Chalk field 4D compaction: Valhall over 40 years

The field and its surveys

• Reservoir: chalk of the Tor and Hod Formations; the Tor and the lower Hod average about 24 and 30 m thick (Hall and Kendall 2003), and the Tor ranges from nothing to 80 m (Norsk Oljemuseum). Permeability is low, typically 0.1 to 15 mD (Norsk Oljemuseum). The logs give a hard chalk top: $V_P$ = 3134 m/s in the chalk under 2141 m/s in the shale above (Hall and Kendall 2003).
• Pressure and fluids: overpressured, undersaturated oil; the pressure in the upper Tor has been below the bubble point since 1988 (Norsk Oljemuseum). Water injection began in the centre of the field in January 2004 and reached the northern flank in 2008 (Norwegian Offshore Directorate; Norsk Oljemuseum). Water weakens chalk, and it adds to the compaction that depletion drives (Kristiansen and Plischke 2010).
• Gas cloud: gas that leaked from the reservoir lies in the overburden over the crest, about 1500 m below the seabed (Norsk Oljemuseum). It slows and attenuates the waves; it hid the structure on the 1960s seismic (Whaley 2009) and still spoils the amplitudes at the crest (Hatchell, Kawar and Savitski 2005).
• Surveys: a streamer survey in 1992, a four-component ocean-bottom-cable survey in 1997 and a repeat streamer survey in 2002 (Hatchell et al. 2005).
• Life of Field Seismic (LoFS): in the summer of 2003, 120 km of seismic cable were trenched into the seabed over 45 km², about 60 % of the field, with 2400 four-component receiver stations (Barkved, Amundsen and Landrø 2009; Norsk Oljemuseum). The first survey was shot in November 2003, and surveys have followed one to three times a year (Norsk Oljemuseum): eleven by 2009 (Barkved et al. 2009). Because the receivers never move, every survey repeats the last, and the fast-track products arrive within days (Barkved et al. 2009; van Gestel et al. 2008).

Exercise: from the chalk to the seabed to the time shift

1. Start as the figure opens: 2010, $R$ = 5 for stretched rock and $R_-$ = 1 for shortened rock, a compacting disc 4 km in radius, plate (a) showing the vertical strain. The overburden over the disc is stretched; beyond its edge, near the chalk, it is shortened. The headline gives the chain: the seabed over the crest has sunk 5.79 m, the chalk beneath has compacted 11.8 m, and the 2.87 m between them is the overburden’s stretch.
2. Switch (a) to Time shift. Down every trace over the crest the shift grows, to 17.9 ms at the top of the chalk. It is a delay: the monitor sees the top of the chalk later, although the chalk itself has compacted and hardened. Its reflection travels only through the overburden, which is longer and slower. Hatchell, Kawar and Savitski (2005) found exactly this between the 1992 and 2002 streamer surveys: shifts that delay the monitor, largest just above the reservoir, mapped at the top of the reservoir on a scale of 0 to 20 ms. Between the starts of 1992 and 2002 the model’s delay over the crest grows by 7.7 ms, the same order.
3. Set $R$ and $R_-$ to 0. The overburden keeps its velocity, and the shift falls to 2.99 ms, the longer path alone; with $R$ = 5 it is six times that. A shift is the product of $1 + R$ and the strain, so on its own it cannot separate the two.
4. Set $R$ back to 5 and $R_-$ to 1, and narrow the disc to 3.5 km. The seabed sinks the same 5.79 m, but the chalk must now compact 13.6 m, the overburden stretches 3.62 m and the shift is 22.6 ms; at 6 km they are 8.3 m, 1.52 m and 9.7 ms. A deep, narrow source spreads its subsidence over a bowl wider than itself, so the seabed shows less of the compaction and the overburden takes up more.
5. Set the disc back to 4 km and the year to 2020, and look beyond the disc in (c). There the overburden near the chalk is shortened, and shortened rock speeds up, but far less than stretched rock slows: to match the shifts they observed over several fields, Hatchell and Bourne (2005b) needed $R$ between 4 and 8 where the rock stretches and between 0 and 2 where it shortens. With $R_-$ = 1 the flank’s shift dips to $-1.2$ ms at 4.2 km from the crest; with $R_-$ = 5, one law for both, to $-4.4$ ms at 4.0 km. The crest, where nothing shortens, stays at 20.4 ms either way.
6. Move the year. Before water injection the model’s shift over the crest grows by 0.77 ms a year; after it, by 0.25 ms a year, as the model’s seabed slows from 0.25 to 0.08 m a year when injection starts, which is the model’s assumption. Yet at one position over the compacting field, between the first and third LoFS surveys, months apart, Røste et al. (2007) measured traveltime changes of about 1.5 ms at 1 km offset. Compaction concentrates around the producing wells, and a smooth disc over the whole field averages it away.

