., “20. Reconsolidation Tests and Sonic

Velocity Measurements of Clay-Rich Sediments from the Nanakai Trough”, Proceedings of the Ocean Drilling Program. Scientific Results, Vol. 131, 1993.

13. Lahann, R., “Impact of Smectite Diagenesis onCompaction Profiles and Compaction Equilibrium”,American Association of Drilling Engineers IndustryForum on Pressure Regimes in Sedimentary Basins andTheir Prediction, Lake Conroe TX., Sept. 2-4, 1998.

14. Smith, D. T., “Acoustic and Mechanical Loading of Marine Sediments”, Physics of Sound in Marine

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15. Sediments, L. D. Hampton, editor, Plenum Press, NewYork, 1974.

16. Stump, B., Flemings, P.B., Finkbeiner, T., and Zoback,M.D., “Pressure Differences Between Overpressure Sandsand Bounding Shales of the Eugene Island 300 field(Offshore Louisiana, U.S.A.) with Implications for Fluid

Flow Induced by Sediment Loading”, Overpressures in Petroleum Exploration, 7th-8th April, 1998, Pau France.

17. Stump, B., Flemings, P.B., and Karig, D. E., “GainingInsight into Pressure History with Shale DeformationExperiments”, American Association of DrillingEngineers Industry Forum on Pressure Regimes inSedimentary Basins and Their Prediction, Lake ConroeTX., Sept. 2-4, 1998.

18. Toksoz, M. N, Cheng, C. H., and Timur, A., “Velocitiesof Seismic Waves in Porous Rocks”, Geophysics, v. 41,no. 4, 1976.

19. Traugott, M.O., 1997, “Pore/Fracture PressureDeterminations In Deep Water”, Deepwater Technology

(supplement to World Oil), August, 1997.20. Tosaya, C.A., “Acoustical Properties of Clay Bearing

Rocks”, Ph.D. Dissertation, Stanford U., 1982.21. Wilhelm, R., Fraceware, L. B., and Guzman, C.E.,

“Seismic Pressure Prediction Method Solve ProblemCommon in Deepwater Gulf of Mexico”, Oil & Gas Journal , Sept. 14, 1998.

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0

2000

4000

6000

8000

10000

12000

14000

16000

8 10 12 14 16 18

Equiv. Mud Wt.

D e p t h ( f t )

Equiv. DepthPress. Tests

Normal

Trend

VB

V A

B

A

σB σ A

VB = V A

Equivalent

Depth

Estimate

For σB

Equivalent

Depth Estimate

For PB

0

2000

4000

6000

8000

10000

12000

14000

16000

5 7.5 10 12.5 15

Velocity (kft/s)

D e p t h ( f t )

5

6

7

8

9

10

11

12

0 1 2 3 4 5 6 7 8

Effective Stress (ksi)

V e l o c i t y ( k f t / s )

Pressure Tests

Reversal

Main Compaction

Trend:

a) b) c)

Fig. 1 – Reversal zones. Case where the Equivalent Depth method fails due to velocityreversal data diverging from the compaction trend for shallower formations

0

2000

4000

6000

8000

10000

12000

14000

16000

8 10 12 14 16 18

Equiv. Mud Wt. (ppg)

D e p t h ( f t )

Pw r Law; E=3

Expon.; E=3

Press. Tests

5

6

7

8

9

10

11

12

13

14

15

0 1 2 3 4 5 6 7 8



Pressure

Tests

0

2000

4000

6000

8000

10000

12000

14000

16000

5 7.5 10 12.5 15

Velocity (kft/s)

D e p t h ( f t )

Pw r Law V n

Exp. Vn

Pwr Law Vn;

E=3

VNB

σNB

Eaton’s Eq.

σB = σNB (V/VNB)3

σB

VB

VNBPwr Law

σB Pwr LawB

VNBPwr Law

VNB

Expon. Vn;

E=3

a) b) c)

Fig. 2 – Reversal zones: Effect of switching from a power law to an exponential normaltrend on Eaton method pore pressure estimates in a velocity reversal.

