Why core plugs mislead: core plug kv/kh, bedding and upscaling permeability

A core plug is a few centimetres of rock, usually cut from the cleanest sandstone in the core. In laminated sandstone that choice hides the thin mud layers that control vertical flow, so paired plugs report a kv/kh near 1 while the bed they came from may flow vertically tens to hundreds of times less easily. Getting vertical permeability right means modelling the bedding and upscaling it by flow, not averaging the plugs.

What core plug kv/kh actually measures

Routine core analysis cuts horizontal plugs at regular spacing and, where asked, a vertical plug beside some of them. The ratio of the vertical to the horizontal value in each pair is the core plug kv/kh. It measures the anisotropy of the rock inside the plug: grain fabric, cross-lamination within the sandstone, cement. It cannot measure anything thicker than the plug, and it is biased by where plugs are cut. Laboratories avoid friable, muddy or broken material because it does not survive cutting, so the plug set over-represents clean sandstone.

That is the scale problem in one sentence: the properties that matter for flow are measured on a sample smaller than the heterogeneity that controls them. Ringrose and Bentley's practitioner's guide gives a whole chapter to upscaling flow properties for this reason [1].

Why the ratio matters

kv/kh is one of the most sensitive inputs in a flow model. It decides how fast gas cones down to a producing well, how far injected CO₂ or hydrogen spreads under a seal before it rises, how quickly cold water from a geothermal injector reaches the producer through the layers, and how pressure communicates between zones. If the model uses the plug value, every one of those answers can be badly wrong, and history matching will try to fix it by changing something else.

A worked case on public data: Zeerijp-3A

Well ZEERIJP-03-SIDETRACK1 (ZRP-3A) was drilled by NAM in 2015 into the Rotliegend (Slochteren) sandstone of the Groningen gas field and cored over about 200 m. Its core analysis and logs are public on NLOG, the Dutch subsurface portal run with the Geological Survey of the Netherlands [2]. We ran KAI-Subsurface's workflow on it in the open; the Zeerijp-3A case has the interactive results.

After quality control, which sets aside plugs described as fractured, broken or cracked because they measure the damage rather than the rock, 409 plugs remain in 8 cores between 3,521 and 3,867 m. Among them are 78 vertical–horizontal plug pairs. Their median kv/kh is 0.95. At plug scale the sandstone looks isotropic.

Vertical permeability anisotropy lives in the bedding

Heterolithic and ripple-laminated sandstones interleave sand and mud at centimetre scale. Studies of the Tilje Formation offshore mid-Norway found a coefficient of variation of permeability of about 0.5 within sandstone beds but 1.0 to 4.0 in heterolithic units, and showed that effective vertical permeability is mainly a function of the mudstone fraction, behaving differently above and below the percolation threshold [3]. Once mud drapes become continuous, vertical flow has to cross them or find a way round.

To see what that means for Zeerijp-3A, we built ripple-laminated bedding models (flaser to wavy to lenticular) whose two components come from the same core: clean sandstone at 46 mD, the median of the sandstone plugs, and claystone below the 0.01 mD detection limit. We then solved single-phase flow through each block, vertically and horizontally, and compared the result at 1 m with what plugs cut from the block would report.

At 1 m the modelled kv/kh is 0.46 with 10% mud, 0.052 (about 1:19) with 20%, 0.0043 (about 1:235) with 30% and 0.0028 (about 1:358) with 40%. Horizontal permeability barely notices the mud at first: 39 mD at 10% and 34 mD at 20%, against 46 mD for clean sand. Vertical permeability collapses: 18 mD at 10%, 1.8 mD at 20%, 0.12 mD at 30%.

Now cut plugs from those blocks the way a laboratory does, in competent sandstone. Their median vertical permeability overstates the bed's by a factor of 2.2 at 10% mud, 22 at 20%, 321 at 30%, 955 at 40% and 1,225 at 50%. That is the "20 to 1,200 times" in the case study. Plugs cut at random positions do better but are still biased: their 90th percentile overstates by 13 times at 20% mud and 28 times at 30%.

