Whole earth 4D: reservoir monitoring geomechanics. P.J. Hatchell*, A. van den Beukel, M.M. Molenaar, K.P. Maron, and C.J. Kenter, Shell International Exploration and Production – Rijswijk; and J.G.F. Stammeijer, J.J. van der Velde, and C.M. Sayers, Shell Expro – Aberdeen. Summary Time-lapse (4D) seismic monitoring of pressure-induced changes in depleting gas fields reveals that detectable differences in seismic arrival times are observed above the reservoir interval. Geomechanical models of depleting reservoirs predict that as a result of reservoir compaction due to pressure depletion, changes in the long-wavelength stress and strain fields occur in the rocks bounding the reservoir. Models incorporating the geomechanical stress and strain field changes predict changes in the two-way arrival times that are compared with actual time-shift observations at a depleting gas field in the North Sea. The geomechanical-based predictions are in good agreement with the observations. Detecting geomechanical changes in the over- and underburden rocks opens up new ways of using 4D data, especially in places where the signal from the reservoir rocks is small. Introduction The use of time-lapse seismic (4D) surveys for monitoring producing oil and gas fields has become widespread in our industry. Many types of physical changes can be detected with time-lapse seismic surveys and published examples include observing effects due to fluid movements (e.g. Koster et al. 2000) as well as pressure depletion (e.g. Guilbot and Smith, 2002; Watts et al., 1996). In a depleting reservoir there are several mechanisms that produce potentially observable 4D effects. There are changes that occur within the reservoir unit such as: • Compaction effects due to the change in the effective stress field. • Changes in compressional and shear velocities due to compaction. • Changes in the pore-fill properties that depend on pressure. There are also changes that occur in the rocks bounding the reservoir. The subsidence that occurs from reservoir compaction is not uniformly distributed above the reservoir because of rock mechanical constraints. The compacting reservoir produces long-wavelength changes in the stress (and strain) tensor of the bounding rocks that are spatially variable. These stress-field changes in the non-reservoir rocks can reveal themselves on our time-lapse seismic as differences in arrival times and possibly as changes in reflection strength.

In this paper we show some examples of how the stress fields change in the non-reservoir rocks and how this affects the two-way arrival times on our seismic. We then compare our model predictions to what is observed on actual time-lapse seismic data and find a good quantitative agreement between them. Stress changes in a compacting earth When the fluid pressure in a buried reservoir is reduced the reservoir rock undergoes compaction as a result of changes in the effective stress field. The change in the effective stress field can be described by the equation:

∆σ eff = ∆S − α∆P ,

(1) where σ is the effective stress tensor, S is the total stress tensor, α is the Biot alpha coefficient and is generally close to one, and P is the fluid pressure. (Note that the sign convention in Eq. 1 is that compressive stresses are negative.) eff

The change in the total stress field, ∆S, is determined by how the overburden and underburden respond to the compacting reservoir. This depends on many physical properties including the rock mechanical properties of the reservoir and non-reservoir rocks and the geometry of the reservoir. It is instructive to look at the vertical components of Eq. 1 which can be written as: eff ∆σ ZZ = ∆S ZZ − α∆P = (γ − α )∆P .

(2)

The term γ in the above equation is referred to as the stressarching coefficient and is used for characterizing how the change in total vertical stress is related to the change in reservoir pressure. For an infinite horizontal reservoir undergoing uniform depletion the stress-arching coefficient will be zero, and the change in the effective vertical stress will be alpha times the negative of the change in fluid pressure. For finite-sized reservoirs, the value of γ depends on the geometry of the reservoir. In the example shown below, γ reaches values in excess of 0.2. Figure 1 shows a seismic profile through an overpressured gas reservoir in the North Sea. The background color in this profile is a geomechanical calculation of the change in the vertical component of the total stress tensor, ∆SZZ, divided by the average change in reservoir pressure.

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Hatchell et al., Whole Earth 4D We note a number of features in Fig. 1. The total vertical stress field above and below the depleting part of the reservoir becomes less compressive as a result of the reservoir compaction. The reservoir becomes thinner in the vertical direction allowing the rocks above and below to expand and consequently reducing the compressive stresses in these rocks. The change in the total stress field directly above the reservoir is large (more than 20 percent of the change in fluid pressure) and decays gradually away from the reservoir. Significant changes are predicted as far as 500 ms (~0.5 km) above the top reservoir. On either side of the depleting reservoir the change in the total vertical stress becomes more compressive. In these zones the compressive stresses increase because they take over some of the weight that was originally supported by the rocks above the reservoir.

Figure 1. Seismic profile through a gas-filled reservoir. Top reservoir is indicated by the upper (yellow) horizon. The background color is the ratio of the change in the total vertical stress field to the change in the average reservoir pressure. Red (blue) indicates areas where the stress field changes are extensional (compressional). Predicting Time-shifts The geomechanical results of the previous section show that long-wavelength changes in the total stress field are created away from the depleting reservoir interval. In this section we make predictions on how these stress-field

changes will appear as arrival time-shifts that are observed in time-lapse seismic surveys. A change in the total-stress field can produce time-shifts in the non-reservoir rocks by 1) changing the physical distance to a reflection surface because of compaction and 2) changes in the rock velocity. Within the reservoir interval there is an additional effect due to the change in the pore-fill properties. The timeshift observed as a function of depth will be the cumulative result of these effects. In previous work looking at time-shifts over the massively compacting Ekofisk field, Guilbot and Smith (2002) noted that the reservoir subsidence could not explain all of the time-shifts seen in that field. Additional time-shifts can come from the change in the stress-fields. For this North Sea field, we calculate the cumulative timeshift based on the calculated geomechanical displacements and a model for how the velocity will change with stress. In Figure 2 we show the same seismic profile as in Fig. 1, but now the background color is the predicted time-shifts generated from the geomechanical model using vertical raypaths.

