Pinpoints and Echoes

Every well ever drilled in the Norwegian North Sea

The map shows 7,033 petroleum wellbores drawn at their true size on the area they span. None of them is visible. At this scale each one is a small fraction of a pixel, and together they have ever been a hole in one part in about 517 million of the area inside the dashed line. Everything known about the rock between them is inferred.

Enlarged thousands of times, the same wells show where the drilling has been: strings of platforms along the field axes, and wide areas between them that no bit has touched.

A hole a hand's width across, and the next one kilometres away

At reservoir depth a wellbore is about 22 cm across. The typical exploration well is 2.3 km from its nearest neighbour, in a range from 0.7 km to 6.8 km. Divide one by the other and the gap is about 11,000 hole widths. The rock in between is never touched, only argued about.

Redrawn with the wellbore as a coin one centimetre across, the nearest well sits about 110 m away and the area the wells span becomes a square about 17 km on a side. Decisions costing billions of kroner rest on what lies in that space.

What one well records

Along its own path a well is generous. The composite log of Volve well F-11 T2 samples the rock every 10 cm over 2,060 m of hole: natural radioactivity, bulk density, electrical resistivity and the speed of sound. Each curve is a measurement with a tool, a calibration and an error of its own. The Hugin Formation, the reservoir, is 101 m thick here and stands out on every track. A metre to the side of the hole, nothing is measured at all.

Within the reservoir the log resolves layers a few tens of centimetres thick: cemented bands, shale breaks, the fine structure that decides how oil moves. This is the detail the echo cannot see.

The same ground as an echo

Sound left the sea surface, travelled down through the water and 3,182 m of rock, and part of it returned from the top of the Hugin Formation after 2.76 seconds. The panel is inline 10,215 of the Volve survey, 720 traces across, with the well as a dashed line. The vertical axis is time, not depth. What looks like a cross-section is a record of arrivals, and turning it into depth is a separate step with its own uncertainty.

On the same panel, the surfaces the Volve interpreters published. Each line is a judgement about which arrival belongs to which rock boundary, carried across the survey from where the wells pin it. Away from the well the lines are interpretation; at the well they are tied.

Around the reservoir the data's dominant frequency is about 22 Hz and the sound travels at 4,012 m/s, so a quarter of a wavelength is 45 m. A synthetic bed thinned from eighty metres to nothing shows what that means: below about 36 m the echoes from its top and base merge, and the thickness the seismic reports stops following the truth. The layers the log resolved in the previous panel are far below this limit.

The limit is set by wavelength, in water as in rock. The same physics maps the sea floor by sonar, and by 2025 only 27.3 per cent of the world's ocean floor had been mapped to modern standards. The rock beneath it is mapped from kilometres further away, through the sea floor, with a longer wave.

Where the pinpoint meets the echo

The two kinds of evidence meet in the well tie. The log's sonic and density give a reflectivity series over 94% of the window; the data's wavelet turns it into a synthetic trace; the check-shot table places it in time. Beside it is the real trace at the well. Without adjustment the two correlate at −0.03. A single bulk shift of 12 ms raises that to 0.32.

After the shift the main reflectors line up and the detail between them does not. The log is sampled every 10 cm; the echo averages tens of metres. Two instruments measuring the same rock agree on the outline and disagree on the detail, which is the whole relationship between a well and a seismic survey in one panel. A working tie would go further: a wavelet extracted from the data rather than assumed, and stretch applied to the synthetic. Each of those steps is a judgement, and this is where the judgements begin.

Every measurement is uncertain, and they stack

Where the well is. What depth is measured from. How fast sound travels. Where a pick sits on the wavelet. Each link in the chain carries an error, and the errors stack. In Volve the horizontal position of a well is known to a median 8 m at the end of its survey, and to 23 m in the worst case. The figure follows the 4 vertical links one at a time, starting with the well's own depth.

A depth reference mixed up between the rotary table and sea level shifts every depth in a well by the height of the rig floor, 55 m for the Volve platform wells. It is a known trap, and one Volve check-shot table turned out to be referenced that way.

Seismic arrives as two-way time, and velocities from check shots convert it to depth. Where the picks and the check shots were made independently they disagree by tens of metres in the worst case. Even after the Volve horizons were adjusted to the wells, the reservoir surface misses the picks by metres typically and by about a hundred in the worst case.

Typical errors combine to about 4 m at the reservoir. The largest on file combine to about 169 m. That is the honest width of the answer to the question "how deep is it?", before any interpretive judgement has been made.

