Seismic pressure-prediction method solves problem common in deepwater Gulf of Mexico

R. Wilhelm
Consultant
Houston

L.B. Franceware, C.E. Guzman
Shell Offshore Inc.
New Orleans

A novel method of predicting pore pressure gradients from seismic velocities has overcome a problem common in the deepwater Gulf of Mexico.

The method, based on a model of geopressures that uses available formation temperature measurements, does not require the normal shale compaction trend. This is crucial in deep water, where geopressures often start shallow below mud line and make establishing the normal trend difficult.

Pore pressure prediction methods that use the shelf's depositional model are not accurate enough for the deep water. The shelf model consists of a significantly thick, hydrostatically pressured section, which is used to establish the normal pressure interval travel time (ITT)-shale compaction trend as a reference.

This article describes the method, discusses preparation of the velocity data, and shows results from one shelf and three deepwater wells in which the method is successful.

Seismic velocities

Seismic velocities are used to predict pore pressure in planning and designing wells. Estimation of the onset of geopressure from velocities is not new. Many workers currently use seismic velocities for qualitative pore pressure prediction.

The general approach is based on the observation that anomalously slow velocities are usually associated with higher pore pressures.1 2 Other workers have made extensive use of well log velocity data for geopressure analysis^{3 4 5 6 7} and prediction of fracture pressure gradients.^{5 6 8 9 10}

In deep water, the deltaic model of a significantly thick hydrostatically pressured section followed by a rapid change into geopressures often does not hold. The start of geopressure often occurs shallow below mud line and is followed by a pressure profile that is more variable and less predictable than profiles typical of shallow water.

In order to increase predictability, one needs to exploit the information inherent in seismic velocity data before drilling. We use seismic velocity data as input to a constitutive equation to predict pore pressures.

A prerequisite for standard fluid pore pressure and fracture gradient prediction methods is the normal (hydrostatic) interval travel time-shale compaction trend that is used as a reference. The early onset of pressures in deep water results in a scarcity of ITT measurements that correspond to the normal pressure. Therefore, determination of the normal shale compaction trend has become more tenuous.

Pore pressure computation

We have implemented and studied two computational methods to transform geophysical velocity data to pore pressure, and pore pressure back to velocities: Eaton's method and Dutta's method.

Both methods make use of Terzaghi's effective stress approach, in which the effective stress gradient (VES in psi/ft) is computed from the seismic interval velocity (or its inverse, the ITT). The result is subtracted from the overburden stress gradient (OBG in psi/ft) to obtain the fluid pore pressure gradient (FPG in psi/ft):

FPG=OBG-VES.

OBG computation

To arrive at the best OBG, we have analyzed published and locally established overburden values and examined Barker's deepwater leak off test (LOT).⁹

We found that Eaton's general Gulf of Mexico overburden trend gives good results when normalized for water depth.5 We have compared our procedure of overburden calculation with a detailed example by Eaton.¹¹

Also, we routinely plot Barker's deepwater LOT trend normalized for water depth and kelly bushing (KB), together with the overburden gradient.

VES: Eaton's method

In 1975, building on Lane and Macpherson's published petrophysical data from deltaic Gulf Coast wells,⁷ Eaton developed an empirical relationship between effective stress gradient and interval travel time that states that:

VES=(OBG-FPG_normal)f

where f is a proper fraction of the form

f=(ITT_normal/ITT_measured)^exponent and ITT is the interval travel time. The exponent serves as a calibration variable.

The effective stress is calculated by using the measured ITTs derived from the seismic velocity data. Furthermore, the normal compaction trend (ITTnormal) and the exponent are required (3.0 is a suggested starting value for wildcats). If the correct normal trend can be determined, the exponent becomes the calibration variable. The method has been reported to work well for stratigraphically controlled pressures beneath significant thickness of normally pressured sediments. Mouchet et al. observed, "Eaton's method is undoubtedly the most widely used at the present time."¹² As mentioned previously, conventional methods to predict effective stress, pore pressure, and fracture gradient require that an accurate normal (hydrostatic) shale compaction trend, ITTnormal, be supplied. This trend is the relationship between ITT and depth for the hydrostatic pressure gradient (~9 ppg). However, defining this normal trend is not straightforward.

We have encountered the following complications in determining the normal trend:

(1) While there is general agreement that the normal compaction trend is linear (except Bowers13), there is disagreement over the proper type of x-axis and y-axis to use to arrive at the linear trend, as shown in Table 1 [11,321 bytes].

