Physics dashboard
Every equation the pressure advisor solves, with its symbols, units, assumptions, validity limits and a number-by-number substitution trace. All values are produced by the shipped solver functions — change an input and every trace below recomputes, so you can validate the physics by hand.
Model editor inputs
Advisor inputs are read from your model editor model “Hydrostatic & surface budget” — 4 of 9 fields mapped from live values and equation results.
| Advisor field | Value | Source |
|---|---|---|
| TVD | 10,000 | input tvd [ft] |
| Reservoir temperature | 170 | advisor default |
| Wellbore pressure | 4,460 | advisor default |
| Mud weight | 12 | input mudWeight [ppg] |
| Pore gradient | 8.6 | advisor default |
| Fracture gradient | 13.8462 | input fracGradient [psi/ft] → ppg (from psi/ft) |
| Annular friction | 350 | input annFriction [psi] |
| Pipe friction | 1,500 | advisor default |
| BHP target | 8,755 | advisor default |
Add a model input or equation named after a field to bind it — unmapped fields keep the advisor default: Reservoir temperature · Wellbore pressure · Pore gradient · Pipe friction · BHP target.
Solved by recommendPressures() on the inputs below — the same function the job builder uses. Bind a well on /well-database and these are your well's numbers.
BHP target
8,755 psi
TVD 10,300 ft · BHT 170 °F
Hydrostatic at TVD
5,063 psi
ρ(T,P) 9.45 ppg · mean T 120 °F
ECD
9.92 ppg
Mud weight 9.50 ppg + annular friction
Max surface pressure
5,192 psi
3,692 psi net above hydrostatic
Breakdown
Estimated breakdown
10,141 psi
Closure 9,641 psi from fracture gradient
Breakdown margin
5,681 psi
BHP target stays below breakdown
Eaton cross-check
8,610 psi
σ_h,min 7,672 psi · k = 0.54
Overburden / pore
10,300 psi / 4,606 psi
σ_v at TVD and pore pressure at TVD
Mud-weight window & margins
Safe window
8.90 ppg – 17.50 ppg
Status: ok
Margin to pore
0.60 ppg
Mud weight above pore-pressure equivalent
Margin to fracture
8.00 ppg
Headroom below fracture-gradient equivalent
Pore / fracture gradient
8.60 ppg / 18.00 ppg
Formation assumptions used for the window
Integrated hydrostatic
5,063 psi
9.45 ppg effective density
ECD at TVD
9.92 ppg
max 9.95 ppg at 258 ft
Tightest frac margin
108 psi
at 258 ft
Tightest pore overbalance
12 psi
at 258 ft
Pressure vs depth (psi)
Margins vs depth (psi)
Stations (12 of 40 solved segments — CSV has all of them)
| TVD (ft) | Temp (°F) | ρ (ppg) | Static (psi) | Circulating (psi) | Pore (psi) | Fracture (psi) | To frac (psi) | Above pore (psi) |
|---|---|---|---|---|---|---|---|---|
| 258 | 71 | 9.48 | 127 | 133 | 115 | 241 | 108 | 12 |
| 1,288 | 81 | 9.47 | 634 | 666 | 576 | 1,205 | 539 | 59 |
| 2,060 | 89 | 9.47 | 1,015 | 1,065 | 921 | 1,928 | 863 | 94 |
| 3,090 | 99 | 9.46 | 1,522 | 1,597 | 1,382 | 2,892 | 1,295 | 140 |
| 3,863 | 106 | 9.46 | 1,902 | 1,996 | 1,727 | 3,615 | 1,620 | 175 |
| 4,893 | 116 | 9.45 | 2,409 | 2,527 | 2,188 | 4,579 | 2,052 | 221 |
| 5,665 | 124 | 9.45 | 2,788 | 2,926 | 2,533 | 5,302 | 2,377 | 255 |
| 6,695 | 134 | 9.44 | 3,294 | 3,457 | 2,994 | 6,267 | 2,810 | 300 |
| 7,468 | 141 | 9.44 | 3,673 | 3,855 | 3,339 | 6,990 | 3,135 | 334 |
| 8,498 | 151 | 9.44 | 4,179 | 4,385 | 3,800 | 7,954 | 3,568 | 379 |
| 9,270 | 159 | 9.43 | 4,558 | 4,783 | 4,146 | 8,677 | 3,894 | 412 |
| 10,300 | 169 | 9.43 | 5,063 | 5,313 | 4,606 | 9,641 | 4,328 | 457 |
Load the “Annular friction & ECD” model in the editor to compute annular velocity, friction loss and ECD from segment diameter, flow rate and fluid properties. Its annularFriction output feeds the advisor’s annular-friction input automatically.