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5

6

7

8

9

10

11

0 1 2 3 4 5



8-15 ppg

15-17 ppg

CEC=22;

Tgrd=1ºF/100’

CEC=22;

Tgrd=2ºF/100’

CEC=12;

Tgrd=2ºF/100’

CEC=12;

Tgrd=1ºF/100’

Fig. 3 –Wilhelm’s velocity-effective stress relations (1998) vs Gulf of Mexico velocity- effective stress data for different equivalent mud weight ranges (referenced to mud line).

Sand Shale

NormalPressure

Deep Shales

Charge Base

Base

Charges

Crest

Crest Charges

Shallow Shales

Overburden Stress

Shale Far Field

Pore Pressure

Reservoir

Pore

Pressure

Fig. 4 – The “Centroid”effect – up-dip transfer of reservoir pressures..

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Overburden

Stress

Pore

Pressure

Top of

Overpressure

Sand Shale

Normal

Undercompaction

Undercompaction

+

Fluid Expansion

Unloading

During

Burial

Effective

Stress

Fig. 5 – Effective stress response to different overpressure mechansisms.

5

7

9

11

13

15

17

0 5 10 15 20



1.6

1.8

2

2.2

2.4

2.6

2.8

0 5 10 15 20


D e n s i t y

( g / c c )

5

7

9

11

13

15

17

1.7 1.9 2.1 2.3 2.5 2.7

Density (g/cc)

V e l o c i t y

( k f t / s )

Estimated

Compaction

Trend

Unloading Curve

Cotton Valley Shale

(Tosaya,1982)

Estimated

Compaction

Trend

Unloading CurveUnloading

Compaction

a) b) c)

Fig. 6 – Shale compaction/unloading behavior.

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Density

NormalTrend

A

B

C’C

Velocity

Normal

Trend

Reversal

D e p t h

A

B

C

V e l o c i t y

Density

A, C

B

C’

Unloading

Compaction

Trend

a) b) c)

Fig. 7 – Identifying unloading within a velocity reversal.

0.01

0.1

1

10

100

0 10 20 30 40 50 60 70

Effective Pressure (MPa)

E

( % )

VSF-1

EJA-2

B-TG-6b

V-8

V-7

0.1

1

10

100

1000

0 10 20 30 40 50 60 70


K ( n d )

1

10

100

1000

10000

0 10 20 30 40 50 60 70


F

a) b) c)

Fig. 8 – Response of porosity (a), permeability (b), and formation factor (c) to changes ineffective confining pressure (Bowers & Katsube, 2001). VSF-1 is a sample of seafloor mud. All other samples are shales.

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P

P

Smin

P

Poor

Good

Good

If P = Smin:

Poor

If P < Smin:

Pore

Shape

Sensitivity

to Fluid Expansion

Basic Pore Types

Storage Pore

ConnectingPore

Storage Pores

• High aspect ratios

• Mechanically stiff

• “Nodes” along the pore network

Connecting Pores

• Low aspect ratios

• Mechanically flexible

• Control transport properties during rebound

Aspect

Ratio

> 0.1

0.001 -0.1

< 0.001

Fig. 9 – Pore structure models used to characterize shale behavior (Bowers & Katsube, 2001).

0

1

2

3

4

5

0 0.5 1 1.5

Res. (ohmm)

0

1

2

3

4

5

1.5 2.5 3.5

Vp (km/s)

0

1

2

3

4

5

2 2.2 2.4 2.6

Density (g/cc)

D e p t h ( k m

0

1

2

3

4

5

8 10 12 14 16 18 20

Equiv. Mud Wt. (ppg)

D e p t h k m )

PPson ic

RFT's

Equiv.

DepthSoln.

