Pore Pressure Estimation From Velocity Data: Accounting for Overpressure Mechanisms Besides UndercompactionGlenn L. Bowers,* Exxon Production Research Co.Summary15-18.

A new method for estimating pore pressure from formation sonic velocity data is presented. Unlike previous techniques, this method accounts for excess pressure generated by both undercompaction, and fluid expansion mechanisms such as aquathermal pressuring, hydrocarbon maturation, clay diagenesis, and charging from other zones. The method is an effective stress approach; the effective stress is computed from the velocity, and the result is subtracted from the overburden stress to obtain pore pressure. To include multiple sources of overpressure, a pair of velocity-vs.-effective-stress relations are introduced. One relation accounts for normal pressure and overpressure caused by undercompaction. The second is applied inside velocity reversal zones caused by fluid expansion mechanisms. Example applications of the method are presented from the U.S. gulf coast, the Gulf of Mexico, and the Central North Sea. Some other pore pressure estimation approaches are also examined to demonstrate how these techniques have unknowingly accounted for overpressure mechanisms other than undercompaction. It is also explained how velocity-vs.-effective-stress data can be used to identify the general cause of overpressure in an area. For instance, the empirical correlation of Hottman and Johnson indicates that overpressure along the U.S. gulf coast cannot be due only to undercompaction.Introduction

gy from soil mechanics, the velocity-effective stress relation for nondecreasing effective stress states will be referred to as the virgin curve. Fig. la plots shale virgin curve data derived from well log and RFT measurements from the Gulf of Mexico slope, and shows an estimate of the complete virgin curve. Effective Stress Reductions. Much (but not all) of the porosity loss/ velocity gain that occurs during compaction is permanent. As a result, the sonic velocity will not go down the virgin curve when the effective stress is reduced (unloading). The velocity will track a different, faster velocityvs.-effective-stress relation that will be called the unloading curve. If the effective stress is subsequently increased, the velocity will follow the unloading curve back to the virgin curve. Fig. lb illustrates unloading behavior with laboratory velocity-effective stress data for Cotton Valley shale (Tosaya4). The velocities measured at effective stresses below the maximum in-situ stress state must be on an unloading curve. For-comparison, the virgin curve for the Gulf of Mexico sediments is replotted in Fig. 1 b.Overpressure Causes/Effects

Normal Pressure. During burial under normal pressure conditions, the effective stress continually increases with depth. Consequently, normal trend velocity-vs.-effective-stress data follow a virgin curve. Undercompaction. Overpressure most commonly occurs when pore fluid trapped by low permeability is squeezed by the weight of newly deposited sediments. This overpressuring process is referred to as undercompaction or compaction disequilibrium. Undercompaction cannot cause the effective stress to decrease. Therefore, the virgin curve also applies for formations overpres-sured by undercompaction. The most undercompaction can do is "freeze" the effective stress in time, which would cause the velocity to become fixed on the virgin curve. On a velocity/depth plot, this would appear as a velocity plateau. Fig. 2 illustrates undercompaction overpressure in the Gulf of Mexico. Pore pressure, sonic velocity, and stress information are shown in Figs. 2a, 2b, and 2c, respectively. Fig. 2d plots velocity-vs.-effective- stress data determined at RFT locations. It can be seen that all of data in Fig. 2d appear to lie on a virgin curve, and that the points below 7200 ft are approaching a fixed point. Fluid Expansion. Overpressure can also be generated by fluid expansion mechanisms such as heating,5-6 hydrocarbon maturation,7 charging from other zones,8 and expulsion/expansion of intergranu-lar water during clay diagenesis.910 Here, excess pressure results from the rock matrix constraining the pore fluid as the fluid tries to increase in volume. Unlike undercompaction, fluid expansion can cause the pore pressure to increase at a faster rate than the overburden stress. This forces the effective stress to decrease as burial continues, which produces a velocity reversal (see Fig. 3b). Velocities inside the reversal will track an unloading curve(s), while velocities outside the reversal will remain on a virgin curve. Fig. 3 illustrates this with data from an Indonesian well. Pore pressure, velocity, and stress data are displayed in Fig. 3a, 3b, and 3c, respectively, while Fig. 3d compares velocity-vs-effective-stress data from inside (open circles) and outside (solid circles) the velocity reversal. The start of the reversal coincides with the top of overpressure at approximately 6350 ft. It can be seen in Fig. 3d that the velocities from inside the reversal track a much faster trend. This suggests that fluid expansion mecha-

