Wellbore Stability and Geomechanics Calculator

Geomechanics skill for wellbore stability analysis, drilling window design, and in-situ stress characterization. Covers the full workflow from log-derived overburden stress through Kirsch borehole wall stresses to safe mud weight selection. Calibrated for Appalachian/Marcellus conditions.

Important: Wellbore stability analysis requires calibration to local well data. The Appalachian reference parameters provided here are representative but basin conditions vary significantly. Always calibrate against offset well data (formation tests, mud logs, caliper, image logs) before applying to a new well. Consult a geomechanics specialist for HPHT or complex well paths.

Module 1 — Vertical (Overburden) Stress

Capabilities

Overburden stress from density log integration
Simplified overburden estimation from average density assumption
Effective overburden stress using Biot coefficient
PNGE applications: input to horizontal stress models, pore pressure prediction, fracture gradient calculation

Overburden Stress Definition

The vertical (overburden) stress S_v is the weight of all rock and fluid above the point of interest:

S_v = integral[rho(z) * g * dz]  from 0 to z

In field units (psi), with depth z in feet and density RHOB in g/cc:

S_v(psi) = integral[RHOB(z) * 0.4335 * dz]

Where 0.4335 converts g/cc * ft to psi (= 0.4335 psi per ft per g/cc).

Simplified (average density):

S_v = rho_avg * 0.4335 * z    (psi, z in ft, rho in g/cc)

Typical Overburden Gradients by Depth

Depth Range	Typical Gradient	Notes
0-3,000 ft	0.85-0.95 psi/ft	Shallow, lower density sediments
3,000-7,000 ft	0.95-1.05 psi/ft	Normal compaction
7,000-12,000 ft	1.0-1.1 psi/ft	Fully compacted, higher density
Appalachian (Marcellus depth)	~1.0-1.05 psi/ft	At 6,000-8,500 ft

Log-Based Overburden Calculation

import math

def overburden_from_log(depths_ft, rhob_gcc):
    """
    Calculate overburden stress from density log.
    depths_ft: list of depth values (measured from surface, ft)
    rhob_gcc: list of bulk density values at each depth (g/cc)
    Returns: list of S_v values in psi at each depth
    """
    conv = 0.4335  # psi/(ft * g/cc)
    Sv = [0.0]
    for i in range(1, len(depths_ft)):
        dz = depths_ft[i] - depths_ft[i-1]
        rho_avg = (rhob_gcc[i] + rhob_gcc[i-1]) / 2
        Sv.append(Sv[-1] + rho_avg * conv * dz)
    return Sv

# Example: 3-layer overburden for 8,000 ft well
depths = [0, 2000, 5000, 8000]
rhob   = [2.10, 2.45, 2.60, 2.65]  # g/cc (increases with compaction)

Sv = overburden_from_log(depths, rhob)
print("Depth (ft) | Sv (psi) | Sv gradient (psi/ft)")
print("-" * 50)
for i, (d, sv) in enumerate(zip(depths, Sv)):
    grad = sv / d if d > 0 else 0
    print(f"{d:10,} | {sv:8,.0f} | {grad:.4f}")

Effective Overburden Stress

The effective overburden (Terzaghi effective stress principle):

sigma_v = S_v - alpha * P_p

Where alpha = Biot coefficient (0.6-1.0 for porous rock; 1.0 is conservative).

For Marcellus shale: alpha = 0.7-0.9 (lower than clean sandstone due to low porosity).

Module 2 — Pore Pressure

Capabilities

Hydrostatic pore pressure for normal-pressured formations
Eaton method for pore pressure from sonic or resistivity logs
Equivalent mud weight (EMW) conversion
PNGE applications: effective stress calculation, mud weight floor, cap rock integrity

Normal Pore Pressure Gradients

Fluid Type	Gradient (psi/ft)	Gradient (ppg equivalent)
Fresh water	0.433	8.33
Seawater	0.442	8.5
Formation brine (typical)	0.452-0.465	8.7-8.9
Marcellus brine (high salinity)	0.462-0.480	8.9-9.2

Marcellus shale context (WV): The Marcellus at 6,000-8,500 ft TVD in West Virginia is generally normally pressured or slightly overpressured in the core of the basin. Use 0.46-0.47 psi/ft as a reasonable default.

