Anisotropic velocity changes in seismic time-lapse data Jorg Herwanger*, Ed Palmer (WesternGeco), Christian Rau Schiøtt (Hess)

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1 Anisotropic velocity changes in seismic time-lapse data Jorg Herwanger*, Ed Palmer (WesternGeco), Christian Rau Schiøtt (Hess) Summary Reservoir production causes subsurface deformations and changes in seismic velocity. These deformations and velocity changes can be monitored using time-lapse seismic data. A fundamental challenge in the interpretation of time shifts observed in time-lapse data is the decomposition of the time delay into a spatial compaction component and a velocity change component. Several authors (Hatchell and Borne, 2005; Janssen et al., 2006) have published the application of pragmatic linear relationships between overburden stretching and velocity changes which, have proved applicable in a wide range of geological settings. In this study, we predict velocity changes through coupled reservoir and geomechanical modeling of the subsurface stress state and subsequent application of a rock physics model that relates changes in subsurface stress and strain to velocity changes. We expand on previously published work by investigating the anisotropy of the velocity changes and relate these to field observations of offset-dependent timelapse time-shifts from the South Arne Field. Our modeling shows that in the overburden, vertical seismic velocities decrease over time, causing traveltimes in a monitor survey to increase compared to traveltimes in a base survey. We furthermore predict that horizontal seismic velocities in the deep overburden increase and for seismic waves propagating at intermediate angles (approx ), the velocity changes are minimal. This suggests, that time-shifts between base- and monitor surveys are largest for zero-offset data and will gradually decrease as a function of offset. We test this prediction on a 4D field data set at South Arne, North Sea. For zero-offset data, we find a maximum traveltime increase in the overburden of 6ms. Time-shifts show a dependence on observation angle, with large offset time-shifts in the overburden being up to 50% smaller than near-offset time-shifts. Introduction Stress-induced traveltime differences in the overburden in 4D seismic data have recently been observed in a number of fields (Table 1) and probably occur far more often than commonly assumed. Conditions favorable for the occurrence of time-lapse time-shifts in the overburden include soft and poorly consolidated reservoir rock, highporosity reservoirs, over-pressured reservoirs and a large reservoir thickness. These conditions are essentially the same that also favor reservoir compaction. Reservoir compaction can assist in pressure maintenance and thus assist in reservoir production, but also leads to subsurface deformation and associated well failures. Understanding, monitoring, and predicting reservoir compaction and subsurface stress changes are of significant interest for well-founded reservoir production and development decisions. Using a combination of 4D seismic analysis and reservoir geomechanical modeling, it is possible to relate, with confidence, production measurements such as pressure changes and hydrocarbon production to the observed change in 4D seismic attributes, such as change in two-way traveltime, and derive reliable estimates of subsurface stress changes. In this paper, we first present a modeling study of combined flow and geomechanical modeling. The predicted subsurface deformations and tensor stress changes from this model are used to predict changes in anisotropic seismic velocities. This modeling leads us to suspect that time-lapse time-shifts as a function of offset are not increasing, as previous publications suggest (e.g. Landrø and Stammeijer, 2004), but should as a matter of fact decrease. We successfully test this prediction in a second part of the paper using 4D seismic data from the Hess operated South Arne field, Danish North Sea. Field Area Operator Geology Reference Mars/Europa GOM Shell Deepwater Tu05 Turbidite Genesis GOM Deepwater Hu05; Turbidite Ri06 Valhall N-Sea BP Chalk Ha05 Ekofisk N-Sea CoP Chalk Ja06 South Arne N-Sea Hess Chalk He06 Shearwater N-Sea Shell HPHT Ha05 Skua N-Sea Shell HPHT St06 Egret N-Sea Shell HPHT St06 Heron N-Sea Shell HPHT St06 Offshore N-Sea Shell Carbonates Ha05 Sarawak Table 1: Reports of production-induced time-shifts in the overburden as 4D signal. The references are Tu05: Tura et al., 2005; Hu05: Hudson et al., 2005 ; Ri06: Rickett et al., 2006 ; Ha05 : Hatchell and Bourne, 2005 ; Ja06: Janssen et al., 2006; He05: Herwanger et al., 2006; St06: Staples et al., 2006; Modeling production-induced subsurface deformation and changes in tensor stress Observed increases in seismic traveltimes can be explained and modeled by a combination of reservoir geomechanical modeling and application of stress-sensitive rock-physics principles. Reservoir geomechanical modeling allows 2883