Figure 2. Same seismic profile as Fig. 1. Background color is the predicted timeshift from the geomechanical model. Blue indicates where the seismic times are expected to arrive time-delayed after depletion. The geomechanical calculation shows that above the depleting reservoir we expect the seismic arrivals to be time-delayed after production. This is largely due to the decrease in the compressional stresses of the rocks above

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Hatchell et al., Whole Earth 4D the reservoir. As the reservoir compacts the neighboring layers expand. The magnitude of the delay at the top reservoir event is as large as 2 ms.

Figure 3 shows the results of applying Eq. 6 to the real baseline and monitor seismic data. We used a triangularfilter time gate with a length of +/- 120 ms and a 7x7 areal average to improve the statistics of the result.

In the model results displayed in Fig. 2, we show only the cumulative time-shifts expected from non-reservoir rocks. We model no change in the time shift through the reservoir interval. Prior to acquiring the time-lapse seismic over this field we expected to observe large upward timeshifts based on velocity-stress measurements of core plugs from this reservoir. As we will see in the next section, most of the observed time-shifts come from the non-reservoir rocks. One explanation for the discrepancy between the seismic results and the core-plug estimates is the effect of core damage. Nes et al. (2000) give a good discussion of the effect of core-damage on velocity-stress measurements. Below the depleting reservoir the timeshift delay increases further with depth. The compressive stresses of the rocks beneath the reservoir also decrease as they expand to accommodate the compacting reservoir. Comparison with the real data In this section we compare the results from the real timelapse seismic acquired in this field to the predictions from the geomechanical model. We find that many of the features observed in the real seismic can be explained by the geomechanical predictions. The time-shifts from the real seismic data are estimated in the following way. Suppose we have a baseline seismic survey B(t) and a monitor survey M(t) which is nearly identical to B(t) except for a small and slowly varying timeshift. If we write, M (t ) = B (t + τ ) , (3) where the time-shift τ=τ(t) is assumed to be small and slowly varying. We expand Eq. 3 in a Taylor series and find:

M (t ) = B (t ) + B ' (t )τ ,

(4)

where we have kept terms to only first order in τ and ignore terms such as dτ/dt which is consistent with the assumption that the time-shifts are slowly varying. We solve for τ by minimizing the objective function

∑ [M (t ) − B(t )] , 2

(5)

and the summation is taken over a time-gate and areal average of interest. Using Eq. 4 and standard minimization techniques we arrive at the following equation for τ:

∑ [M (t ) − B(t )]B (t ) . ∑ B (t ) B (t ) '

τ=

'

'

Figure 3. Seismic profile of Fig. 1. Background color is the timeshift estimated using the small time-shift approximation (Eq. 6). The time shifts observed in the real time-lapse seismic are similar in many respects to the model prediction. We see at the top reservoir a time-delay on the monitor survey consistent with what is expected based on the geomechanical considerations. The physical location of these timeshifts appears also similar to that predicted by geomechanics. As mentioned in the previous section, we see only a modest effect within the reservoir interval (base reservoir lies ~40ms above the bottom [green] horizon). Below the reservoir, the time-shift delay increases further, also consistent with the geomechanical results. The predicted time-shifts shown in Fig. 2 are approximate because they are based on vertical raypath summation through the geomechanical model. A more exact comparison with the real seismic data will involve prestack raytracing followed by integration through the geomechanical model.

(6)

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Hatchell et al., Whole Earth 4D In Figs. 4 and 5 we compare the time shift calculated at the top reservoir event from the geomechanical model with the real time-lapse seismic. We see a good agreement between the model predictions and the real seismic and note that the largest time-delays occur directly above the depleting gas zones.

Detecting geomechanical changes in the over- and underburden rocks opens up new ways of using 4D data, especially in places where the signal from the reservoir rocks is small.

Figure 4. Timeshift calculated at the top reservoir horizon from the geomechanical model

Figure 5. Timeshift calculated at the top reservoir horizon from the real seismic and the approx GWC.

Conclusions

References:

A model incorporating geomechanical predictions of the stress and strain field changes resulting from reservoir compaction is used to explain time-shifts that occur on real 4D seismic.

Guilbot, J. and Smith, B., 2002, 4D-constrained depth conversion for reservoir compaction estimation. Application to the Ekofisk field. The Leading Edge, 21, 302-308.

One main result of the geomechanical study is that stress arching creates a zone of stress relaxation above and below the compacting reservoir. This zone creates time-delays that are observable on our time-lapse seismic. On the sides of the compacting reservoir the stresses are predicted to increase and result in a time pull-up.

Koster, K., Gabriels, P., Hartung, M., Verbeek, J., Deinum, G., and Staples, R., 2000, Time-lapse seismic surveys in the North Sea and their business impact. The Leading Edge, 19(3), 286-293.

In the North Sea field example, the largest time-shifts that are observed come from the non-reservoir rocks. Understanding these is important because they can be used to calibrate the geomechanical models used to predict well failure and help monitor reservoir depletion.

Nes, O.M., Holt, R.M., and Fjaer, E., 2000, The reliability of core data as input to reservoir monitoring studies. SPE European Petr. Conf., Paris, SPE #65180. Watts, R.F., Jizba, D., Gawith, D.E. and Gutteridge, P., 1996, Reservoir monitoring of the Magnus Field through 4D time-lapse analysis, Petroleum Geoscience, 2, 361-372.

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