Between the wells the surface is drawn, not measured

Take one surface, the top of the Ty Formation, along a 4.2 km line between wells. At the 24 well picks near the line (circles) the depth was observed and its time comes from a check-shot table. Everywhere between them the surface is drawn, by an interpreter, by software, or by both.

The base survey gives one surface and the reprocessed survey another. They agree on the broad shape and differ in the detail. Along this line they differ by a median 17 ms and by up to 40 ms, which is up to about 47 m of depth at the Volve average velocity.

Neither is wrong. Neither passes through the picks either: on average they miss them by 30 and 28 ms.

The textbook picture is that interpretations agree near the wells and part away from them. The Volve versions show a weaker form of it. Within a quarter of a kilometre of a well pick the median difference is already 4 to 20 ms, depending on the surface. Beyond two kilometres, where 3 of the 4 surfaces have enough nodes to compare, it is 5 to 19 ms.

One time, six depths

Converting time to depth needs a velocity, and the velocity comes from check shots in a few wells. Volve has 6 check-shot tables from 4 wellbore folders. Read every one at 2.65 seconds of two-way time and the depth comes back between 2,992 and 3,060 m below sea level, a spread of 68 m.

Close in, the curves fan out. Some of the spread is real, because the wells are kilometres apart and the rock between them changes. Some of it is measurement. A horizon mapped in time can be placed in depth anywhere inside that band, and the trap's size changes with it. Between the wells there is no way to say which table applies, which is the point.

The depth of the oil-water contact decides how much of a structure holds oil. On the smoothed Hugin top surface the area inside the closing contour does not grow smoothly with depth. Where the contact drops below a saddle that joins two highs, the trap takes in the second high at once, and the curve steps.

Volve's 2005 plan for development gave the contact as a distribution: P90 3,105 m, P50 3,135 m, P10 3,260 m below sea level, with P90 the shallow, low case.

The area is 7.5 km² at the P90 contact and 19.7 km² at the P50, 2.6 times as much for 30 m more depth, because the P50 contact lies just below the saddle. The P10 contact lies deeper than the mapped surface can hold.

Carried through to oil, the contact becomes a curve

Carry the contact through to recoverable oil and the width of the answer becomes visible. With the closure curve above, the plan's contact distribution and illustrative ranges for pay, porosity, saturation, shrinkage and recovery (20,000 draws, parameters in the ledger), the simulation gives a P90 of 8, a P50 of 18 and a P10 of 34 million Sm³. The high case is 4.3 times the low.

The exercise is illustrative and is not an estimate of Volve: every range was chosen for the story, and 13% of the draws fall deeper than the mapped surface and take its deepest area. Its shape is the shape every such number has. Weather forecasters publish the same thing when they run 51 versions of tomorrow and show how far they spread.

Twenty years of one field's number

Drilling and production are the test of every estimate. Sodir has published its own recoverable estimate for Volve each year since 2,005: 13.7 million Sm³ of oil equivalent at first, 15.3 at the peak in 2,008, 9.2 at the low in 2,010, and 11.4 in 2,025, with the field produced out. The highest estimate was 1.7 times the lowest, for the same rock, as the wells and the production history arrived.

Half the fields grew, half shrank

Volve is not unusual. For the 59 Norwegian fields with a development plan approved since 2003 and at least five years of Sodir snapshots, the latest estimate divided by the first is 1.02 at the median, but 0.31 at the 10th percentile and 1.91 at the 90th.

47% fell by more than five per cent and 47% grew by more than that; 17% at least halved and 8% at least doubled. The median estimate was about right. Almost no single field was, and Volve, highlighted, is one dot among them.

Three words for any subsurface claim

Every number above carries one of three words. Observed means measured or published, with a source: the log, the trace, Sodir's estimate. Derived means calculated from observed data by a stated method: the distance between wells, the tuning thickness, the fan. Interpreted means dependent on a model or a judgement, and given with its range: the horizons, the closure area, the simulated volume.

Other trades infer between boreholes and live with the consequences. A review of 84 tunnels found contract costs rising as the length of exploration drilling fell relative to the tunnel, and hydropower projects that had spent on average under 1 per cent of their cost on investigation before design overran by 27 per cent.

The subsurface case is the same case with deeper holes.

The questions to ask of any claim about the subsurface are the same three: which word applies, what it was compared with, and how wide the range is. The wells remain the only points where the rock has been touched. Everything between them is echo and inference.