Eaton Method (Resistivity-Based)

Overpressure from compaction disequilibrium can be detected from resistivity log trends:

P_p = S_v - (S_v - P_p_normal) * (Ro/Rn)^1.2

Where:

Ro = observed resistivity at depth of interest (ohm-m)
Rn = normal (expected) resistivity at same depth from trend line (ohm-m)
Exponent 1.2 is Eaton's empirical value (commonly used; range 0.6-2.0)

Sonic (interval transit time) version:

P_p = S_v - (S_v - P_p_normal) * (DTCn/DTC)^3.0

Where DTC = observed transit time, DTCn = normal trend transit time.

def eaton_resistivity(Sv_psi, Pp_normal_psi, Ro, Rn, n=1.2):
    """
    Eaton pore pressure from resistivity log.
    Sv_psi: overburden stress (psi)
    Pp_normal_psi: normal pore pressure at this depth (psi)
    Ro: observed resistivity (ohm-m)
    Rn: normal trend resistivity (ohm-m)
    n: Eaton exponent (default 1.2)
    """
    Pp = Sv_psi - (Sv_psi - Pp_normal_psi) * (Ro / Rn)**n
    return Pp

# Example: 7,500 ft depth
Sv = 7875
Pp_n = 7500 * 0.46
Ro = 8.0   # observed resistivity
Rn = 12.0  # normal trend (higher = more compacted = normal)

Pp_calc = eaton_resistivity(Sv, Pp_n, Ro, Rn)
EMW = Pp_calc / (7500 * 0.052)
print(f"Eaton pore pressure: {Pp_calc:.0f} psi")
print(f"Equivalent mud weight: {EMW:.2f} ppg")

Equivalent Mud Weight (EMW)

Convert any pressure to equivalent mud weight at a given depth:

EMW (ppg) = P (psi) / (0.052 * depth_ft)

Module 3 — Horizontal Stress Estimation

Capabilities

Minimum horizontal stress (S_hmin) from poroelastic model
Maximum horizontal stress (S_Hmax) from stress polygon (Zoback frictional limit)
Stress regime classification
Appalachian reference stress gradients and stress orientation
PNGE applications: hydraulic fracture orientation, wellbore stability design

Poroelastic Model for S_hmin

The minimum horizontal stress from poroelastic theory (for a laterally constrained basin with no tectonic strain):

S_hmin = [nu/(1-nu)] * (S_v - alpha*P_p) + alpha*P_p + S_tect

Where:

nu = Poisson's ratio of the rock
alpha = Biot coefficient
P_p = pore pressure
S_tect = tectonic stress component (can be positive or negative)

For a basin with no active tectonic loading (S_tect = 0):

S_hmin = [nu/(1-nu)] * (S_v - alpha*P_p) + alpha*P_p

Frictional Equilibrium (Zoback Stress Polygon)

The maximum horizontal stress is bounded by the frictional strength of pre-existing faults. For coefficient of friction mu_f:

(S1/S3)_max = [(mu_f^2 + 1)^0.5 + mu_f]^2

Typical rock friction coefficient: mu_f = 0.6-0.8 (Byerlee's law).

Appalachian/Marcellus Reference Stress State

The Appalachian basin is in a strike-slip faulting regime in the deep Devonian/Mississippian section where the Marcellus resides:

S_Hmax > S_v > S_hmin

Appalachian reference stress gradients (TVD depth range 6,000-9,000 ft):

Stress Component	Gradient (psi/ft)	Gradient (ppg)	Notes
S_v (overburden)	1.00-1.05	19.2-20.2	From density log
P_p (pore pressure)	0.46-0.47	8.85-9.04	Normal-pressured WV
S_hmin	0.65-0.75	12.5-14.4	From ISIP/closure data
S_Hmax	0.80-0.95	15.4-18.3	From image logs, LOT
S_Hmax orientation	N60-80E	—	ENE-WSW, consistent regionally

Source: Multiple published studies on Appalachian/Marcellus geomechanics (Lash and Engelder, 2011; Gale et al., 2014; Zoback et al., various).

def horizontal_stress_poroelastic(Sv, Pp, nu, alpha, S_tect=0):
    """
    Estimate minimum horizontal stress using poroelastic model.
    All pressures in psi, same depth.
    S_tect: tectonic stress additive term (psi). Positive = compression.
    """
    sigma_v_eff = Sv - alpha * Pp
    Shmin = (nu / (1 - nu)) * sigma_v_eff + alpha * Pp + S_tect
    return Shmin