(2) In deltaic environments, where often a thick interval of normal-pressured shales precedes the sudden onset of geopressures, development of the normal trend table is not difficult. In the deeper water of the Gulf of Mexico, where the onset of geopressures often occurs shallow below the mud line, the determination of the normal trend is based on fewer measurements. Therefore, establishing the normal trend in deep water becomes more speculative. For example, an error of 5.0 ms in ITT corresponds to the difference between hydrostatic pressure and 10.0 ppg at approximately 8,000 ft in the MC No. 1 well (Fig. 3 [55,908 bytes]).

(3) Additionally, no general law has been published that predicts either the shape of the normal trend or its ITT values. Eaton summarizes it best: "The methods used to establish normal trends varies as much as the number of people who do it."⁶

(4) While excellent results of using normal trend-based methods have been reported,¹¹ the scarcity of normal trend measurements in the deepwater Gulf of Mexico has increased the need for a pore-pressure prediction method that incorporates the mechanisms of geopressure in the model.

Bowers¹³ and Audet¹⁴ have published geopressure models that address the causes of geopressure. Neither of these models considers the influence of temperature.

VES: Dutta's method

Dutta has published a unique model of geopressure that takes into account its causes.^{15 16 17 18} The model is applicable to continuously depositing basins, works in deltaic and turbidite environments, and does not require the normal compaction trend.

According to Dutta, "Seismic interpretation in formations with abnormally high pore pressures (geopressure), such as in the Clastic basin of the Texas-Louisiana Gulf Coast area, requires an understanding of how density and velocity of geopressured rocks vary with such key geologic parameters as sedimentation rates, geothermal gradient, sediment deposition sequence and thickness, etc. With this objective, we developed a model of the compaction of fine-grained, low permeability sediments (shales) and its relation to the evolution of geopressures. This model is an extension of unpublished work of the late R. L. Chuoke of Shell Development Co., and incorporates effects of temperature on shale compaction."¹⁵

Dutta's¹⁸ constitutive relation to compute effective stress (s in psi/ft) is modeled with the Arrhenius equation:

s=s_oexp[-eA(T)/B(t)], where s_o is a constant, e is the void ratio of shales (and can be derived from the seismic velocity data),

A(T) is a polynomial in temperature, and

B(t) is related to a diagenetic integral depending on time (and temperature) and describes smectite to illite conversion.

Again quoting Dutta: "In the present model, the effect of the shale mineralogy change with burial diagenesis was incorporated by including a cation exchange capacity (CEC) term in the constitutive relation for shale void ratio, temperature, and effective stress. The term is an explicit function of time (t)-temperature (T) history of sediment."¹⁶

Dutta's method allows the calculation of ITT corresponding to any pore pressure gradient. In particular, the ITT corresponding to the hydrostatic trend (ITT_normal) can be calculated. To solve for ITT_normal one simply rearranges the equations.

Fig. 1 [48,239 bytes] displays families of normal shale compaction trends computed with Dutta's method. The trend curves are a function of formation temperature and mineralogy (CEC). The graph shows that at a low temperature gradient (10.0° F./1,000 ft) but high CEC (22.0 milliequivalents [meq]/100 g), the normal compaction trend does indeed approach a straight line on a plot of depth (linear scale) vs. ITT (log scale). However, a linear relationship is not evident for the higher temperature gradient (20.0° F./1,000 ft) and the CEC value of 12.0 meq/100 g that corresponds to faster shales.

Parameters

The use of Dutta's method is simple. The input consists of the ITTs derived from seismic velocity data, the formation temperature gradient, and the CEC, which is the fitting parameter.

The determination of a workable temperature function is often trivial: Formation temperature information is recorded routinely when wells are logged. The CEC value is obtained by going to a suitable control well site and fitting the ITTs computed from pore pressure measurements (repeat formation testers [RFTs], mud weights) to the seismically derived ITTs.

Table 2 [9,772 bytes] shows the range of some temperature and CEC values we have used in the Gulf of Mexico.

Data preparation, calibration

To predict an accurate pore pressure profile at a proposed well location through use of seismic velocity data, it is useful to go to a near well location to calibrate the velocity data, RFTs, mud weights, LOTs, temperature gradient, and mineralogy.

For a successful calibration it is necessary to begin with data preparation. Check shot, vertical seismic profile (VSP), and sonic data can be over-sampled and too noisy for calibration to seismic velocity data and for pore pressure prediction. We "smooth" the data using the best linear unbiased estimator from point estimation statistics: The irregularly spaced data points within adjacent windows are replaced by their centroid.

