Pore pressure, fracture gradient and the mud-weight window

Every mud weight is a choice between two failures. Too light and the formation flows into the well; too heavy and the rock fractures and the mud is lost. The space between pore pressure and fracture gradient is the mud-weight window, and on a deep gas well it can close to a few hundredths of an SG. This article builds the window for a 4,600 m well onshore Abu Dhabi, from the logs through the leak-off tests to the casing seats, and checks the key numbers by hand.

What sets the window

Four curves make the window, all expressed as an equivalent mud density so they can be read against the mud weight directly. Here that is SG: 1 SG is 0.0981 bar per metre, 0.433 psi/ft or 8.345 ppg.

Pore pressure is the pressure of the fluid in the rock's pores. Where the pore water connects to surface it is hydrostatic; onshore Abu Dhabi the formation water is a strong brine, so normal pressure is about 1.07 SG, 0.464 psi/ft. Overpressure forms where the water could not escape as the rock was buried. In shale, with almost no permeability, the water ends up carrying part of the load the grains should carry. The shale stays porous for its depth, and its logs show it.

Overburden is the weight of everything above a depth. It bounds the other stresses and starts both the pore-pressure and the fracture calculations.

Fracture gradient is the well pressure at which the rock opens and takes mud. In practice it sits close to the smallest horizontal stress, and the leak-off test at each casing shoe is the one direct measurement of it.

The mud weight has to sit between pore pressure and fracture gradient with margins on both sides: above pore pressure by enough to cover swab when pulling pipe, below the fracture gradient by enough to cover surge and the circulating density. At each casing shoe there is one more margin, for the extra pressure of a kick. Where the margins no longer fit, a casing string has to go in.

The methods

Overburden is the density log integrated from surface. Eaton's method turns the departure of the shale's logs from a normal compaction trend into pore pressure, through the effective stress (overburden less pore pressure). The fracture gradient follows from the same effective stress through a stress ratio.

OBG

overburden gradient at true vertical depth z, from the bulk density ρ_b

P_h

normal (hydrostatic) pore pressure gradient, 1.07 SG here

Δt, Δt_n

shale sonic slowness, and the normal compaction trend's value at the same depth (µs/ft)

R, R_n

shale resistivity and its normal trend

ν

Poisson's ratio in Eaton's fracture relation; in practice a factor fitted to the leak-off tests

The exponents, 3 for sonic and 1.2 for resistivity, are Eaton's published values for the US Gulf Coast. Bowers' method is the common cross-check. It relates sonic velocity to effective stress on a loading curve, V = 5,000 + A·σ^B (ft/s and psi), and adds an unloading branch for pressure from fluid expansion, which Eaton under-reads. Its constants are basin-specific and have to be fitted to normally pressured shale before they mean anything.

Everything rests on the normal compaction trend. It is fitted on shale only, against true vertical depth, over the interval where the shale is known to be normally pressured. Fit it through the top of an overpressured zone and the trend bends towards the anomaly, and every pressure below reads too low.

The example well

The example is a vertical gas well set in conditions typical of onshore Abu Dhabi. Below Neogene sands, marls and evaporites it drills a Paleocene–Eocene carbonate aquifer, a thick Cretaceous carbonate section with two shale intervals, an Upper Jurassic anhydrite and Jurassic carbonates. Then come 550 m of Triassic shale and claystone, overpressured from about 3,720 m, over a Permo-Triassic carbonate gas reservoir at 4,150 m. TD is 4,600 m. Gamma ray, sonic, density and resistivity logs cover the well from 300 m, and the rig floor is 9 m above ground.

The carbonates have no compaction trend to read, so their pore pressure is taken from pressure tests and offset wells: 1.07 SG down to the shale, 1.50 SG in the reservoir. The shales carry the log-derived pressure.

Eaton by hand at 4,000 m

One depth in the overpressured shale, worked through with the trend the engine fitted.

1. The trend. The fitted sonic trend is Δt_n = 55 + 10^{(1.9264 − 0.0001745 z)}. At 4,000 m it gives 71.9 µs/ft. The shale reads 86.4 µs/ft: slower, so more porous than its depth should allow.
2. The ratio. 71.9 / 86.4 = 0.832, and cubed, 0.576.
3. The overburden. Integrated from the density log, 2.41 SG at 4,000 m, or 1.04 psi/ft. Normal pressure is 1.07 SG.
4. Pore pressure. 2.41 − (2.41 − 1.07) × 0.576 = 1.64 SG: 642 bar, 9,310 psi, 13.65 ppg.
5. Fracture gradient. With ν = 0.39, ν / (1 − ν) = 0.639, and 1.64 + 0.639 × (2.41 − 1.64) = 2.13 SG.
6. Sensitivity. Moving the trend by 1 µs/ft moves the pore pressure by 0.03 SG. An exponent of 2.5 or 3.5 instead of 3 gives 1.56 or 1.70 SG.