# Marcellus at 7,500 ft TVD
depth = 7500
Sv = depth * 1.02
Pp = depth * 0.465
nu = 0.25
alpha = 0.8

Shmin_pe = horizontal_stress_poroelastic(Sv, Pp, nu, alpha)
Shmin_ref_lo = depth * 0.65
Shmin_ref_hi = depth * 0.75
Shmax_est = depth * 0.87

print(f"Depth: {depth} ft")
print(f"S_v:   {Sv:,.0f} psi  ({Sv/depth:.3f} psi/ft)")
print(f"P_p:   {Pp:,.0f} psi  ({Pp/depth:.3f} psi/ft)")
print(f"\nPoroelastic S_hmin (no tectonic): {Shmin_pe:,.0f} psi ({Shmin_pe/depth:.3f} psi/ft)")
print(f"Appalachian reference range:      {Shmin_ref_lo:,.0f}-{Shmin_ref_hi:,.0f} psi")
print(f"Estimated S_Hmax:                 {Shmax_est:,.0f} psi ({Shmax_est/depth:.3f} psi/ft)")

if Sv > Shmax_est > Shmin_pe:
    regime = "NORMAL FAULTING (S_v > S_Hmax > S_hmin)"
elif Shmax_est > Sv > Shmin_pe:
    regime = "STRIKE-SLIP (S_Hmax > S_v > S_hmin)"
elif Shmax_est > Shmin_pe > Sv:
    regime = "REVERSE FAULTING (S_Hmax > S_hmin > S_v)"
else:
    regime = "INDETERMINATE"
print(f"Stress regime: {regime}")

Module 4 — Mud Weight Window (Kirsch Equations)

Capabilities

Kirsch equations for stress concentration at borehole wall
Minimum mud weight to prevent shear failure (borehole breakout)
Maximum mud weight to prevent tensile fracture initiation
Complete mud weight window calculation with risk classification
PNGE applications: MW selection, casing seat design, well planning

Kirsch Equations for Vertical Borehole

For a vertical borehole in a biaxial far-field stress (S_Hmax, S_hmin), the total stresses at the borehole wall (r = r_w) at azimuth theta from S_Hmax:

Total hoop (tangential) stress:

sigma_theta = (S_Hmax + S_hmin) - 2*(S_Hmax - S_hmin)*cos(2*theta) - P_mud

Total radial stress (at borehole wall):

sigma_r = P_mud    (boundary condition — support pressure equals mud pressure)

Effective stresses (subtract pore pressure where formation is permeable):

sigma_theta_eff = sigma_theta - P_p
sigma_r_eff = sigma_r - P_p = P_mud - P_p

Critical Azimuths

At theta = 90 degrees (S_hmin direction — breakout location): The hoop stress is maximum compressive here:

sigma_theta_max = 3*S_Hmax - S_hmin - P_mud
sigma_theta_eff(breakout) = 3*S_Hmax - S_hmin - P_mud - P_p

At theta = 0 degrees (S_Hmax direction — tensile fracture location): The hoop stress is minimum here:

sigma_theta_min = 3*S_hmin - S_Hmax - P_mud
sigma_theta_eff(frac) = 3*S_hmin - S_Hmax - P_mud - P_p

Failure Criteria

Shear failure (breakout) — Mohr-Coulomb:

Breakout initiates when the effective hoop stress exceeds the rock strength. With sigma_r_eff = 0 at the borehole wall (free surface approximation):

Breakout when: sigma_theta_eff(breakout) > UCS
i.e., 3*S_Hmax - S_hmin - P_mud - P_p > UCS

Solving for minimum mud weight to prevent breakout:

P_mud_min(shear) = 3*S_Hmax - S_hmin - P_p - UCS

Tensile fracture initiation:

Tensile fracture initiates when effective hoop stress at theta=0 goes sufficiently tensile to overcome the rock's tensile strength T_0:

Frac initiates when: sigma_theta_eff(frac) < -T_0
i.e., 3*S_hmin - S_Hmax - P_mud - P_p < -T_0

Solving for maximum mud weight:

P_mud_max = 3*S_hmin - S_Hmax - P_p + T_0

Conservative upper bound (zero tensile strength):

P_mud_max_conservative = 3*S_hmin - S_Hmax - P_p

And the ultimate upper limit is always S_hmin (fractures extend when wellbore pressure equals the minimum principal stress):

P_mud_upper_limit = S_hmin  (absolute maximum — reopens existing fractures)

In practice: use min(3*S_hmin - S_Hmax - P_p + T_0, S_hmin).

