OTC 15290

Emerging Trends in Pressure Prediction Mark W. Alberty and Michael R. McLean/BP Exploration

Introduction Copyright 2003, Offshore Technology Conference

The prediction of pore and fracture pressure along a proposed well path are key inputs to well design. Accurate predictions of these parameters can have significant impact on the cost of wells, both from design and operational perspectives. Recent observations have an important impact upon the prediction of these properties.

This paper was prepared for presentation at the 2003 Offshore Technology Conference held in Houston, Texas, U.S.A., 5–8 May 2003. This paper was selected for presentation by an OTC Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Offshore Technology Conference or its officers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent 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. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented.

Pore pressure is most commonly estimated in shale based upon the observed changes in shale porosity. As effective stress1 increases in shale, the porosity decreases in response to that stress. A ‘compaction trend’ defines the porosity response to effective stress. Compaction trends are the basis upon which pressure is computed from porosity measurements.

Abstract Recognition of some recent observations regarding pressure prediction may significantly impact traditional methods used to predict pore and fracture pressures. These observations include the influence of clay diagenesis upon compaction trends and pressure models, the influence of unloading upon pressure prediction methods, and the influence of whole mud systems upon apparent fracture gradient behavior in sands.

Compaction trends are most accurately characterized as plots of effective stress versus porosity. However, they are typically presented in terms of interval velocity or transit time versus depth, in which case acoustic velocity is used as a proxy for porosity and effective stress is correlated to depth on the basis that the overburden is normally pressured. Thus, at each point the compaction trend shows the interval velocity or transit time for the appropriate lithology at that depth if it were normally pressured. Different practitioners may substitute for acoustic velocity other porosity sensitive log measurements such as resistivity, density, nuclear magnetic resonance determined porosity, and drilling exponent.

Many basins have smectite/illite-dominated shale. It has been observed that smectite and illite have significantly different compaction trends. Transition from smectite to illite is primarily driven by temperature and therefore the composite compaction trend will depend on the temperature gradient in the region. Properly interpreting and defining the compaction trend through knowledge of this process can significantly impact well planning pressure prediction techniques. The key to success in predicting pressure is to accurately

define the compaction trend that is appropriate for the formation being analyzed. A number of factors can affect these curves including the clay type and the relationship between vertical stress and mean stress.

A study of recent wells indicates that the horizontal stress at a given depth below mud line is typically greater in regions subject to erosion. The closer to mud line the more notable the effect. The leak-off tests used to determine the horizontal stress magnitude imply that virtually all the horizontal stress built up during deposition remains after erosion. Compaction trends used to calculate pore pressure need to account for the unloading effects of erosion on the sediments under investigation. However, with little or no unloading of horizontal stresses, the reduction in mean stress in response to erosion may be far less than our algorithms previously assumed.

Clay Diagenesis and Compaction Trends A fundamental assumption that serves as the foundation for pressure prediction from velocity measurements is that all rocks of common lithology, clay type and content, morphology, temperature, fluid, and stress display the same velocity. Without this assumption, all techniques for estimating pressure from log measurements of porosity in shale break down. This common rock behavior is described by compaction trends. The accuracy of any pressure prediction will therefore be dependent upon the similarity of the rock being investigated to the attributes of the rocks used to calibrate the compaction trend.

The design of an appropriate casing program is dependent on fracture resistance of intervals to be drilled as well as the pore pressure. The fracture resistance of sand is seen to be dependent on the presence or absence of solids in the drilling fluid.

The industry practices a number of different methods to calibrate compaction trends2. Empirical observations are most commonly used to characterize a compaction trend. The normally pressured sediments in the well define the trend and

Incorporation of the above observations and principles in pressure and fracture gradient prediction will result in significantly different well design needs.

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then this normal pressure trend is extrapolated to intervals where abnormal pressure is suspected. Of course, this technique is subject to significant error if abnormally pressured sediments are mistakenly assumed to be normally pressured or if the lithology, clay type or content, morphology, temperature or fluid type significantly changes.

Observations made in smectite/illite rich basins, including the Gulf of Mexico (both deep water and on the shelf), the deepwater Caspian Sea, the deepwater Nile delta, offshore Brazil, deepwater Norway and the North Sea, have lead to a more prescriptive set of compaction trends for both smectite and illite rich shale that can be used more universally without the need for normalization.

The density versus sonic crossplot is a useful tool to identify clay type. See Figure 1. Smectite dominant clays tend to group around the dashed/green smectite line with high effective stress moving the points along or parallel to the line toward lower porosity values (increased density or fast interval transit times). Illite dominant clays tend to group around the continuous/brown illite line with higher effective stress moving the points along or parallel to the line toward lower porosity values as well. The exact placement of these lines will vary slightly with clay volume. Similar trends have been observed by others3.

