Mud Weight Window

Summary

The mud weight window is the range of mud weights that keeps a well open: above the larger of the Pore pressure (equivalent mud weight) and the collapse mud weight, and below the smaller of the Minimum horizontal stress (equivalent mud weight) and the breakdown mud weight. It ties together pore pressure, the stress model and rock strength into the one chart a drilling engineer uses. Its width, and where the planned mud weight sits in it, are the result.

Inputs and outputs

Equations

Every stress and pressure is expressed as an equivalent mud weight, the pressure in psi divided by \(0.052\) times true vertical depth in feet:

The calculator builds the stresses from the gradients. The minimum horizontal stress is Eaton's uniaxial strain, and the maximum horizontal stress is set from the minimum with the stress ratio \(\gmAniso\), the ratio of effective maximum to effective minimum horizontal stress:

Collapse and breakdown are those of the previous page, with friction factor \(\gmQf\):

The window is bounded below by the larger of pore pressure and collapse, and above by the smaller of the minimum horizontal stress (the pressure at which existing fractures open and fluid is lost) and the breakdown pressure:

Single-value calculator

Behavior

The depth plot uses fixed gradients for the vertical stress (19 ppg), pore pressure (9 ppg) and a fixed UCS of 30 MPa, so that the only depth effect is the strength term, which is a fixed pressure and so becomes a smaller share of the mud weight as depth increases. This is an illustration of how to read the figure, not a realistic well: a real window comes from the log-derived stress and strength curves. At 3000 ft the collapse mud weight is 4.19 ppg, below the pore pressure, so the lower limit is the pore pressure (9.00 ppg). At 10000 ft it is 9.07 ppg (lower limit 9.07) and at 18000 ft it is 10.00 ppg, which is now above the pore pressure and sets the lower limit. The upper limit is set by Shmin (12.33 ppg at every depth here, since the gradients are fixed), because the breakdown mud weight is higher (15.77 ppg at 10000 ft). At 10000 ft the window is 9.07 to 12.33 ppg, 3.26 ppg wide, and a planned mud weight of 10.5 ppg sits 1.43 ppg above the lower limit and 1.83 ppg below the upper limit. Three changes alter the window. Raising the pore pressure to 13 ppg raises the lower limit to 13.00 ppg and leaves a width of 2.00 ppg. A higher stress ratio of 1.8 raises collapse to 10.57 ppg and lowers breakdown to 13.77 ppg (the window is 1.76 ppg wide); equal horizontal stresses (ratio 1) widen it to 3.33 ppg. A weak rock, with UCS of 10 MPa, raises the lower limit to 10.47 ppg.

Parameter guidance

Reading a window plot. A standard plot has depth on the vertical axis and mud weight in ppg on the horizontal axis. Four curves are drawn: pore pressure and the collapse mud weight on the left, and the minimum horizontal stress and the breakdown on the right. The window is the area between the larger of the left-hand curves and the smaller of the right-hand ones. The actual or planned mud weight is overlaid. A mud weight to the left of the window risks kicks (below pore pressure) or breakouts and tight hole (below collapse); to the right it risks lost circulation (above Shmin) and fracturing (above breakdown). Where the window narrows to nothing, a casing point is needed.

Pore pressure. From Pore Pressure. It sets both the lower limit directly and, through effective stress, all the stresses.

Moduli, strength and stress. From the Geomechanics and the previous Wellbore Stability pages. If the shear log is modelled, see Shear Log Modeling and Dynamic Elastic Moduli.

Safety margins. The window is a calculated result with large uncertainty. Practical programs add a margin on the lower bound, typically a few tenths of a ppg of overbalance for kick control, and keep the equivalent circulating density, not the static mud weight, below the upper limit. The size of these margins is an operator policy.

Uncertainty. Run the window with a low, mid and high case for pore pressure, SHmax and strength, and plot the envelope. A window that is open only in the mid case is not a plan.

Ppg conversions. The factor 0.052 is psi per foot per ppg. 1 ppg is 0.052 psi/ft, and 1 psi/ft is 19.23 ppg.

Worked example

A mud weight window at 10000 ft from the stress gradients, with a planned mud weight of 10.5 ppg, and the sensitivity of the lower limit to pore pressure and strength:

import math
def window(tvd=10000.0, sv_ppg=19.0, pp_ppg=9.0, nu=0.25, ratio=1.2, ucs_mpa=30.0, ifa=30.0, T=400.0):
    f = 0.052 * tvd
    sv, pp = sv_ppg * f, pp_ppg * f
    sh = nu / (1 - nu) * (sv - pp) + pp
    SH = pp + ratio * (sh - pp)
    q = (1 + math.sin(math.radians(ifa))) / (1 - math.sin(math.radians(ifa)))
    collapse = (3 * SH - sh - ucs_mpa * 145.038 + (q - 1) * pp) / (1 + q) / f
    breakdown = (3 * sh - SH - pp + T) / f
    lower = max(pp_ppg, collapse)
    upper = min(sh / f, breakdown)
    return pp_ppg, collapse, sh / f, breakdown, lower, upper
pp, col, shm, bd, lo, up = window()
print(f"pore pressure {pp:.2f}, collapse {col:.2f}, Shmin {shm:.2f}, breakdown {bd:.2f} ppg")
print(f"window: {lo:.2f} to {up:.2f} ppg, width {up - lo:.2f}")
mw = 10.5
print(f"planned {mw} ppg: {mw - lo:+.2f} ppg above the lower limit, {up - mw:+.2f} below the upper limit")
for label, kw in (('Pp 13 ppg', dict(pp_ppg=13.0)), ('UCS 10 MPa', dict(ucs_mpa=10.0)), ('ratio 1.8', dict(ratio=1.8))):
    r = window(**kw)
    print(f"{label:10s} window {r[4]:.2f} to {r[5]:.2f} ppg (width {r[5] - r[4]:.2f})")

Output

pore pressure 9.00, collapse 9.07, Shmin 12.33, breakdown 15.77 ppg
window: 9.07 to 12.33 ppg, width 3.26
planned 10.5 ppg: +1.43 ppg above the lower limit, +1.83 below the upper limit
Pp 13 ppg  window 13.00 to 15.00 ppg (width 2.00)
UCS 10 MPa window 10.47 to 12.33 ppg (width 1.86)
ratio 1.8  window 10.57 to 12.33 ppg (width 1.76)

Assumptions and limitations

• A vertical well in a stress state where the vertical stress is a principal stress, and with the wall stresses from the Kirsch solution. Inclined and horizontal wells have different windows, and often narrower ones.
• The stress model, the strength and the pore pressure are each correct. The window is built from differences between large numbers, so errors of a few percent in any one input become large errors in the window.
• The upper limit is the smaller of Shmin and the breakdown pressure. Taking Shmin recognises that natural fractures and weak planes open at about that pressure. Some programs allow the mud weight to rise above Shmin, or use leak-off tests as the limit.
• The lower limit is the larger of pore pressure and collapse. Some operators drill below the collapse mud weight and manage breakouts, so that the lower limit is relaxed.
• The static mud weight is the relevant one. During circulation and tripping, the equivalent circulating density and the swab and surge pressures move the downhole pressure above and below it.
• Time effects and chemistry, such as shale swelling, are not included.
• The depth profile in the calculator uses constant gradients and constant strength, which is a simplification. The principle of the chart does not depend on it.

QC checks

• The window's lower limit is never below pore pressure, and its upper limit is never above Shmin, by construction. Check that Shmin is above pore pressure.
• The mud weights actually used in offset wells fall within the window. Where they do not, either the well had problems at that depth, which the logs and reports should show, or the model is wrong there.
• Observed breakouts in image or caliper logs correspond to depths where the mud weight was below the collapse mud weight, and tight hole, cavings and pack-offs line up with them.
• Observed losses correspond to depths where the mud weight or ECD exceeded Shmin or the breakdown pressure. Leak-off and extended leak-off tests are the direct check on the upper limit.
• The window is wide in clean, strong rock and narrow in weak shale, in overpressured intervals and where stress anisotropy is high. A uniform window over variable lithology is a sign of a smoothed input.
• The result is shown with its uncertainty: low and high cases, not a single line.

Going Deeper

The window is the practical product of the whole sequence of pages on this site from the sonic log to the stress state. It is also a good test of that sequence, because its predictions are checked directly by drilling events, which most of the earlier steps lack. For that reason a 1D geomechanical model is calibrated against the drilling history of offset wells: the strength is adjusted until breakouts are predicted where they were seen, and the stress until losses and leak-offs match. A calibrated model is then used to plan the next well. Two cautions follow. Calibration with only one kind of event, usually breakouts, does not constrain the other bound. And a model calibrated on vertical wells does not carry over to deviated wells without the full three-dimensional wall stress, because wellbore trajectory changes the window significantly. In deepwater and in depleted reservoirs the window is narrow, and the techniques that follow from this, such as managed pressure drilling and extra casing strings, are ways of operating in a window that is narrower than the uncertainty in the model.

References

1. Zoback, M.D., 2007. Reservoir Geomechanics. Cambridge University Press.
2. Fjær, E., Holt, R.M., Horsrud, P., Raaen, A.M. and Risnes, R., 2008. Petroleum Related Rock Mechanics, 2nd edition. Elsevier.
3. Moos, D., Peska, P., Zoback, M.D. et al., 2003. Comprehensive wellbore stability analysis utilizing quantitative risk assessment. Journal of Petroleum Science and Engineering, 38(3–4), 97–109.
4. Eaton, B.A., 1969. Fracture gradient prediction and its application in oilfield operations. Journal of Petroleum Technology, 21(10), 1353–1360.

Python reference implementation

Related methods

• Vertical Stress
• Horizontal Stress Methods
• Near-Wellbore Stress State
• Breakout and Breakdown Pressures
• Pore Pressure
• Shear Log Modeling
• UCS Correlations