Full Mud Weight Window Calculation

import math

def mud_weight_window(depth_ft, Sv_grad, Shmin_grad, SHmax_grad, Pp_grad,
                      UCS_psi, phi_deg=30, T0_psi=None, alpha=1.0):
    """
    Calculate safe mud weight window for a vertical borehole.
    All gradient inputs in psi/ft.
    Returns a dict with MW limits in psi and ppg.
    """
    Sv    = Sv_grad    * depth_ft
    Shmin = Shmin_grad * depth_ft
    SHmax = SHmax_grad * depth_ft
    Pp    = Pp_grad    * depth_ft
    T0    = T0_psi if T0_psi is not None else 0.1 * UCS_psi

    # Mohr-Coulomb friction
    phi = math.radians(phi_deg)
    q = (1 + math.sin(phi)) / (1 - math.sin(phi))

    # Minimum MW: prevent shear failure at breakout azimuth
    MW_min_shear = 3 * SHmax - Shmin - Pp - UCS_psi

    # Minimum MW: prevent kick (must exceed pore pressure)
    MW_min_kick = Pp

    MW_min = max(MW_min_shear, MW_min_kick)

    # Maximum MW: prevent tensile fracture
    MW_max_kirsch = 3 * Shmin - SHmax - Pp + T0
    MW_max_absolute = Shmin  # hard upper limit
    MW_max = min(MW_max_kirsch, MW_max_absolute)

    def ppg(P): return P / (0.052 * depth_ft) if depth_ft > 0 else 0

    window_psi = MW_max - MW_min
    window_ppg = ppg(MW_max) - ppg(MW_min)

    return {
        "depth_ft": depth_ft,
        "Sv_psi": Sv, "Shmin_psi": Shmin, "SHmax_psi": SHmax, "Pp_psi": Pp,
        "UCS_psi": UCS_psi, "T0_psi": T0,
        "MW_min_psi": MW_min, "MW_max_psi": MW_max,
        "MW_min_ppg": ppg(MW_min), "MW_max_ppg": ppg(MW_max),
        "MW_min_kick_psi": MW_min_kick, "MW_min_kick_ppg": ppg(MW_min_kick),
        "MW_min_shear_psi": MW_min_shear, "MW_min_shear_ppg": ppg(max(MW_min_shear, 0)),
        "window_psi": window_psi, "window_ppg": window_ppg,
    }

# Marcellus at 7,500 ft TVD (WV) — base case
res = mud_weight_window(
    depth_ft=7500,
    Sv_grad=1.02,
    Shmin_grad=0.70,
    SHmax_grad=0.87,
    Pp_grad=0.465,
    UCS_psi=10000,
    phi_deg=30,
    alpha=0.8
)

print(f"{'='*60}")
print(f"WELLBORE STABILITY — {res['depth_ft']:,} ft TVD")
print(f"{'='*60}")
print(f"S_v:    {res['Sv_psi']:6,.0f} psi  |  {res['Sv_psi']/res['depth_ft']:.3f} psi/ft")
print(f"S_Hmax: {res['SHmax_psi']:6,.0f} psi  |  {res['SHmax_psi']/res['depth_ft']:.3f} psi/ft")
print(f"S_hmin: {res['Shmin_psi']:6,.0f} psi  |  {res['Shmin_psi']/res['depth_ft']:.3f} psi/ft")
print(f"P_p:    {res['Pp_psi']:6,.0f} psi  |  {res['Pp_psi']/res['depth_ft']:.3f} psi/ft")
print()
print(f"MW min (kick):   {res['MW_min_kick_ppg']:.2f} ppg")
print(f"MW min (shear):  {res['MW_min_shear_ppg']:.2f} ppg  <- CONTROLS")
print(f"MW max (frac):   {res['MW_max_ppg']:.2f} ppg")
print(f"Window:          {res['window_ppg']:.2f} ppg")
risk = "LOW" if res['window_ppg'] > 1.5 else ("MODERATE" if res['window_ppg'] > 0.5 else "HIGH")
print(f"Risk:            {risk}")