Much has already been published on the on the diagenetic conversion of smectite to illite4-7. Smectite will diagenetically convert to illite as part of a complex kinetic reaction, but primarily associated with the addition of potassium. Potassium can come from a number of different sources, but the most common source is from the thermal breakdown of potassium feldspar, typically occurring between 71 degrees Centigrade and 104 degrees Centigrade (160 deg Fahrenheit and 220 deg Fahrenheit). As the smectite clay diagenetically converts to illite, the density/sonic response transitions from the smectite to the illite trend. In cases where the water released from the diagenetic conversion is able to escape from the shale rapidly relative to the conversion rate, then the transition to the illite line is gradational toward decreasing porosity. In cases where the released water is unable to escape from the reacting shale, the transition can be very abrupt at a constant density moving to slower interval velocity. In this latter case, the frame shrinks while releasing the waters of hydration resulting in a transfer of the overburden stress onto the pore fluids producing a significantly increased overpressure.

The same relationships shown in Figure 1 could be expressed as functions of porosity and interval velocity. The porosity is related to effective mean stress, either through empirical observation or through porosity stress models, ultimately enabling compaction curves to be derived. Smectite and illite have distinctly different compaction trends as a function of stress. Smectite, which has a significantly greater water of hydration, displays a slower trend. See Figure 2.

The conversion of smectite to illite causes the observed compaction trend to shift from the smectite trend to the illite trend, typically between 71 degrees Centigrade and 104 degrees Centigrade (160 deg Fahrenheit and 220 deg Fahrenheit). If the depth range corresponding to this temperature range is short, the transition between the two trends can be abrupt. Where the depth range corresponding to

these temperature ranges is large, the transition between the two trends can be very gradual.

The Amoco heritage brought to BP a generalized global compaction trend developed from empirical observations in primarily smectite/illite-dominated basins. The trend, called “Presgraf Compaction” trend, is the best-fit trend to global shale sediments and has been traditionally used as a starting point for pressure prediction in most basins within the company. The generalized “Presgraf Compaction” trend is compared to the new smectite and illite trends in Figure 3. The trend compares very favorably to the smectite trend shallow and also compares well to the illite trend deep with a gentle transition between the two. If considered in the context of the smectite and illite trends and the associated kinetic diagenesis, the “Presgraf” trend would have an implied geothermal gradient.

In reality, one would expect a compaction trend honoring the smectite and illite characterizations, to follow the smectite trend down to the onset of the diagenetic conversion and then cross over to the illite trend within the diagenetic window and then follow the illite trend thereafter. An example of this is shown in Figure 4. Given the importance of the thermal gradient upon the diagenetic process, one should expect the compaction trend to change as a function of the local temperature profile.

The kinetic model needs to be calibrated to the local kinetic conditions. This can be facilitated using the density sonic relationships defined in Figure 1 coupled with a temperature based kinetic model to transition between the two relationships. Using this tool one can easily calibrate the model by overlaying the density log with a pseudo density from the sonic, based upon the kinetic model and the density/sonic relationship in Figure 1, and adjusting the kinetic parameters until they match. Figure 5 shows such an example. Note that the pseudo density does not match the measured density in either sands or poor hole conditions that also makes the tool useful in editing and interpreting logs.

Recognition of the existence of these trends points toward the weaknesses of previous methods of estimating and applying the trends. First, the trends should not be considered a single trend but rather the coupling of multiple trends based upon diagenetic processes. This would suggest that the normalization of compaction trends in shallow sediments should only be applied at depths above the diagenetic window for the illitization of smectite (effectively restricts this practice to depths where temperature is less than 71 degrees Centigrade [160 deg Fahrenheit]). Second, these observations would suggest that the principles used in the equivalent depth method of pressure estimation across or within the diagenetic window would not be valid.

Observations Regarding Unloading In the pore pressure community stress is invariably taken to mean the overburden stress. However, stress is a tensor and the normal stress compressing a body (soil/rock) is dependent on the direction the body is viewed. Thus, depending on our perspective, the compressive stress could be the overburden or could be a horizontal stress. With porosity being a purely volumetric function, it seems reasonable that its value be a function of all the compressive stresses acting and not simply

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the overburden stress. This is accommodated using the mean stress which is calculated from the principal stresses using the following relationship: (1) 3/)( axHminHmVmean SSSS ++=

Where is the mean stress, meanS is the vertical stress, VS is the minimum horizontal stress, and

is the maximum horizontal stress. inHmS

maxHS The above are ‘total’ stresses. In terms of effective stress, σ , we have PSVV −=σ (2) (3) PS inHminHm −=σ

, and (4) PS xHmaaxHm −=σ

PSmeanmean −=σ (5) Where P is the pore pressure. The determination of mean stress is more difficult and significantly more controversial than the estimation of vertical stress. Mean stress requires that one characterize all three principal stresses, vertical, minimum horizontal, and maximum horizontal. Vertical stress can be determined relatively easily from the integration of density and pseudo density logs. Minimum horizontal stress can be determined from leak-off tests, but it is difficult to determine this value at any more than a few points in a well without encountering significant cost.

