Time-lapse (4D) seismic: monitoring reservoir changes

The baseline, the monitor and their difference

A 4D project needs two or more surveys over the same area at different dates:

• Baseline: the survey before production, or early in it. Every later survey is compared with it.
• Monitor: a repeat survey, typically one to a few years later. Its difference from the baseline is the cumulative change since then.

The difficulty is repeatability. Production changes the reflections from a reservoir by a few to some tens of per cent. Anything else that differs between the surveys, the positions of sources and receivers, the source wavelet, the water's temperature and the tide, the noise, the processing, makes a difference of its own, and in the difference the two cannot be told apart. Hence the effort 4D projects spend on repeating the first survey: the same geometry, the same source, the same season, and both surveys processed together through one flow. Permanent receivers on the seabed, which stay in place between surveys, repeat best.

Repeatability is measured where nothing can have changed, in a window above the reservoir, as the normalised RMS difference of Kragh and Christie (2002):

with $m$ and $b$ the monitor and baseline traces. It is 0 for a perfect repeat and 141 for two unrelated traces of equal energy. Pairs recorded on permanent or ocean-bottom receivers have reached a few per cent; towed-streamer pairs commonly lie between about 10 and 30 per cent, and surveys never designed to be repeated above that. No value is a universal cut-off: what decides whether a change can be seen is its size against this floor, the headline number of Figure 8.2.

Reading Figure 8.2

The figure produces a faulted anticline four ways and computes both surveys from it. Plate (a) is the truth in depth; (b) the baseline or the monitor; (c) their difference at three times the gain; (d) the shift of two deep, flat reflectors, the beacons, along the section; (e) the shift down the crest against two-way time; (f) the change of intercept and gradient at the sand's top. Saturations and effective stress become rock properties through Gassmann's equation, with Figure 5.3's brine and gas, the book's oil and a frame that stiffens under stress; traveltimes are integrated through each survey's own velocities, so the shifts come out of the physics. The figure opens on five years of waterflood with the noise at 5.6 per cent of the signal: NRMS 12.4 per cent, and the swept sand's difference 6.0 times the floor.

1. Set the years to 0 with the noise at 10 per cent of the signal. Nothing in the earth has changed, but (c) is not blank: NRMS is 22.0 per cent, and the reservoir window's difference is 1.0 times the overburden's, the same noise. This is the floor every anomaly must rise above.
2. Take the waterflood to year 5 and the noise to its maximum. NRMS rises to 42.6 per cent and the flood's difference falls to 2.0 times the floor; five years of depletion stand at 1.2 times. The change did not shrink; the floor rose.
3. Choose Gas out of solution and ten years. Gas, even a little of it, collapses the pore fluid's modulus (here 35 per cent of the pores take it to 0.022 GPa), the sand under the crest slows by 8.6 per cent and its impedance falls 11 per cent, and in (d) the beacons arrive 1.38 ms later (the model's own shift is 1.44 ms): push-down. Then Depletion: they arrive 1.26 ms earlier. Then Waterflood: 0.97 ms earlier as well, because brine is stiffer than oil. The sign separates softening from hardening, not a flood from a depletion; the ratio of shift to amplitude change does, 0.056 ms per per cent for depletion against 0.028 for the flood.
4. With Depletion at year 10, read (e). The shift is flat through the overburden, which the model holds rigid, and steps by 1.23 ms across the sand's 33.6 ms: a time strain of $-3.6$ per cent, the change of the sand's slowness. Windows that straddle the sand read some of the change of its reflections as a shift as well.
5. Choose Injection at year 10 and read (f). Water replacing oil raises the intercept; the rise in pore pressure softens the frame and lowers it. At 1.48 km the two nearly cancel in the intercept while the gradient still changes, and the table splits the pair into +0.078 of water saturation and +0.67 MPa of pore pressure, against a truth of +0.077 and +0.67.

Rock physics of the 4D signal

Each change has its own elastic fingerprint. The numbers below are Figure 8.2's soft sand at 500 m, with Figure 5.3's fluids at its 5 MPa and 30 °C. Five hundred metres is shallow for an oil field: most fields monitored with 4D lie 1.5 to 3 km down, at several times this sand's 4.5 MPa of effective stress, and a frame at low stress is the more sensitive to it, so the pressure effects below are larger than a deeper reservoir would show.

• Water replacing oil. Brine is stiffer and denser than oil. Gassmann's equation raises the fluid's modulus from 1.11 to 1.89 GPa as the water saturation goes from 0.22 to 0.75, and the swept sand's $V_{\mathrm{P}}$ rises 5.8 per cent and its impedance 7.0 per cent. The shear modulus does not change, so $V_{\mathrm{S}}$ falls slightly as the density rises. The sand speeds up, so reflectors below are pulled up: by 0.97 ms after ten years here, not a negligible amount.
• Gas coming out of solution. When the pressure falls below the bubble point, gas appears in the pores. By Wood's average a little gas dominates the fluid's compressibility: 35 per cent of gas brings the fluid's modulus to 0.022 GPa. $V_{\mathrm{P}}$ falls 8.6 per cent and the impedance 11 per cent, the strongest softening in the figure, and the reflectors below are pushed down.
• A change of pressure. Effective stress, the overburden's weight less the pore pressure, holds the grains together. Depletion raises it and the frame stiffens; injection lowers it and the frame softens. Here MacBeth's (2004) law stiffens the frame moduli 12.9 per cent for the 3.5 MPa of ten years' depletion, and softens them 9.5 per cent for 2.5 MPa of injection, against 9.3 per cent of stiffening for 2.5 MPa of depletion: at this stress the law is nearly symmetric. Depletion speeds the sand, so reflectors below are pulled up.
• Compaction and the overburden. A depleting reservoir also shortens. In this soft sand the strain its drained frame allows for 3.5 MPa is only 0.026 per cent, so its time shift is almost all velocity. In weak, thick reservoirs, chalks above all, compaction reaches metres; the rock above then stretches, slows, and shifts reflections later before the reservoir is even reached (Hatchell and Bourne 2005). Figure 8.2's overburden is held rigid.
• $\mathrm{CO_2}$ injection. Dense $\mathrm{CO_2}$ is far more compressible than brine, and like gas it softens the rock strongly; the plume's edge is the anomaly to map. Section 8.6 follows it.