DrillIQ's engine gives 1.636 and 2.128 SG at the same depth, the same as the hand figures. The last step matters more than the match. The answer depends on a trend line drawn by an interpreter and an exponent borrowed from another basin, and their combined error at 4,000 m is larger than the trip margin.

Reading the window

The overburden rises from 2.19 SG at the 18⅝″ shoe to 2.42 SG at TD, about 1.05 psi/ft. Dense carbonates and the anhydrite keep it high. Pore pressure is normal at 1.07 SG down to about 3,720 m, then climbs 0.59 SG in 365 m to a peak of 1.66 SG at 4,085 m, and falls back to 1.55 SG at the liner shoe and 1.50 SG in the reservoir. The fracture gradient follows its own path: 1.79 SG at 1,250 m, 1.92 SG at the 9⅝″ shoe, then up to 2.14 SG in the overpressured shale, because Eaton's relation lifts the fracture gradient with the pore pressure.

Between the 18⅝″ shoe and 3,640 m the window is wide, 0.58 to 0.74 SG between the mud and the fracture gradient. The 8½″ section is where it closes, and the narrowest point is at its top. The hole needs 1.69 SG at 4,085 m, the peak pore pressure plus a 0.03 SG margin, while the most the section allows is 1.86 SG at 3,660 m, just below the shoe. The need is set at the bottom of the section and the limit at the top, and the 1.71 SG mud weight has to satisfy both.

Finding the top of overpressure

The engine fits the sonic trend on the 144 shale points from 1,250 m down, growing the fit step by step and stopping where the next 150 m of shale runs more than about 7 % off it. Here it stops at 3,720 m. Above that, the shale scatters around the trend. Below it, every shale point is slower, by 14.5 µs/ft at 4,000 m. The carbonates and the anhydrite are left out: they read 50–65 µs/ft whatever their pressure.

The log-based top of overpressure is a prediction until the bit gets there. While drilling the last 100 m of the 12¼″ section, the checks are the corrected d-exponent (Dxc) from rate of penetration, weight, rotary speed and mud density, background and connection gas, cavings at the shakers, torque and drag, and flowline temperature. A Dxc trend that bends away from its own normal trend, with connection gas starting to show, is the signal to stop and set the 9⅝″ casing early.

Three methods and their spread

At 4,000 m the three methods agree within 0.02 SG: 1.64 SG from sonic, 1.63 SG from resistivity and 1.65 SG from Bowers, its loading curve fitted to the normal shale above 3,720 m (A = 83.7, B = 0.52). They agree because this overpressure comes from undercompaction, which all three describe. Where pressure comes from gas generation or fluid expansion instead, the shale unloads, the sonic hardly slows, and Eaton reads low while Bowers' unloading branch does not. Disagreement between methods is a clue to the mechanism; never average it away.

The spread that matters is the uncertainty band. The module's correlated uncertainty runs, 150 draws with 10 % on Eaton's exponent and 5 % on the trend, put the P10 and P90 at 4,000 m at 1.45 and 1.79 SG. The 1.71 SG mud sits between the P50 and the P90: on log evidence alone, more than one case in ten has the shale above the mud weight. This is why the section is drilled with the bottom-hole pressure measured, gas and flow watched at every connection, and a kick tolerance worked out before the shoe is drilled out (see kick tolerance and the kill sheet for the same well).

Calibrating the fracture gradient

Poisson's ratio in Eaton's fracture relation works as a calibration factor, so it is fitted to the shoe tests. The engine's fit, rerunning the study for each trial value, settles on 0.39 with a root-mean-square misfit of 0.026 SG. The fit is good at depth, within 0.005 SG at the 13⅜″ and 9⅝″ shoes. At the 18⅝″ shoe the model says 1.79 SG and the test said 1.74 SG, 0.05 SG lower. The FIT at the liner shoe is a lower bound, since the rock did not break, and the model's 2.10 SG sits above its 2.00 SG, so it counts as no misfit.

Only Poisson's ratio was fitted. Leak-off tests measure the fracture side; letting them move the pore-pressure exponents would tune the shale pressure to fracture data, which a fitting routine will happily do.