The maximum horizontal stress cannot be measured directly. It must be inferred from structural geology and wellbore response, e.g. extent of any breakout8. In most tectonically relaxed basins it is usually safe to assume that the maximum horizontal stress is very close to the minimum horizontal stress. Most compaction trends are generally expressed as a function of the easily determined vertical effective stress to avoid the complexity in determining all three principal stresses. In passive basins in may be reasonable to assume a generalized relationship in a shale between effective overburden and effective horizontal stress, in which case it is reasonable to use effective overburden as a proxy for effective mean stress. However, it is important to understand when this may not be reasonable, for example, where tectonic actions have significantly affected the present or past stress state.

The erosion of sediments at the surface in a location where shale pore pressures are being estimated using porosity sensitive log measurements has always proven problematic. The loss of these overlying sediments decreases the vertical stress on the underlying sediments that results in a decrease in the effective stress at all underlying points as well. The decrease in effective stress should result in an increase in porosity, assuming sediments behave in an elastic manner. However, the porosity rebound associated with the reduction in effective stress does not appear to follow the ‘virgin’

compaction trends observed during primary loading. Bowers9 and others have proposed unloading limbs to the normal compaction curve to enable pore pressure prediction associated with overburden removal. These unloading limbs are typically much ‘flatter’ than the virgin compaction curve, such that porosity recovery on unloading is only a fraction of the porosity lost during initial loading. In many cases this technique has proven effective, but the characterization of the unloading limbs requires considerable experience in any given area and there is effectively a different unloading limb for each point in the well.

There are a number of different physical phenomena that could be described as unloading. For the moment, we will only consider the case of unloading associated with the removal of overburden.

Recent experience in areas where significant surface erosion has occurred has lead to some new observations that impact the concepts one should apply in dealing with erosion based unloaded sediments. The minimum horizontal stress measured in leak-offs conducted in the unloaded sediments is significantly higher than one would expect based upon the weight of the present day overburden. The shallow overburden is denser than it would be if there had been no erosion, so this will contribute somewhat to a higher than expected fracture gradient through the Poisson effect. However, even taking into account this effect, measured fracture gradients in unloaded areas are still much higher than expected. Indeed, these measured results imply that the measured horizontal stress is consistent with the expected Poisson induced horizontal stress that would be expected if erosion had not occurred.

Figure 6a is an example from a well drilled in the Storrega slide in offshore Norway. The Storrega slide is a commonly studied failure of the seafloor that occurred approximately 8000 years ago. At the well location, it is estimated that 300 meters of sediment has been removed as a result of the slide. A well was drilled and a leak-off test run at a depth of 2146 mTVDss. This leak-off measured a minimum horizontal stress of 3980 psi (1.29 SG). The current vertical total stress is calculated to be 4097 psi. That includes the effect on density of compaction previous to the slope failure. The pore pressure is 3130 psi (1.03 SG), which results in a vertical effective stress, Vσ , of 967 psi and a minimum horizontal effective stress, , of 850 psi. The ratio of horizontal to vertical effective stress suggests an apparent Poisson’s ratio of 0.47, which is excessive at this relatively shallow depth by any regional correlations.

inHmσ

[It is recognized that the generation of horizontal stress can seldom be modeled correctly assuming a linear-elastic behavior coupled with a one-dimensional compaction model. Therefore, we use the term ‘apparent’ Poisson’s ratio, which is the Poisson’s ratio required to match horizontal stress data with an Eaton fracture gradient model10.]

Prior to slide failure the vertical stress is calculated to be 4445 psi, which gives an effective vertical stress of 1315 psi. Using correlations from regions not subject to uplift/erosion we would adopt an apparent Poisson’s ratio at the depths concerned of around 0.39, thus computing a horizontal effective stress of 867 psi (see Figure 6b). This is very similar to the post slide horizontal effect stress of 850 psi, implying

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little or no unloading in the horizontal plane associated with the vertical unloading. The observation that the horizontal stress has not unloaded has been made at other erosion-unloaded structures around the world.