Numerous methods have been developed for estimating pore fluid pressure from geophysical data, and the list continues to grow. Empirical approaches equate departures from the normal trend line of some porositydependent measurement to an equivalent pore pressure gradient. Recent methods have followed the more fundamental effective stress approach pioneered by Foster and Whalen,1 Ham,2 and Eaton.3 All current pore pressure estimation methods fail to formally take into account the cause of overpressure. It will be demonstrated that this can lead to significant errors. For a given velocity at a given depth, the pore pressure can vary by 4 lbm/gal or more, depending upon how the excess pressure was generated. This paper presents a method for estimating pore pressure from sonic velocity data that systematically accounts for the cause of pressure. When applied to wireline sonic logs, it is preferable to only use shale data to minimize the effects of lithology changes. However, the method is also applicable for pre-drill predictions from seismic interval velocities. The paper begins with a review of fundamental aspects of shale compaction behavior that form the foundation of this method. This is followed by a discussion of how different causes of overpressure affect the sonic velocity. Some current pore pressure estimation methods are then examined in light of these concepts. The new method is then described, and example applications are presented and discussed.Compaction Behavior

Non-Decreasing Effective Stress States. Under increasing effective pressure, sediments compact, and their sonic velocity goes up. At the limit, their porosity approaches zero, and their sonic velocity approaches the value for the sediment grains. Borrowing terminolo*Now with Applied Mechanics Technologies. Copyright 1995 Society of Petroleum Engineers Original SPE manuscript received for review March 10.1994. Revised manuscript received Nov. 30,1994. Paper accepted tor publication Feb. 27,1995. Paper (SPE 27488) first presented at the 1994 IAOC/SPE Drilling Conference held in Dallas. Feb.

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Virgin Curve

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SPE Drilling & Completion, June 1995

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This assumes that the overpressure data are on a virgin curve. If fluid ?2 expansion has driven the data onto an unloading curve, as in Fig. 3, the Vmaxtor Wed *1 effective stress will be overestimated, and the pore pressure will be underestimated, as Magara observed. 2 3 4 5 6 7 8 Effective Stress (ksi) Fig. 5Fluid expansion overpressure, central North Sea. Plumley13 discussed unloading caused by fluid expansion overpressure, and presented a U.S. gulf coast example of its occurrence. He compared porosities from Pore Pressure 8-13 normally pressured interval having an overpressured and ppg O 14-18 ppg .Virgin stresses. The porosity in the overpressured zone was the same effectiveCurve half the value in normal pressure (17.6% vs. 38%). Plumley concluded this was because the high pressure zone had undergone unloading. Berg and Habeck14 came up with a similar conclusion using density log data from a south Texas well. Velocity Reversal Without Unloading. Not all velocity reversals are caused by fluid expansion mechanisms. The velocity will also drop across the transition from a normally pressured sand/shale sequence to a massive undercompacted shale. If fluid expansion is not the cause, the velocity-vs.effective-stress data from the reversal will follow a virgin curve. Determining the Cause of Overpressure In Velocity Reversals. A reliable way has not been found to determine from velocity data alone whether a reversal was caused by undercompaction or fluid expansion. However, some general guidelines can be offered on the geologic conditions that are conducive to each of these causes of pressure (Miller and Luk6). The amount of overpressure generated by undercompaction depends upon the relative compressibility of the rock matrix and the pore fluid. They act like two springs in parallel. If the rock matrix is much more compressible, increases in overburden stress will be carried primarily by the pore fluid. If the rock matrix is much less compressible, then it will bear most of the overburden. Therefore, undercompaction will typically generate the greatest overpressure at shallower depths, where formations are soft.