Mud

Weight

a) b) c) d)

Fig. 10 – Determining from wireline logs when the equivalent depth method will fall. Thesonic and resistivity logs undergo reversals not seen by the density log.

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Density (g/cc)

V e l o c i t y ( k

f t / s )

Density

D e p t h

Velocity

D e p t h

ρMaxρV ρ

VMax

V

V VMax ρ ρMax

µ=0µ=1

V = V0 + A (ρ-ρ0)B

Compaction Trend:

Unloading Trend:

ρ- ρ0 = (ρMax-ρ0)ρV -ρ0

ρMax -ρ0( )µ

a) b) c)

Fig. 13 – Equations for determining VMax and ρMax.

0

5

10

15

5 10 15Vp (kft/s)

D e p t h

( k f t )

0

5

10

15

2 2.4 2.8

Density (g/cc)

D e p t h

( k f t )

5

6

7

8

9

10

11

12

2 2.1 2.2 2.3 2.4 2.5

Density (g/cc)

V e l o c i t y ( k

f t / s )

A

B

C

A

B

C

VMaxB ρMaxB

VMaxC ρMaxC

A

B, C

Compaction Trend:

a) b) c)

Fig. 14 – Velocity reversal with constant Vmax.

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0

5

10

15

5 10 15Vp (kft/s)

D e p t h

( k f t )

0

5

10

15

2 2.4 2.8

Density (g/cc)

D e p t h

( k f t )

5

6

7

8

9

10

11

12

2 2.1 2.2 2.3 2.4 2.5

Density (g/cc)

V e l o c i t y

( k f t / s )

A

B

C

A

B

C

VMaxB ρMaxB

VMaxC ρMaxC

A

B

C

Compaction Trend:

a) b) c)

Fig. 15 – Velocity Reversal with Decreasing Vmax.

0

5

10

15

5 10 15Vp (kft/s)

D e p t h

( k f t )

0

5

10

15

2 2.4 2.8

Density (g/cc)

D e p t h

( k f t )

5

6

7

8

9

10

11

12

2 2.1 2.2 2.3 2.4 2.5

Density (g/cc)

V e l o c i t y

( k f t / s )

A

B

C

A

B

C

VMaxB ρMaxB

VMaxC ρMaxC

A

C

Β

Compaction Trend:

a) b) c)

Fig. 16 – Velocity Reversal with increasing Vmax.

8/18/2019 OTC-13042-MS

14/14


1

2

3

4

5

6

7

8

9

6 7 8 9 10 11

Vp (kft/s)

T V D r k b

( k f t )

1

2

3

4

5

6

7

8

9

2 2.1 2.2 2.3 2.4

Rho (g/cc)

T V D r k b

( k f t )

A

B

Vmax

C Unloading Unloading

ρmax

A

B

C

5

6

7

8

9

10

1.9 2 2.1 2.2 2.3 2.4

Rho (g/cc)

V p

( k f t / s )

4.17-5.02 kft

5.12-5.77

5.84-6.36

6.40-7.81

Unloading

A

B

C

Compaction

Trend

Vmax, ρmax From

A to C

a) b) c)

Fig. 17 – Velocity/density data from EI 330-20AS/T.

3

4

5

6

7

8

9

10

0 2 4 6 8

Pore Pressure (ksi)

T V D r k b

( k f t )

P

P @ Sigmax

RFT's

3

4

5

6

7

8

9

10

0 1 2 3


T V D r k b

( k f t )

SigmaSigmax

Sigma @ RFT'sLab Sigmax

3

4

5

6

7

8

9

10

0 1 2 3 4 5

Sigmax/Sigma

T V D r k b

( k f t )

Sand PressuresTransferred Up-dip

Unloading Above

& Below Sand

P @

Sigmax

P Sigma

Sigmax

a) b) c)

Fig. 18 – Unloading zone induced by up-dip transfer of reservoir pressures.

Date post:	07-Jul-2018
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