However, field observations have repeatedly noted that sands frequently withstand higher consistent hydraulic pressure from the drilling mud than predicted by calibrated algorithms or measured by subsequent hydraulic fracture jobs. These observations are confirmed through the comparison of measurement while drilling (MWD) resistivity devices in real time and measurement after drilling (MAD) in oil base and synthetic mud. The real time measurement establishes a base line resistivity profile that can be compared against MAD logs to determine where the highly resistive mud has entered fractures in the formation. Repeated use of these logs over the past ten years have demonstrated that most lost circulation events occur in shale, even when sands are nearby. If we are able to understand why drilling mud produces higher fracture resistance in sand than fracturing with clear fluids, then lower cost well designs can be made.

Most pressure analysts use the vertical stress as a proxy for mean stress as a convenience. This would imply that there is a fixed relationship between vertical stress and mean stress. On loading we would expect an apparent Poisson’s ratio of around 0.39, as previously stated. The relationship between change in horizontal effective stress, , and change in vertical

effective stresses, inHmσ∆

Vσ∆ , is given by

VaxHminHm συ

υσσ ∆−

=∆=∆1

(6)

where υ is the apparent, static, drained Poisson’s ratio.

A flaw in applying the conventional model is the assumption that the generation of a fracture necessarily leads to major drilling losses. Figure 7 depicts the propagation of a fracture in a porous, permeable formation. As the fracture opens and whole mud moves along the fracture face, the filtrate of the mud invades into the adjacent formation dehydrating the mud as it travels down the fracture. Ultimately, the mud slurry becomes so dehydrated that it becomes immobile, blocking the fracture and preventing further fracture growth. Additionally, the dehydrated mud in the fracture creates a displacement between the two fracture faces that raises the stress field in the near well bore environment. In this manner the near well bore stress environment is incrementally raised relative to the original conditions. This process is well documented in the analogous problem of propped fracture stimulation and known as fracture “screen-out”11.

Thus, for a Poisson’s ratio during loading of 0.39 we get

, and (7) VaxHminHm σσσ ∆×=∆=∆ 64.0

VaxHminHmVmean σσσσσ ∆×=+∆+∆=∆ 76.03/)( (8)

During unloading there appears to be little or no change in the horizontal stress. Thus, and are virtually zero. Hence, for unloading

inHmσ∆ axHmσ∆

VVmean σσσ ∆×=++∆=∆ 33.03/)00( (9)

Therefore, the vertical stress cannot be used as a proxy for

mean stress on both loading and unloading limbs as its relationship with mean stress will be entirely different. In this example, using the vertical stress could over-predict the extent of unloading of the mean stress by a factor of 2.3. When this estimation error is incorporated into compaction trends, erosion-unloading estimates based upon vertical stress proxies, will exaggerate the effects on compaction plots resulting in apparent unloading limbs that are significantly different from the primary compaction trend. Cases of unloading caused by erosion should be analyzed using mean effective stress or be reduced by a factor of around 2 when using vertical stress proxies.

The increase in near well bore stress state as a result of a fracture screen-out will raise the pressure necessary to re-fracture the formation. Successive re-fracturing and screen-out will further increase the local stress state12. Ultimately, the adjacent shale will become easier to fracture than the sand. At this point further fracturing can lead to massive mud losses as the dehydration of the mud is insufficient in shale to screen-out and block the fracture.

It is important to recognize that the far field minimum horizontal stress in the sand is still lower than the far field minimum horizontal stress in the adjacent shale. However, the pressure in the borehole is unable to penetrate through the high near well stress zone, so substantial losses do not occur in the sand.

Observations Regarding Inducing Fractures Associated with Sands A pressure prediction for the purposes of well design would not be complete without a prediction of fracture gradient. Much has been published on techniques to predict fracture gradient, and most methods work well when properly calibrated. A proper fracture gradient prediction would include prediction of fracture gradients in both sand and shale. A common approach is to use a Poisson technique to determine a relationship between vertical and horizontal stresses and then apply regional Poisson trends to the different sediment types. Typically, we would expect sand to have a lower Poisson’s ratio than shale based upon both laboratory measurements and results from sand fracture jobs and leak-off measurements.

Conclusions The normalization of compaction trends in shallow sediments should only be applied at depths above the diagenetic window for the illitization of smectite (effectively restricts this practice to depths where temperature is less than 71 degrees Centigrade [160 deg Fahrenheit]).

The principles used in the equivalent depth method of pressure estimation would not be valid when applied across or within the clay diagenetic window.