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a) b) Fig. 4Fluid expansion overpressure, Gulf of Mexico. nisms contributed to the overpressure inside the reversal. Note the similarity between the unloading curve in Fig. 3d and the trend followed by the Cotton Valley shale data in Fig. lb. Fig. 3d also demonstrates the importance of accounting for the cause of overpressure when estimating pore pressures. The virgin curve would overestimate the effective stress at 6950 ft by 1700 psi, which means the pore pressure would be underestimated by the same amount. This would correspond to a 4.7 lbm/gal error in the equivalent mudweight prediction. Fig. 4 present further evidence of unloading. Fig. 4a shows velocityeffective stress data derived from RFT and well log measurements along the Gulf of Mexico slope. The data are divided into two groups according to the magnitude of overpressure. Solid circles are in the 9 to 15 lbm/gal equivalent mudweight range, while the open circles are in "hard" overpressure. Contrary to what might be expected, the higher pressure data tend to have faster velocities. As Fig. 4b indicates, a possible explanation is that most of these data are from formations that have undergone some unloading. Similar trends are evident in the Central North Sea velocityvs.-effective-stress data plotted in Fig. S. Others have also reported evidence of unloading caused by high pressure. Magara1' found that the Equivalent Depth method underpredicted the pore pressure data of Hottman and Johnson.12 The equivalent depth method2 equates the effective stress in an over-pressured zone to that in a normally pressure interval with the same velocity (see Fig. 6).

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Fig. 7Case where equivalent depth method failsoffshore Indonesia.

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Fig. 8U.S. gulf coast application of the Hottman & Johnson and equivalent depth methods. On the other hand, the activity of many fluid expansion mechanisms increases with temperature, and therefore depth. To be a strong source of overpressure, fluid expansion also requires a fairly rigid, well-compacted rock matrix that can adequately constrain the pore fluid. Consequently, fluid expansion is more likely to be an important source of overpressure at deeper depths, in stiffer rocks. The only sure way to determine the cause of overpressure in a velocity reversal is with measured pore pressures. One way is to plot velocity-vs.effective-stress data from inside and outside the reversal, as in Fig. 3d. The reversal data will track a much faster trend if fluid expansion mechanisms were active. Another approach is to compare measured pore pressures with those computed with the equivalent depth method. The equivalent depth method will underestimate pore pressure caused by fluid expansion. Figs. 6 and 7 present cases where the equivalent depth method works and fails. Cementation. Unloading may not be the only reason that velocity reversal data deviate from the virgin curve; cementation could also be a factor. From the standpoint of pore pressure estimation, this is inconsequential. What counts is that the separate trend tracked by the reversal data be recognized and accounted for. However, cementation does complicate diagnosing the cause of overpressure within a reversal. Even with petrographic analyses, it can be difficult to sort out the relative effects of unloading and cementation. What can be said is that cementation is conducive to fluid expansion overpressure, because it increases the rock matrix's constraint of the pore fluid. Consequently, while local geologic conditions must be considered, there is reason to believe that undercompaction is generally not the sole source of overpressure when velocity reversal data diverge significantly from the virgin curve.Pore Pressure (ppg) 10 14 15 16 1B 12

Current Pore Pressure Estimation Methods

Most pore pressure estimation methods claim to only be applicable for overpressure caused by undercompaction. However, it turns out that many current pore pressure estimation methods are (unknowingly) predicting fluid expansion overpressure. To illustrate this, two popular techniques are examined Hottman and Johnson. The Hottman and Johnson (H&J) method empirically correlates departures from the velocity normal trend line to an equivalent pore pressure gradient.12 Empirical correlations have no inherent

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bias towards one particular overpressure mechanism. They simply reflect whatever the dominant cause of overpressure is in the area in which they were developed. For their U.S. gulf coast correlation, H&J assumed this was undercompaction. If this is true, then the Equivalent Depth and H&J methods should give similar results. As a test, both approaches were o applied to shale sonic log data from H&J's original paper12 (Well "R"). Fig. 8a shows the velocities, while Fig. 8b compares the estimated pore pressures with bottomhole pressure measurements. It can be seen that the equivalent depth method underpredicts the pressure, while the H&J correlation performs well. This has two possible c)