Two rules follow for the rig. Design with the model, and drill with the test: the shoe's own leak-off sets the maximum allowable annular surface pressure. At the 9⅝″ shoe that is (1.92 − 1.71) × 0.0981 × 3,640 = 75.0 bar, 1,088 psi. And where a test and the model disagree, as at 1,250 m, the test wins, and the model is recalibrated before the next well.

From the window to casing seats

The module's bottom-up seat selection works from pressure alone. From TD upwards it carries the heaviest mud the open hole needs, 1.69 SG here, and sets a shoe where the fracture gradient less a 0.06 SG kick margin can no longer hold it. On this well that is 895 m, and nothing deeper. By pressure alone, one open hole from 895 m to TD would hold.

That is the minimum. The plan uses four strings below the conductor, for reasons the pressure curves do not show.

• Differential sticking. The 1.71 SG mud against the 1.07 SG Jurassic carbonates at 3,600 m would be (1.71 − 1.07) × 0.0981 × 3,600 = 226 bar, 3,280 psi, of overbalance on permeable rock, above the 2,000–3,000 psi often used as a planning limit. So the 9⅝″ casing covers the carbonates before the mud goes up, with its shoe in the 120 m of normal shale between the last carbonate and the top of overpressure.
• The reservoir. Drilled with 1.71 SG, the reservoir at 4,300 m would see 89 bar of overbalance, enough to damage it and to stick pipe across it. The 7″ liner isolates the shale so the 6″ hole can use 1.56 SG, 25 bar over the reservoir.
• The shallow hole. The 18⅝″ casing covers the loss-prone aquifer carbonates with a shoe in shale; the 13⅜″ covers the Cretaceous carbonates and gives a 1.88 SG shoe for the 12¼″ hole.

The tightest choice is the 9⅝″ seat. Deeper, the shoe is in rock that needs more than the 12¼″ mud; shallower, the carbonates see the heavy mud. That leaves 120 m of hole, which is why the top of overpressure is worth the effort. The loads the strings then carry are worked through in casing design load cases.

A checklist for the rig team

• Fit the normal compaction trend on shale only, against TVD, and know where it stops.
• Run at least two pore-pressure methods in the shale and read the spread, never a single line.
• Check the overburden integral, including the shallow density above the first log.
• Calibrate the fracture gradient to every leak-off test; treat a FIT as a lower bound.
• Use the measured shoe test, never the model, for the maximum allowable annular surface pressure.
• Check each section's window at the shoe and at the peak pressure, with all margins applied.
• Approaching the predicted top of overpressure, watch Dxc, gas and cavings, and be ready to set casing early.
• Rerun the window whenever a test, a kick or a pressure point disagrees with it.

How DrillIQ handles it

DrillIQ's Pore Pressure & Geomechanics module reads the well's logs from WITSML or a LAS file, fits the normal compaction trend automatically on TVD, and runs Eaton on resistivity, sonic and Dxc and Bowers with unloading, on shale and filled across the sands. It offers Eaton, Matthews–Kelly, Hubbert–Willis and a mechanical earth model for the fracture gradient, adds wellbore-stability collapse to the lower limit, calibrates to leak-off, FIT and pressure tests, runs P10–P90 uncertainty, and turns the window into seats and a mud programme by section. While drilling, it checks the ECD at the bit against the window and alerts Well Control. The published window feeds Well Control, Casing & Tubing Design, Hydraulics and Cementing. The numbers above come from that engine and the hand checks shown.

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References

1. Eaton, B.A. The Equation for Geopressure Prediction from Well Logs. SPE 5544, 1975.
2. Eaton, B.A. Fracture Gradient Prediction and Its Application in Oilfield Operations. Journal of Petroleum Technology, SPE 2163, 1969.
3. Bowers, G.L. Pore Pressure Estimation From Velocity Data: Accounting for Overpressure Mechanisms Besides Undercompaction. SPE Drilling & Completion, SPE 27488, 1995.
4. Hottmann, C.E. and Johnson, R.K. Estimation of Formation Pressures from Log-Derived Shale Properties. Journal of Petroleum Technology, SPE 1110, 1965.
5. Jorden, J.R. and Shirley, O.J. Application of Drilling Performance Data to Overpressure Detection. Journal of Petroleum Technology, SPE 1407, 1966.
6. Zoback, M.D. Reservoir Geomechanics. Cambridge University Press, 2007.

About this example. The well in this article is a representative scenario set in typical onshore Abu Dhabi, UAE conditions and worked through with DrillIQ's engines. It is not a client's well, and its figures are not field results.