No single fingerprint is unique, and the quantitative reading of any of them is forward modelling: take the rock physics, apply the change the reservoir engineers expect, compute the 4D signal it would make, and compare it with the one observed.

Time shifts and time strain

A time shift is the change in two-way time to a reflector. It integrates the change of slowness along the whole path above the reflector, so it builds up down through a change and then stays constant below it. Its derivative with respect to two-way time, the time strain, locates the change: zero where nothing changed, nonzero across the layer that did. Two things change the traveltime through a layer: its thickness and its velocity. Hatchell and Bourne (2005) and Landrø and Stammeijer (2004) tie them together with one factor, $\Delta v/v = -R\,\varepsilon_{zz}$ for a vertical strain $\varepsilon_{zz}$ (positive in extension), so that

Hatchell and Bourne fitted the overburden shifts over the fields they studied with $R$ near 5; values reported since are smaller, about 1 to 3, inside compacting reservoirs than in stretched overburden, so $R$ depends both on the rock and on whether it is stretched or compressed. With a calibrated value a measured time strain can be turned into strain, and the strain into compaction and subsidence. $R$ is a property of the rock. In Figure 8.2's sand the velocity is far more sensitive to stress than its drained strain is: read with $R = 5$, its time strain of $-3.6$ per cent would imply a compaction of 0.61 per cent, more than twenty times what its frame allows.

Separating pressure from saturation

Often pressure and saturation change together, injection beside a sweep, depletion beside gas coming out of solution, and a stack sees only their sum. They act on different properties: a fluid change alters the density and the bulk modulus but not the shear modulus, while a pressure change alters the frame, shear modulus included, and hardly the density. With angle stacks the change of the intercept $A$ and of the gradient $B$ give two equations for the two unknowns (Landrø 2001):

with coefficients from the rock physics: Landrø took the fluid term from Gassmann's equation and the pressure term from laboratory measurements on core. Solving gives a saturation-change and a pressure-change map from the same data. Plate (f) of Figure 8.2 does this at the top of its sand, noise-free and with coefficients from the very model that made the change, so only the curvature of the laws is left as error: ten years of depletion, 3.5 MPa, are read as 3.3. Landrø kept a second-order term in pressure for that reason; the figure keeps only the linear terms, which hold while the changes are small. On real data the coefficients come from a model of the rock, the near and far stacks carry noise, and the split inherits both.

Repeatability and common pitfalls

• Geometry that did not repeat. Sources and receivers a few tens of metres from where they were change the fold, offsets and azimuths, and with them the amplitudes. Remedies: steer the monitor to the baseline's positions, keep only the traces that repeat, and cross-equalise the two surveys.
• The water column. Sound travels faster in warm water than in cold, so a winter baseline and a summer monitor differ in traveltime before the reservoir is reached; tides change the water depth. Remedies: acquire in the same season, and correct with measured water velocities and tide tables.
• Processing. Two surveys processed apart, with different parameters, differ for that reason alone. Remedy: process them together through one flow.
• Changes in the overburden. Production elsewhere, or the stretching above a compacting reservoir, changes the velocities above the target and shifts and distorts everything below. Remedy: measure the time shifts and time strains above the reservoir and correct for them before reading the reservoir's amplitudes.
• Noise read as signal. A reservoir anomaly no stronger than the difference in the overburden is noise. Compare every anomaly with the floor measured where nothing changed, and ask whether its edge follows geology, a contact or a fault, or the acquisition.
• Gaps in coverage. Where an obstruction or a missing line left no monitor data the difference is meaningless. Flag those areas and do not interpret their edges.

Applications in practice

• Ekofisk and Valhall, Norwegian North Sea: compacting chalk reservoirs whose depletion has lowered the seabed by metres; 4D time shifts there map the compaction and the stretching of the overburden, and Valhall has had a permanent seabed receiver array since 2003.
• Gullfaks, Norwegian North Sea: repeated surveys over a waterflood located the water's advance and undrained oil for new wells.
• Sleipner, Norway: $\mathrm{CO_2}$ injected into the Utsira sand since 1996 and followed by repeat surveys since 1999. Section 8.6 takes up the case.
• Deep-water developments: repeat surveys on ocean-bottom nodes have become a standard tool for managing high-value subsea fields.
• Unconventional reservoirs: repeat surveys and fibre-optic distributed acoustic sensing (DAS) in wells are being used to watch completions and stimulated fractures.