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implications. First, because the Equivalent Depth method failed, this suggests that fluid expansion is an important source of overpressure. Second, because the H&J method worked, H&J's Gulf Coast correlation appears to have fluid expansion "built" into it. As further evidence, Fig. 8c plots velocity-vs.-effective-stress data from the well. Solid circles are from the normal trend line. Eaton's U.S. gulf coast overburden stress curve15 and a normal pressure gradient of 0.465 psi/ft were used to estimate effective stresses at these points. Open circles are from the three pressure tests insideEffective Stress (ksi)

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the velocity reversal. The faster trend tracked by the reversal data is characteristic of unloading. The solid line in Fig. 8c is the velocity-vs.-effective-stress path defined by H&J's pore pressure estimates inside the reversal. This curve clearly deviates from the normal pressure data, which again suggests the H&J Gulf Coast correlation is biased towards fluid expansion overpressure. This also means that this correlation will overestimate the pore pressure at wells where undercompaction truly is the dominant cause of overpressure, as in Fig. 2. Eaton. Original Eaton Method. Eaton's method3 is an effective stress approach, with the effective stress, o, computed from the equation:

low, Eq. 1 can be adjusted to yield lower effective stresses. One way is to increase vnorm by shifting and rotating the normal trend line (Weakley16). Another, simpler alternative, is to raise the exponent in Eq. 1. Either way, the net effect is the same; it allows the original Eaton virgin curve relation to be transformed into an unloading curve. For example, by raising the exponent from 3 to 5, the revised Eaton solution (dotted line in Fig. 9b) is able to closely match the Well R pressure data. As Fig. 9c shows, this is because the higher exponent has allowed Eaton's equation to simulate an unloading curve.New Method

Here v is the measured velocity, and onorm and vnorm are the values the effective stress and velocity should have under normal pressure conditions. Eq. 1 implies that normally pressured and overpressured formations both follow a virgin curve relation of the form: v = Co/3.............................................................................................(2) Consequently, Eaton's method should underestimate fluid expansion overpressure. The velocity normal trend line is usually assumed to be a straight line on a plot of log(vnorm) vs. depth. However, according to Eq. 1, v and v norm should both satisfy Eq. 2. Therefore, to be consistent, vnorm should actually be calculated from Eq. 2 using onorm values determined from the overburden stress and normal pore pressure profiles. If this were done, the normal trend line would not be a semilog straight line. Fig. 9a compares H&J's semi-log normal trend for Well R (dot-dashed curve) with one analytically computed from Eq. 2 (solid line). The parameter C = 564 was obtained by fitting Eq. 2 through the normal trend velocity-effective stress data in Fig. 9c. It can be seen that the semi-log normal trend line is faster than the analytical solution below the top of overpressure. By overestimating vnorm, the semi-log normal trend will make Eq. 1 predict lower effective stresses, and therefore higher pore pressures than Eq. 2. This will generally be true. However, unless unreasonably large values are assumed for vnorm, Eq. 1 will still underestimate fluid expansion overpressure. This is the case with the Eaton pore pressure estimates for Well R, which are plotted as a solid line in Fig. 9b. The dot-dashed line is the equivalent depth solution. It can be seen that both methods fall well short of the measured pressures in the velocity reversal. The velocity-effective stress data in Fig. 9c explain why. Even with the semi-log normal trend line, the Eaton solution inside the reversal remains close to the virgin curve defined by Eq. 2. Modified Eaton Method. If the Eaton pore pressure estimates are too

Overview. The new method is an effective stress approach that employs virgin and unloading curve relations to account for both undercompaction and fluid expansion overpressure. Effective stresses outside of velocity reversal zones are computed from the virgin curve. Inside a velocity reversal, offset well data are used to decide which equation is appropriate. For rank wildcats, the pore pressure can be computed both ways to establish lower and upper bounds on the pressure. The unloading curve will always yield higher pore pressure estimates. Virgin Curve. Over stress ranges of practical interest, it has been found that the virgin curve for shale, as shown in Fig. la, can be adequately represented by the following equation: v = 5000 + AoB...................................................................................(3) where v is velocity (ft/s), o is effective stress (psi), and A and B are parameters calibrated with offset velocity-vs-effective-stress data. Unloading Curve. The unloading curve is defined by the empirical relation: v = 5000 +AIomax(o/omi)