Bingham plastic (τ = YP + PV·γ̇), Herschel–Bulkley (τ = τ₀ + K·γ̇ⁿ) and Power-law (τ₀ = 0) solved on the same annulus. Fann dials are reconstructed from PV/YP (R600 = 2·PV + YP): R600 48.0 · R300 30.0 · R6 6.0 · R3 4.8.
| Law | n | τ₀ (lbf/100ft²) | Regime | Friction (psi) | ECD (ppg) | Surface budget (psi) | Δ ECD vs Bingham |
|---|---|---|---|---|---|---|---|
| Bingham plastic | 1.000 | 12.0 | laminar | 225 | 12.43 | 735 | baseline |
| Herschel–Bulkley | 0.750 | 3.8 | turbulent | 183 | 12.35 | 777 | −0.08 ppg |
| Power-law | 0.678 | 0.0 | turbulent | 167 | 12.32 | 793 | −0.11 ppg |
ECD vs rate — all three laws
Herschel–Bulkley and Bingham diverge by up to 4.86 ppg ECD near 735 gpm. The fit is shear-thinning (n = 0.750, τ₀ = 3.8 lbf/100ft²), so the Bingham answer carries real ECD error at that rate.
Each stored job is solved three ways on its own geometry and mud weight — Bingham plastic (τ = YP + PV·γ̇), Herschel–Bulkley (τ = τ₀ + K·γ̇ⁿ) and Power-law (τ₀ = 0). Jobs with a stored Fann sweep use their own regressed n / K / τ₀; the rest fall back to the shared PV/YP dials. Tolerance 0.05 ppg ECD.
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Each stored job is solved three ways at identical inputs: the shipped Bingham-plastic solver (the advisor reference), the live model-editor equations, and Herschel–Bulkley (τ = τ₀ + K·γ̇ⁿ) fitted to the Fann sweep. Model deltas are ≈0 with the stock model loaded; the Herschel–Bulkley column shows where shear-thinning (n < 1) changes ECD and the surface budget on your real jobs.
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| Equation | Advisor | Editor | Δ | Δ % |
|---|---|---|---|---|
| Hydrostatic pressure [psi] 0.052 * mudWeight * tvd | 5,062.73 | 5,088.20 | +25.47 | +0.503 |
| Equivalent circulating density [ppg] mudWeight + annFriction / (0.052 * tvd) | 9.92 | 9.97 | +0.05 | +0.479 |
| Breakdown pressure [psi] fracGradient * tvd | 10,140.80 | 9,640.80 | -500.00 | -4.931 |
| Surface budget [psi] max(pBreakdown - pHydro - annFriction, 0) | 5,192.27 | 4,302.60 | -889.67 | -17.135 |
Hydrostatic pressure: Advisor corrects mud density for column temperature and pressure (ρ(T,P)); the editor equation uses the nominal pit density.
Equivalent circulating density: Same ρ(T,P) correction as hydrostatic, expressed as density.
Breakdown pressure: Advisor adds rock tensile strength on top of closure (fracture gradient × TVD) and cross-checks against a Hubbert–Willis / Eaton stress model.
Surface budget: Advisor budgets to the BHP target (BHP target − hydrostatic + pipe friction); the editor equation budgets to breakdown instead, so the two answer different questions.
Editor inputs overridden with this well's values: True vertical depth = 10,300.00 ft, Mud weight = 9.50 ppg, Annular friction = 250.00 psi, Fracture gradient = 0.94 psi/ft.
Store the well, parameters and solved results of each advisor run, then compare any two scenarios side by side to see how a change moved BHP target, ECD, breakdown and margins.
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Closed form p_hydro
5,062.7 psi
Integrated (40 seg)
5,062.8 psi
Residual
0.040 psi
Residual (tol ±0.25%)
0.0008 %
First loss depth
none
First influx depth
none
Agreement
within tolerance
Surface temperature
70 °F
Thermal expansion α
0.00021 1/°F
Compressibility c_f
0.000003 1/psi
Overburden gradient
1 psi/ft
Poisson's ratio ν
0.35
Tensile strength T₀
500 psi
Average fluid temperature over the column, used to thermally expand the mud from its 60 °F pit measurement.
T_bar = (T_surf + T_bh) / 2
Symbols and units
| Symbol | Meaning | Units | Source | Value |
|---|---|---|---|---|
| T_surf | Surface / mud-pit temperature | °F | physics constant | 70.00000 |
| T_bh | Static bottom-hole (reservoir) temperature | °F | your input | 170.00000 |
Numeric substitution trace
- (70 + 170) / 2= 120.0000 °F
Assumptions
- Linear geotherm between surface and bottom-hole temperature.
- Static (non-circulating) column; no cool-down from injection is credited here.
Validity limits
- Under sustained cold injection the true column is cooler than this average — apply the cooling credit path instead.