These bedding models are 2D and two-component, and the mud fractions are scenarios, not measurements from this core. They show the size of the scale effect for this rock, not the measured bed-scale kv/kh of Zeerijp-3A, which would need image logs, vertical interference tests or production data to pin down.

The representative elementary volume

The representative elementary volume (REV) is the smallest sample beyond which a property stops changing as the sample grows. Below it, every sample gives a different answer; above it, samples agree. Nordahl, Ringrose and Wen used REV analysis on a process-based model of a heterolithic interval to rescale core plug data and to quantify uncertainty in log-based porosity and horizontal permeability [4].

In the Zeerijp-3A bedding models, horizontal permeability settles at 4 to 5 cm for 10–20% mud and about 23 cm at 30%. Vertical permeability needs more: 8.5 cm at 10% mud, but 78 cm at 20% and 61 cm at 30%. A 2.5 cm plug is well below the vertical REV of any bedding with continuous mud drapes. At high mud fractions (50–60%) the vertical REV shrinks again, because the rock is now mud with sand lenses and the plug is cut from the minority component.

Upscaling permeability honestly

1. Describe the bedding, not just the plugs. Mud fraction, lamina thickness and continuity from core photos or image logs are the inputs that control kv/kh.
2. Calibrate components on plugs. Use the plugs for what they measure well: the permeability of each component.
3. Upscale by flow. Arithmetic and harmonic averages bracket the answer only for perfect layers. Ripples, lenses and broken drapes need a flow solution on the bedding model [3].
4. Sample each scale for what it can tell you. Where vertical permeability matters, measure the components at lamina scale rather than adding plugs in clean sand: probe-permeameter traverses across the laminae for the sandstone, and dedicated tight-rock (for example pulse-decay) measurements for the mudstone, as in the Tilje studies [3]. Full-diameter vertical measurements on whole core sample more bedding than a plug, but at about 10 cm they are still below the 60 to 80 cm vertical REV of these models, so the bed-scale value has to come from the bedding model or from well tests.
5. Carry the uncertainty. Report a range of kv/kh from several realisations, and keep it through to the reservoir model.

Permeability from logs: where there is no core

Most wells have logs but no core. On Zeerijp-3A, three rock types defined by the flow zone indicator put 96% of the 409 plugs within a factor of 3 of the measured permeability, against 77% for one porosity–permeability trend. Hiding each of the 8 cores in turn and predicting it from logs alone, a random forest placed 60% of plugs within a factor of 3 and 93% within a factor of 10. Rock types predicted from logs did not help (55% within a factor of 3; the right type 59% of the time): logs read about half a metre of rock and cannot see the centimetre laminae that separate the types. Only 44% of the logged interval falls inside the range of cored log responses, and the rest is marked as untrusted. A permeability log is a horizontal estimate at log scale; it does not give kv/kh.

What KAI offers, and what it does not

• The Plug-to-Block Lab builds flaser, wavy or lenticular bedding in the browser, solves its flow and drills virtual plugs, with the 78 Zeerijp-3A plug pairs for comparison.
• The Heterogeneity Lab carries those properties between wells in facies ensembles conditioned on every log.
• KAI-Subsurface offers fixed-price well-log interpretation, rock typing and permeability with its uncertainty, calibrated on your core.

KAI does not drill, cut or measure core, hire out equipment or run field acquisition such as logging or well tests. We work remotely on data you already hold or license. The notebooks behind the Zeerijp-3A case are open, and the NLOG files are fetched from NLOG, not redistributed.

Next step

Open the Plug-to-Block Lab, set the mud fraction of your own laminated interval and see which sample size gives a vertical permeability you can trust. If you have core and logs, ask us for a free quality check of one well's logs.