Noise in the velocity data is treated statistically: Given n velocity sets normally distributed about their mean with variance s², the chosen output point will be from a population normally distributed about its mean with variance s²/n (Central Limit Theorem of probability theory).

To arrive at a single representative seismic velocity function to be transformed to effective stress, several seismic velocity sets are bundled (averaged). Velocity sets are selected in the neighborhood of the well location. However, the seismic location may have to be biased in the down-dip direction if the seismic velocity gathers are not adequately migrated.

We have found that a smoothing window or sample interval of about 1,000 ft and a bundle of approximately nine 2D or 3D seismic velocity sets used in the calibration can improve results. However, for pressure prediction in the shallow section, increased areal and temporal sampling of the seismic velocity data is required.

Check shot to seismic velocity calibration is used to determine the magnitude of the necessary anisotropy compensation.19 The seismic velocity data is adjusted to remove the systematic bias that arises from the differences between the check shot velocity and seismic velocity data. The determined anisotropy factor (Table 2) is then applied to the seismically derived time-to-depth function at the proposed well location. Failure to apply anisotropy correction can result in a biased depth prediction of pressures.

Furthermore, to assure repeatability, all velocity computations that involve calibration and prediction are performed in the time-depth domain because it is linear.

Interpretation of field samples

Fig. 2 [77,606 bytes] shows check shot and seismic velocity data with mud weights for a well in less than 100 ft of water on the Louisiana shelf. The check shot and seismic velocity data are in close agreement. The sudden increase in interval travel time at about 10,000 feet is associated with the onset of geopressure.

From the depth vs. interval travel time plot (Fig. 2a) one can gauge the outcome of Dutta's method and Eaton's method (using the standard exponent of 3.0). Eaton's method underestimates the pore pressure near total depth. Fig. 2b presents the same data on a depth vs. pore pressure gradient plot. To increase prediction accuracy with Eaton, the exponent must be raised to 5.0, in agreement with Bowers.¹³

The seismic and check shot velocity data suggest difficult drilling from 12,000 ft on because the hard pressure (16.5 ppg) line has been crossed (Fig. 2a). The 16.5 ppg line overlaps Barker's 90% of overburden curve.⁹

Deepwater well

Fig. 3 shows velocity and pressure data from a deepwater well that encountered significant drilling challenges. In the MC No. 1, the ITT line crosses the 12.5 ppg curve relative to mud line (ML; onset of geopressure) approximately 3,000 ft below mud line (BML) and crosses Barker's 90% of overburden curve (hard pressures) about 4,800 ft BML.

According to Barker, "lost returns occur when the mud weight is raised above 90% of overburden at any depth. Often the lost returns is followed by formation ballooning where mud flows back into the well ellipse Usually drilling is able to resume after cutting the mud weight to a value below 90% of overburden. A possible cause for the lost returns/ballooning is the raising of mud weight to over 90% of overburden, and elastic deformation occurs in the formation." The high mud weights required to drill the MC No. 1 were justified as seen from the RFT measurements that match the high mud weights actually used. The ITTs show a marked break on the depth vs. pore pressure gradient plot (Fig. 3b) at about 5,000 ft BML where the well encountered major drilling difficulties. The magnitude of the break is more subtle on the depth vs. ITT plot (Fig. 3a).

Four LOTs taken at the MC No. 1 well are displayed. They fall right on Barker's deepwater LOT trend, confirming what drilling engineers have been saying when comparing shelf drilling to deepwater drilling: LOTs appear to fall closer to overburden gradient in deeper water.

One cause of the drilling difficulties at the MC No. 1 well may be glimpsed from the extremely high temperature gradient encountered in this deepwater well (Table 1). The high temperature environment results in increased smectite to illite conversion with accompanying water expulsion (smectite CEC range 22-24 meq/100 g, illite CEC range 7-14 meq/100 g16). The extra water in the low permeable environment is generated faster than it can drain, thus increasing the fluid pore pressure.

This is best summarized by Dutta: "The temperature plays an important role on fluid pressure profiles in geopressured formations in that the increasing temperature further lowers the effective stress on geopressured rocks drastically."¹⁶

Drilling problems

Fig. 4 [33,056 bytes] shows check shot data, 2D seismic velocity data, RFTs, and mud weights for the GB No. 1 well. According to drilling reports, the exploratory well experienced significant borehole and mechanical problems, including stuck casing, stuck drill pipe, and high torque and drag.