2 Main Menu Figure 1: (a) Simulated change in pore pressure and (b) Resulting change in vertical effective stress during three years of reservoir production. Applying a stress-sensitive rock-physics model allows prediction of changes in (c) Vertical P-wave velocity and computation of (d) Changes in vertical two-way-traveltime. Change in tensor stress at three representative locations in the (e) Shallow overburden, (f) The deep overburden and (g) The reservoir. Red double-arrows indicate an increase in compressive stress and green arrows indicate a decrease in compressive stress. The locations at which the stress changes are evaluated are indicated in (b). computation of deformation of the reservoir and overburden rock and stress changes associated with the deformation (Stone et al., 2000). As pore pressure decreases in the reservoir (Figure 1a), the weight of the overburden rock is successively transferred to the reservoir rock, increasing the vertical effective stress inside the reservoir (Figure 1b, red colors; Compressive stress is defined as negative). To maintain static stress equilibrium, an increase in stress in the reservoir leads to a decrease in stress in the overburden and underburden (Figure 1b, blue colors). Stress changes in the vertical direction cannot occur, due to the free boundary at the earth s surface (Figure 1e). In the reservoir, the decrease in pore pressure leads to a strong increase in vertical effective stress and reservoir compaction. In the horizontal directions, stress increases slightly (Figure 1g). Reservoir compaction causes the overburden to stretch, thereby, causing a decrease in vertical stress (Figure 1f). Note also, that the principal directions of the stress change tensor are no longer aligned with vertical and horizontal. Predicting anisotropic velocity changes Stress changes (i.e., force change per unit surface area) occur not only in the vertical direction, but also in the horizontal directions, and in the most general case, in arbitrary directions. The exact pattern of stress changes will depend on the geometry of the reservoir, the locations and production rates of the wells, and the elastic properties of the earth. The production-induced stress change inside each cell of a gridded model of the earth needs thereby to be described by a tensor. In Figures 1 (e) (g), we show representative tensors of stress change in the shallow overburden, the deep overburden, and the reservoir, respectively. The stress tensors are plotted by three sets of orthogonal double arrows. The direction of the double arrows gives the directions of the principal stresses and the length of the double arrows is proportional to the magnitude of stress change. The red, inward-pointing, arrows indicate a stress increase and the green, outwardpointing, arrows indicate a stress decrease. In the near surface, stress changes occur in horizontal directions only. Laboratory measurements on rock samples show that velocity of elastic wave propagation is sensitive to the triaxial stress state of the sample. The observed changes in velocities resulting from changes in the triaxial stress state are dependant on the direction of wave propagation, i.e. the change in velocity is an anisotropic property. We therefore need employ a theory that allows us to predict anisotropic velocity changes from changes in the triaxial effective stress Δσ. We use the theory and laboratory measurements described in Prioul et al., (2004) to calculate the stiffness tensor in a stressed state from the stiffness tensor in a reference stress state and use stress predictions from geomechanical modeling. The rock-physics model is applied in a coordinate system aligned with the principal directions of the stress change tensor. Subsequently, we rotate the stiffness tensor into the global coordinate system with axes given by the north, south and the vertical direction (Chapman, 2004, eq ). From the stiffness 2884

3 Main Menu Figure 2: Change in triaxial stress state (left) causes anisotropic changes in seismic propagation velocity (right). In near-vertical directions, (i.e., at the North pole of the half-sphere), the velocities slow down, due to the decrease in effective stress. Around the equator, the velocities increase due to an increase in effective stress. tensor in a stressed state, we can calculate P-wave velocities in any propagation direction parameterized by azimuth and elevation angle of the propagation direction (Helbig, 1994, eq. 4B.3). In Figure 2, we plot the changes in P-wave velocity as a function of propagation direction, together with the change in stress tensor causing the velocity changes. From the figure, it becomes immediately obvious that the largest velocity decrease occurs in the same direction as a decrease in effective stress occurs (green double arrow on the left). Vice versa, velocity increase is largest in the direction of the largest stress increase. Predicting 4D time-shifts Time-lapse seismic monitoring allows observations of production-induced traveltime changes or time-shifts. Using a velocity model at initial conditions and predicted changes in anisotropic velocity in each cell of a geocellular model, combined with changes in cell-geometry computed from strain changes, allows for computation of travel times at various stages of reservoir production. Travel times computed for the dates of base survey and a monitor survey are then subtracted to yield a time-shift field. This is demonstrated in Figures 1c and d for vertically propagating P-waves. The predicted vertical velocities in the overburden and underburden show a decrease due to stretching and an increase inside the reservoir due to compaction (Figure 1c). Note that these velocity changes are purely stress-induced and do not include velocity changes due to changes in pore-fluid content. The predicted time-shifts (Figure 1d) are largest at the top of the reservoir, with two lobes of large time-shifts centered on the location of the producing wells. Inside the reservoir, time-shifts decrease slightly and increase further in the underburden. Field observations of 4D time-shifts The predicted behavior of time-lapse time-shifts is observed in field data from South Arne, North Sea (Figure 3). In Figure 3a, we show a time-migrated image of the base survey, with top, intra and bottom reservoir interpretations given by green lines. Time-lapse time-shifts can be observed by comparison of single traces from base and monitor survey (Figure 3b). The top reservoir reflector (at 2.75 s) is seen to increase in traveltime and brightens (i.e. increases in amplitude) over time. The bottom reservoir reflector (at 2.8 s) also increases in traveltime, but dims. Automated measurements of time-shifts show maximum increases in traveltime between base and monitor survey of up to 6 ms (Figure 3c). The largest traveltime increase is measured over a fault-block being drained by a well-producing horizontal well. Also note the increase in time-shifts in the upper reservoir and the decrease in time-shifts in the lower reservoir (providing the majority of production). 4D time-shifts as function of observation direction Time-lapse time-shifts are caused by a combination of change in path length (due to strain) and a change in propagation velocity. In the case of isotropic time-lapse velocity changes, Landrø and Stammeijer (2004) derived an elegant method to separate time-shifts Δt due to changes in layer thickness Δz and (isotropic) velocity changes Δv by evaluating time-shifts as a function of incidence angle Θ: Δt( Θ) Δz 2 Δv (1) t = z (1 + tan Θ) In the overburden, this equation predicts an increase in traveltime due to an increase in path length (positive Δz) and a slowdown in velocity (negative Δv). This equation furthermore predicts that for increasing angles of incidence, the time-lapse time-shifts increase. Based on our modeling, we expect anisotropic velocity changes and a decrease of time-shifts with increasing incidence angle. We therefore test the behavior of timeshifts as a function of incidence angle, by measuring timeshifts between base- and monitor surveys in angle-band gathers (Figure 4). Our observation show that time-shifts decrease as the angle of incidence increases. This observation strongly supports the idea of anisotropic v 2885