Module 5 — Breakout Analysis and UCS from Logs

Capabilities

Breakout angular half-width from Mohr-Coulomb criterion
UCS estimation from sonic log (McNally, Militzer correlations)
Breakout depth (radial extent) estimation
PNGE applications: caliper interpretation, image log analysis, strength calibration

Breakout Angular Width

The angular half-width of borehole breakout is the angle from the S_hmin azimuth to the edge of the failed zone. Beyond this angle, the borehole wall is intact:

Breakout occurs at azimuth theta where sigma_theta_eff > UCS. Setting sigma_theta_eff(theta) = UCS and solving:

cos(2*theta_BO) = [(S_Hmax + S_hmin) - P_mud - P_p - UCS] / [2*(S_Hmax - S_hmin)]

If RHS > 1: no breakout (stable at this MW)
If RHS < -1: entire wall fails (highly unstable)
Otherwise: theta_BO is measured from S_Hmax direction; breakout half-width from S_hmin direction = 90 - theta_BO

Total breakout width = 2 * halfwidth.

UCS from Sonic Log

When no core data is available, estimate UCS from the sonic log DTC (interval transit time, us/ft):

McNally (1987) — shales and mudstones:

UCS_MPa = 1200 * exp(-0.036 * DTC_usft)

Militzer and Stoll (1973) — sandstones:

UCS_MPa = (7682 / DTC_usft)^1.82

Typical Marcellus DTC range: 55-75 us/ft, giving UCS = 8,000-18,000 psi.

import math

def ucs_from_dtc_shale(dtc_usft):
    """McNally (1987) UCS for shales from sonic log DTC."""
    UCS_MPa = 1200 * math.exp(-0.036 * dtc_usft)
    UCS_psi = UCS_MPa * 145.04
    return UCS_MPa, UCS_psi

def breakout_halfwidth_deg(SHmax, Shmin, Pp, Pmud, UCS_psi):
    """
    Breakout half-width from S_hmin azimuth (degrees).
    Returns 0 if no breakout, 90 if entire wall fails.
    All inputs in psi.
    """
    num = (SHmax + Shmin) - Pmud - Pp - UCS_psi
    den = 2 * (SHmax - Shmin)
    if abs(den) < 1e-6:
        return 0.0
    cos_2theta = num / den
    if cos_2theta > 1.0:
        return 0.0   # no breakout
    if cos_2theta < -1.0:
        return 90.0  # entire wall fails
    theta_from_SHmax = math.degrees(math.acos(cos_2theta)) / 2
    halfwidth = 90.0 - theta_from_SHmax
    return max(0.0, halfwidth)

# Marcellus sensitivity: MW=9.5 ppg at 7,500 ft
depth = 7500
SHmax = 0.87 * depth
Shmin = 0.70 * depth
Pp = 0.465 * depth
Pmud = 9.5 * 0.052 * depth

print("UCS and Breakout Width Sensitivity (MW = 9.5 ppg, 7,500 ft)")
print("-" * 65)
print(f"{'DTC (us/ft)':>12} | {'UCS (psi)':>10} | {'UCS (MPa)':>9} | {'Breakout HW (deg)':>17} | {'Total (deg)':>11}")
print("-" * 65)
for dtc in [55, 60, 65, 70, 75]:
    ucs_MPa, ucs_psi = ucs_from_dtc_shale(dtc)
    hw = breakout_halfwidth_deg(SHmax, Shmin, Pp, Pmud, ucs_psi)
    print(f"{dtc:12.0f} | {ucs_psi:10,.0f} | {ucs_MPa:9.0f} | {hw:17.1f} | {2*hw:11.1f}")

Module 6 — Wellbore Stability Risk Classification

Risk Classification Framework

Window (ppg)	Risk Level	Typical Field Response
> 2.0	VERY LOW	Standard practices, monitor caliper
1.0-2.0	LOW	Standard + caliper log every string
0.5-1.0	MODERATE	Enhanced monitoring, ECD management, real-time PWD
0.25-0.5	HIGH	Managed pressure drilling, careful ECD control
< 0.25	CRITICAL	MPD required, smaller MW increments, review casing architecture