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Erosion-unloading estimates based upon vertical stress proxies, will exaggerate the effects on compaction plots resulting in apparent unloading limbs that are significantly different from the primary compaction trend. Cases of unloading caused by erosion should be analyzed using mean effective stress or reduced by a factor of around 2 when using vertical stress proxies.

11. Smith, M.B., Miller, W.K. II, and Haga, J., “Tip screenout fracturing: A technique for soft unstable formations”, SPE Pet. Eng., May, 1987, pp.95-103.

12. Moschovidis, Z. A., Gardner, D. C., Sund, G. and Veatch, R. W., “Disposal of Oily Cuttings by Downhole Periodic Fracturing in Valhall, North Sea: A Case Study and Modelling Concepts”, SPE/IADC 25757, 1993.

13. Alberty, M. W.; and McLean, M. R.: “Fracture Gradients in Depleted Reservoirs – Drilling Wells in Late Reservoir Life”, paper SPE/IADC 67740 presented at the 2001 SPE/IADC Drilling Conference, Amsterdam, 27 February – 1 March.

Conventional fracture gradient models take no account of the ‘healing’ properties associated with sands resulting from the screen-out effect. As a result, conventional models will lead to overly pessimistic assessments of drillability, particularly in depleted reservoirs13.

Properly designed particulate laden fluids will screen-out

or block the fluid progress along fractures in sand, significantly increasing the fracture resistance of sands.

Acknowledgements

The authors would like to recognize the technical contributions of Nader Dutta, Wayne Wendt, and Harlan Rich for unpublished foundation work over the years that have allowed us to build upon and develop the current understanding. The authors would also like to thank BP for permission and support in producing this publication.

References

1. Terzaghi, K. and Peck, R.B. Soil Mechanics in Engineering Practice. John Wiley & Sons, New Jersey, June 1967, pp.676-684.

2. Mouchet, J. P; and Mitchell, A.: Abnormal Pressures While Drilling, Elf Aquitaine, Boussens, 1989.

3. Lahann, R. W.; McCarty, D. K.; and Hsieh, J. C. C.: “Influence of Clay Diagenesis on Shale Velocities and Fluid-Pressure”, paper OTC 13046 presented at the 2001 Offshore Technology Conference, Houston, 30 April-3 May, 2001.

4. Freed, R. L.: “Clay Diagenesis and Abnormally High Fluid Pressure”, paper presented at the 52nd Annual International Meeting of SEG, Dallas, October 17-21, 1982.

RHOB/DT CLAY CHARACTERISTICS

2

2.2

2.4

2.6

80 100 120 140 160 180

DT (usec/ft)

RH

OB

(gm

/cc)

Smectite

Illite

<175 deg F

>275 deg F

5. Foster, W. R.: “The Smectite-Illite Transformation: Its Role in Generating and Maintaining Geopressure”, Paper presented at the 94th Annual Meeting of the Geological Society of America, Cincinnati, Ohio, November 2-5, 1981.

Figure 1: Smectite and illite trends on a density sonic crossplot.

6. McCubbin, D. G.; and Patton, J. W.: “Burial Diagenesis of Illite/Smectite: The Kinetic Model”; 1981 Annual Meeting of the American Association of Petroleum Geologists, San Francisco, 1981.

7. Perry, E. and Hower, J.; “Burial Diagenesis in Gulf Coast

Pelitic Sediments”; Clays and Clay Minerals, v. 18, 1970. 8. Barton, C.A., D. Moos, P. Peska, and M.D. Zoback.

Utilizing wellbore image data to determine the complete stress tensor: Application to permeability anisotropy and wellbore stability, The Log Analyst, 1997, pp. 21-33.

9. Bowers, G. L.: “Pore Pressure Estimation from Velocity

Data: Accounting for Overpressure Mechanisms Besides Undercompaction”, SPE Drilling and Completions, June 1995.

10. Eaton, B.A. “Fracture gradient prediction and its

application in oil field operations”, J. Petroleum Tech., V21, 1969, pp1353-1360.

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0

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Smectite .Dt Illite .Dt Presgraf .Dt Illite-smectite .Dt

Figure 4: Comparison of computed smectite/illite trend to other

trends.

Figure 2: Smectite and Illite trends on a effective stress sonic

crossplot.

0 1.8 120 2.8GR Density

'acoustic-derived'1600

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Figure 5: Comparison of pseudo density and actual density using the kinetic model.

Figure 3: Comparison of smectite, illite and “Presgraf”

compaction trends.

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Equivalent Mud Weight, g/cc1 1.6

meters

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Figure 6a: Leak-off compared to expected fracture gradient Figure 6b: Lot-off compared to pre-erosion expected fracture gradient

Figure 7. Fracture screen out in permeable sands.