Subsequent analysis of these drilling problems indicated the following: The (shaded) interval marked as 1 in Fig. 4 at about 8,000 ft consists of a potentially pressured sand. Interval 2, from 11,000 to 12,000 ft TVD, consists of an overpressured and undercompacted massive shale section. Interval 3, from 12,000 ft to 15,000 ft, is characterized by underpressured laminated sand-shale intervals. The last interval, from 13,000 ft to TD, contains hydrocarbon-bearing sands.

The check shot and seismic velocity data are in close agreement. Both indicate higher pore pressure (lower effective stress) at 8,000 ft, and again below 12,000 ft, and marked underpressure (higher effective stress) at about 14,000 ft. The higher pore pressure suggested below 15,000 ft appears to be related to the lower interval velocity associated with the hydrocarbons in that interval.

Below 15,000 ft, RFTs and mud weights are up to 1 ppg apart. The RFTs are closely aligned with the pore pressures calculated from the seismic velocity data.

The drilling difficulties reported are not due to hard geopressures as encountered in the high temperature MC No. 1 well, since the RFTs and mud weights used to drill this well never reached Barker's 90% of overburden line (related to fracture pressure). Instead, the drilling difficulties appear to be caused by the alternating pressure profile.

Fig. 5 [35,869 bytes] shows depth vs. ITT at the GB No. 2 well, which is located less than 20 miles from the GB No. 1. Mud weights converted to ITT with Dutta's method are plotted together with 2D seismic velocity data. The temperature and CEC parameters obtained by calibration at the GB No. 1 were used to obtain a good seismic velocity to mud weight fit.

This well is geopressured from at least 3,000 ft BML. The normal compaction trend computed with Dutta's method with the available temperature and CEC from the GB No. 1 well is also shown. The estimation of the normal compaction trend using the standard method of extrapolating a straight line on a depth vs. log of ITT plot would have resulted in a pressure estimate different from the actual pressures encountered by the drill bit.

Predicting pressures

Use of Dutta's method of undercompacted shales to improve predrill prediction of fluid pore pressures thus can help solve the problem of insufficient travel time measurements corresponding to hydrostatic pressure. This problem is common in the deepwater Gulf of Mexico, where geopressures start shallow below mud line.

Dutta's model of undercompacted shales differs from other published pressure models in that the calculation of pore pressure is independent of the normal trend. The model takes into account the predominant causes of geopressure: namely, mineralogy and temperature. Since formation temperature is readily available, using Dutta's constitutive equation reduces pore pressure prediction to calibration of the mineralogy dependency.

Using Dutta's equation, we computed normal compaction trends as a function of temperature gradient and CEC and showed that only at low temperature gradient and high CEC does the expected normal trend approach a straight line on a plot of depth (linear scale) vs. interval travel time (log scale).

Our field examples show that seismic velocity data can help anticipate pressure regimes in deepwater turbidite environments before drilling.

Acknowledgments

We thank J.W. Barker, P.G. Behrman, R.M. Gassett, K.W. Katahara, and K.M. Turner of Vastar Resources Inc. We are much indebted to our former and present Shell colleagues A.J. Bassett, M.S. Costello, V.K. Cung, N.C. Dutta, D.A. Johnson, M.S. Leonard, D.J. Lewis, B.R. Meroney, J.B. Rhodes, H.J. Ritch, P.A. Santogrossi, W.E. Sims, C.L. West, and H.S. Wright. We thank Shell Oil Co. for permission to publish this report.

References

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5. Eaton, B.A., "A theory on the effect of over-burden stress on geopressure prediction from well logs," SPE preprint 3719, 1972.
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16. Dutta, N.C., "Shale compaction, burial diagenesis, and geopressures: A dynamic model, solution and some results," Thermal Modeling in Sedimentary Basins, J. Burrus, Ed., Editions Technip, Paris, 1986, 1st IFP Exploration Research Conference, Carcans, France, June 3-7, 1985.
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The Authors

R. Wilhelm retired from Shell Oil Co. with 20 years of experience and is now a consulting geophysicist. He holds an MS in physics from the University of Texas and an MS in petroleum engineering from Tulane University.

L. B. Franceware is a geophysicist in the Deepwater E&P Division of Shell Offshore. He has been with Shell Oil Co. since 1972 and holds a BS and MS in physics from the University of Texas.

Carlos E. Guzman is a geophysicist on the New Ventures Team, Deepwater E&P Division, of Shell Offshore. He has worked with Shell Oil Co. since 1977. He holds a BS in physics from the University of New Orleans and an MS in physics from Purdue University.

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