Risk Factors Narrowing the Window

Risk Factor	Effect	Mitigation
Natural fractures	Reduces effective rock strength	Lower max MW limit; use weakened UCS
Swelling clays (illite/smectite)	Time-dependent weakening	Inhibitive mud (KCl), minimize exposure time
Laminated shale	Bedding-parallel failure	Check well azimuth relative to bedding dip
High tectonic stress (SHmax/Shmin > 1.5)	Wide anisotropy, larger breakout zone	Increase MW; evaluate deviated azimuth
Abnormal pore pressure	Shifts both bounds	Accurate Pp prediction is critical
High ECD during drilling	Effective MW increase	Optimize flow rate and pipe rotation

Deviated Well Stability

For deviated or horizontal wells, the effective stress concentration at the borehole wall depends on wellbore inclination and azimuth relative to all three principal stresses. Key points for Marcellus horizontal wells:

NW-SE azimuth wells (perpendicular to ENE S_Hmax): Generally the most stable orientation. S_Hmax acts axially along the borehole, reducing stress concentration at the borehole wall.
ENE-WSW azimuth wells (parallel to S_Hmax): Higher stress concentration; avoid for horizontal wells if possible.
For a full 3D stability analysis use the Aadnoy and Ong (2003) formulation or a dedicated geomechanics tool. This skill covers the vertical well case.

Stability Profile With Depth

def stability_profile(depths_ft, Sv_grad, Shmin_grad, SHmax_grad,
                       Pp_grad, UCS_psi, T0_psi=None):
    """
    Print stability summary at multiple depths.
    """
    T0 = T0_psi if T0_psi else 0.1 * UCS_psi
    print(f"{'Depth':>7} | {'MW_min':>7} | {'MW_max':>7} | {'Window':>7} | {'Risk'}")
    print(f"{'(ft)':>7} | {'(ppg)':>7} | {'(ppg)':>7} | {'(ppg)':>7} | ")
    print("-" * 55)
    for d in depths_ft:
        res = mud_weight_window(
            depth_ft=d, Sv_grad=Sv_grad, Shmin_grad=Shmin_grad,
            SHmax_grad=SHmax_grad, Pp_grad=Pp_grad,
            UCS_psi=UCS_psi, T0_psi=T0
        )
        risk = "LOW" if res['window_ppg'] > 1.5 else ("MOD" if res['window_ppg'] > 0.5 else "HIGH")
        print(f"{d:7,} | {res['MW_min_ppg']:7.2f} | {res['MW_max_ppg']:7.2f} | {res['window_ppg']:7.2f} | {risk}")

# Marcellus well depth profile
stability_profile(
    depths_ft=[4000, 5000, 6000, 7000, 7500, 8000, 8500],
    Sv_grad=1.02, Shmin_grad=0.70, SHmax_grad=0.87, Pp_grad=0.465,
    UCS_psi=10000
)

Workflow Summary

Step 1 — Identify Calculation

User Request	Module
Overburden gradient, density log integration	Module 1
Pore pressure, EMW, Eaton method	Module 2
Horizontal stress, stress regime, S_hmin/S_Hmax	Module 3
Mud weight window, breakout limit, fracture limit	Module 4
Breakout width, UCS from logs, image log	Module 5
Risk classification, deviated well, stability profile	Module 6

Step 2 — Gather Inputs

Minimum required:

Depth (TVD, ft)
At least one of: density log, average density, or Sv gradient
Pore pressure (or assume hydrostatic)

For full window calculation, also needed:

S_hmin (from ISIP, XLOT, or estimated gradient)
S_Hmax (from image log, stress polygon, or estimated gradient)
UCS (from core, DTC log, or published range for formation)

If user lacks specific data, apply Appalachian reference gradients and state clearly that results are reference estimates pending calibration.

Step 3 — Calculate

Follow the module sequence: S_v → P_p → effective stresses → S_hmin → S_Hmax → Kirsch equations → MW window → risk classification. Use Python (stdlib: math, statistics). Show each step with units and intermediate values.