4 Main Menu Figure 3: (a) Time-migrated image with top, intra and base reservoir interpretations. (b) Single trace from base- and monitor survey show timeshifts and amplitude changes. (c) Time-lapse time-shifts between base- and monitor surveys. Figure 4: (a) and (b) Time-lapse time-shifts between base- and monitor surveys for angle-band stacks between 5-15 and 25-35, respectively. (c) A comparison between (a) and (b) shows, that time-lapse time-shifts decrease with increasing incidence angle Θ. velocity changes. Another inference of this observation is that equations to estimate compaction based on time-shifts as a function of incidence angle (or offset) must be expanded to include anisotropic velocity changes incidence). This prediction was tested and verified using measurements of time-lapse time-shifts in angle-band gathers. These measurements strongly suggest that stressinduced velocity changes are indeed anisotropic and need to be treated accordingly. Conclusions We have shown that reservoir production can cause anisotropic velocity changes. We did this using a modeling approach of predicting triaxial stress changes and associated anisotropic velocity changes. The modeling suggested that time-lapse time-shifts should decrease as a function of propagation direction (measured by angle of Time-lapse time-shifts have become popular to measure reservoir compaction. However, the equations used in this process assume isotropic velocity changes. This will lead to erroneous estimates of compaction if far-offset data are included. Future work will therefore need to expand this method of estimating reservoir compaction to include anisotropic velocity changes. 2886

5 Main Menu EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2007 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web. REFERENCES Chapman, C., 2004, Fundamentals of seismic wave propagation: Cambridge University Press. Hatchell, P., and S. Bourne, 2005, Rocks under strain: Strain-induced time-lapse time shifts are observed for depleting reservoirs: The Leading Edge, 12, Helbig, K., 1994, Foundations of anisotropy for exploration seismics: Handbook of Geophysical Exploration, 22: Pergamon. Herwanger, J. V., E. Palmer, and C. Schiott, 2006, Field-observations and modelling of production-induced time shifts in 4D seismic data from South Arne, Danish North Sea: PETEX. Hudson, T., B. Regel, J. Bretches, P. Condon, J. Rickett, B. Cerney, P. Inderwiesen, and R. Ewy, 2005, Genesis Field, Gulf of Mexico, 4-D project status and preliminary lookback: 75th Annual International Meeting, SEG, Expanded Abstracts, Janssen, A. L., B. A. Smith, and G. W. Byerley, 2006, Measuring velocity sensitivity to production-induced strain at the Ekofisk field using time-lapse time-shifts and compaction logs: 76th Annual International Meeting, SEG, Expanded Abstracts, Landrø, M., and J. Stammeijer, 2004, Quantitative estimation of compaction and velocity changes using 4D impedance and traveltime changes, Geophysics, 69, Prioul, R., A. Bakulin, and V. Bakulin, 2004, Non-linear rock physics model for estimation of 3-D subsurface stress in anisotropic formations: Theory and laboratory verification: Geophysics, 69, Rickett, J., L. Duranti, T. Hudson, and N. Hodgson, 2006, Compaction and 4-D time strain at the Genesis Field, 2006: 76th Annual International Meeting, SEG, Expanded Abstracts, Staples, R., R. Nash, P. Hague, J. Ita, and R. Burrell, 2006, Using 4D seismic data and geomechanical modelling to understand pressure depletion in HPHT fields of the Central North Sea: PETEX. Stone, T., G. Bowen, P. Papanastasiou, and J. Fuller, 2000, Fully coupled geomechanics in a commercial reservoir simulator: Society for Petroleum Engineers Annual Meeting, Paper Tura, A., T. Barker, P. Cattermole, C. Collins, J. Davis, P. Hatchell, K. Koster, P. Schutjens, and P. Wills, 2005, Monitoring primary depletion reservoirs using amplitudes and time-shifts from high-repeat seismic surveys: The Leading Edge, 12,