Why the overburden slows

A thin layer whose thickness changes by the vertical strain $\varepsilon_{zz}$ and whose velocity changes by $\Delta v/v$ changes its vertical two-way time by $\Delta t/t = \varepsilon_{zz} - \Delta v/v$ (Landrø and Stammeijer 2004). Hatchell, Kawar and Savitski (2005) and Hatchell and Bourne (2005a) tied the velocity to the strain, $\Delta v/v = -R\,\varepsilon_{zz}$, so that

the law of Figure 8.2. Summed from the seabed down to the top of the reservoir, the shift is proportional to the overburden’s stretch (Hatchell et al. 2005). At Valhall, matching the observed shifts with a geomechanical model of the compaction gave $R$ about 5 (Hatchell et al. 2005), and Røste et al. (2007), with the dilation factor $\alpha = -R$, found $\alpha = -5$ from prestack LoFS data. Stretched rock slows five times more than its extra length alone would delay a wave. Shortened rock answers far less: over several fields Hatchell and Bourne (2005b) needed $R$ between 4 and 8 where the rock stretches and between 0 and 2 where it shortens, and Figure 9.2 gives shortened rock its own ratio, $R_-$.

Hatchell et al. (2005) found the shifts and the amplitude changes complementary. The amplitudes change at the top and base of the chalk, where it hardens and thins, and they depend on the reservoir’s thickness through tuning. The shifts integrate the overburden’s stretch over long time windows, so they are robust, and they stayed reliable at the edge of the gas cloud, where the amplitudes were attenuated. Below the chalk the shift is reduced again by the chalk’s own hardening; the figure leaves that out, because the chalk’s strain of more than 10 % is beyond a linear velocity law.

Why chalk compacts so much

Chalk is a fine-grained limestone of coccolith debris. Buried normally it loses porosity; Valhall’s chalk kept its porosity because overpressure carried much of the overburden’s weight (Angus et al. 2015). Production removed that support:

• the effective stress on the grains rose with every megapascal of depletion (Section 8.1);
• the weak, highly porous frame compacted, and compaction by pore collapse is largely permanent: it is not recovered when the pressure returns;
• water injected from 2004 restored some pressure but weakens chalk, so compaction went on (Kristiansen and Plischke 2010; Norwegian Offshore Directorate).

The compaction passes upward to the seabed through the overburden, which sags into a bowl wider than the reservoir. Geertsma (1973) computed that bowl for a compacting disc in an elastic half-space, and Figure 9.2 uses his solution: for the figure’s disc, 4 km in radius at Valhall’s depth, the seabed over the crest sinks 0.49 of the compaction there. Valhall’s operators use full-field geomechanical models history-matched to the measured subsidence for the same purpose (Kristiansen and Plischke 2010); the model of Angus et al. (2015) reproduces the subsidence measured by GPS at the central QP platform over about 25 years of production.

Workflow: geomechanics, simulation and 4D together

1. Baseline: the pre-production surveys and the well logs give the structure, the chalk’s thickness and porosity, and the velocities and densities (Parts 5 and 7).
2. Reservoir simulation: pressure, saturation and pore volume through time; from the pore-volume change, the compaction, assuming uniaxial strain (Hatchell et al. 2005).
3. Geomechanics: the compaction applied to an elastic model of the overburden gives the stresses and strains above the reservoir, and the seabed subsidence to compare with the measured (Section 8.1; Hatchell et al. 2005; Kristiansen and Plischke 2010).
4. Synthetic 4D: velocities changed by the strains, the chalk’s by its new porosity, then synthetic time shifts and amplitude changes for each monitor (Section 8.2).
5. Comparison: where the observed shifts exceed the synthetic ones the compaction is larger than the model’s, and where they fall short it is smaller. Hatchell et al. (2005) found the south of the field compacting more than the model near some producing wells, and the north less.
6. Decisions: with LoFS images fast-tracked within days, the 4D changes show production at the level of individual perforations (Barkved et al. 2009) and guide the placing of wells and the water injection (Barkved et al. 2009; van Gestel et al. 2008).

Outcomes and lessons

Valhall has produced about three times what its development plan expected (Norwegian Offshore Directorate), and a new production and wellhead platform approved in 2023 is to start in 2027. The 4D record behind that is long: three surveys before 2003 and a permanent array surveyed one to three times a year since. Three lessons carry beyond chalk:

• A compacting reservoir moves everything above it. The time shift over a compacting field is the overburden’s, and it is a delay; the reservoir’s own speed-up shows only beneath it.
• A shift is strain and velocity together. Splitting it needs $R$, which only a calibrated geomechanical model provides; the subsidence, measured at the seabed, is one of its anchors.
• Compaction is local. It concentrates around producing wells and changes with water injection, which only frequent, repeatable surveys resolve; this is what the permanent array was built for.

Where Valhall-style 4D generalizes

• Ekofisk, in the same chalk of the same basin, has subsided more than 8 m since production began in 1971 (Whaley 2009), and its overburden shows time shifts of the same kind (Guilbot and Smith 2002).
• Other depleting fields: overburden delays like Valhall’s have been reported over other compacting reservoirs (Hatchell et al. 2005), and Hatchell and Bourne (2005b) found $R$ between 4 and 8 for the stretched overburden over several depleting fields. Smaller compaction makes smaller shifts, but the method carries over.
• Pressure rising instead of falling: over a reservoir that is pressurized, by injection or by CO₂ storage (Section 8.6), the overburden is compressed and uplifted, and the shifts change sign. The same law and the same geomechanics read them.