Step 4 — Output

Input parameters table — all values with units and source (user/default)
In-situ stress state table — S_v, S_Hmax, S_hmin, P_p in psi, psi/ft, ppg
Kirsch hoop stress at critical azimuths
Mud weight window table — min/max in psi and ppg, controlling constraint
Risk classification — window width and risk level
Recommendations — operating MW, ECD limit, monitoring requirements
Caveats — data quality, calibration needs, simplifying assumptions

Output Format

## Wellbore Stability Analysis — [Well or Depth]

### In-Situ Stress State
| Stress | psi | MPa | psi/ft | ppg |
|--------|-----|-----|--------|-----|
| S_v | ... | ... | ... | ... |
| S_Hmax | ... | ... | ... | ... |
| S_hmin | ... | ... | ... | ... |
| P_p | ... | ... | ... | ... |

Stress regime: [NORMAL / STRIKE-SLIP / REVERSE FAULTING]

### Mud Weight Window
| Limit | psi | ppg | Controlling Factor |
|-------|-----|-----|--------------------|
| MW min (kick prevention) | ... | ... | Pore pressure balance |
| MW min (shear failure) | ... | ... | Kirsch + Mohr-Coulomb |
| MW max (fracture initiation) | ... | ... | Kirsch + tensile criterion |
| Window width | — | ... | MW_max - MW_min |

**Risk Level:** [LOW / MODERATE / HIGH / CRITICAL]
**Recommended Operating MW:** [X.X ppg]
**Maximum ECD:** [X.X ppg (= MW_max - 0.3 ppg safety margin)]

**Summary:** [2-3 sentences on stability outlook and recommendation]

**Caveats:**
- [Data source: "Appalachian reference gradients used — calibrate to offset wells"]
- [Assumptions: "Vertical borehole assumed — deviated well requires 3D analysis"]
- [Rock strength: "UCS from log correlation — validate against core if available"]

Error Handling

Condition	Action
MW_min > MW_max (no safe window)	Report zero window; recommend MPD, review casing architecture
MW_min_shear < 0 (very strong rock)	Kick prevention governs; breakout will not occur
UCS not provided	Use Marcellus range 8,000-18,000 psi; report sensitivity at low/mid/high
Only S_hmin available (not S_Hmax)	Use stress polygon upper bound; label as bounding analysis
Depth given as measured depth (MD)	Request TVD; use inclination to estimate TVD if available
Pore pressure given in ppg	Convert: Pp_psi = ppg * 0.052 * depth_ft; confirm with user
Deviated well request	Perform vertical-well analysis; note 3D extension is needed for deviated

Units Reference

Quantity	Field Unit	SI Unit	Conversion
Stress/Pressure	psi	MPa	1 psi = 0.006895 MPa
Depth	ft	m	1 ft = 0.3048 m
Density	g/cc	kg/m^3	1 g/cc = 1,000 kg/m^3
Mud weight	ppg	kg/m^3	1 ppg = 119.8 kg/m^3
Pressure gradient	psi/ft	kPa/m	1 psi/ft = 22.62 kPa/m
EMW conversion	ppg	—	EMW(ppg) = P(psi) / (0.052 * depth_ft)
UCS	psi	MPa	1,000 psi = 6.895 MPa
Sonic log	us/ft	us/m	1 us/ft = 3.281 us/m
Angle	degrees	radians	1 deg = pi/180 rad

See references/equations.md for the complete Kirsch derivation, full Mohr-Coulomb and Mogi-Coulomb failure criteria, and Appalachian basin reference stress gradient table.

wellbore-stability

Wellbore Stability and Geomechanics Calculator

Module 1 — Vertical (Overburden) Stress

Capabilities

Overburden Stress Definition

Typical Overburden Gradients by Depth

Log-Based Overburden Calculation

Effective Overburden Stress

Module 2 — Pore Pressure

Capabilities

Normal Pore Pressure Gradients

Eaton Method (Resistivity-Based)

Equivalent Mud Weight (EMW)

Module 3 — Horizontal Stress Estimation

Capabilities

Poroelastic Model for S_hmin

Frictional Equilibrium (Zoback Stress Polygon)

Appalachian/Marcellus Reference Stress State

Module 4 — Mud Weight Window (Kirsch Equations)

Capabilities

Kirsch Equations for Vertical Borehole

Critical Azimuths

Failure Criteria

Full Mud Weight Window Calculation

Module 5 — Breakout Analysis and UCS from Logs

Capabilities

Breakout Angular Width

UCS from Sonic Log

Module 6 — Wellbore Stability Risk Classification

Risk Classification Framework

Risk Factors Narrowing the Window

Deviated Well Stability

Stability Profile With Depth

Workflow Summary

Step 1 — Identify Calculation

Step 2 — Gather Inputs

Step 3 — Calculate

Step 4 — Output

Output Format

Error Handling

Units Reference