Coupled Water-Steam Thermal and Pressure Profile Calculator

Integrate water/steam pressure, enthalpy, temperature and equilibrium vapor fraction with heat exchange, friction, acceleration and elevation.

Results

Calculate to view linked results. Default values are examples, not recommended operating inputs.

Calculation sequence

Supply pure-water inlet absolute pressure and specific static enthalpy, total mass flow and a uniform circular pipe. Enthalpy, not an ambiguous saturation temperature alone, determines the liquid/steam split. Enter distance along flow and inclination from horizontal: positive uphill, negative downhill. The solver uses Pa and J/kg internally; displayed MPa and kJ/kg are converted explicitly.
Choose a Darcy friction factor and overall U based on the pipe inside area. These are prescribed closure inputs, not automatic two-phase friction/boiling correlations or recommended values. U represents total resistance to the specified constant surroundings; do not add formation resistance twice. U=0 gives adiabatic flow. The geothermal Ramey history model is separate and is not silently coupled to this constant-surroundings calculation.
At every integration stage, solve the local IAPWS pressure-enthalpy state and update temperature, density and phase fraction. In the two-phase region both phases share saturation temperature and velocity. Solve momentum and total energy together, including changing kinetic energy and signed elevation. The same calculation can cool/condense steam, heat/boil water, or flash water as pressure falls, provided the entire trajectory remains inside the accepted envelope.
Integrate again at tighter tolerance and compare 51 stations. Independently accumulate external heat, friction and gravitational pressure terms, then check integrated total-energy and momentum identities before returning results. The CSV includes pressure, temperature, enthalpy, vapor mass fraction, density, velocity, heat and IF97 phase-region code. A point lying on the saturation-temperature curve is not by itself proof of high steam quality.

Worked check

The synthetic upward case starts at 2 MPa and 900 kJ/kg in a 0.1 m pipe, at 5 kg/s over 200 m, with 550 K surroundings, U=100 W/(m2.K), Darcy fD=0.02 and 90-degree uphill flow. It enters as liquid, then flashes/boils into equilibrium wet steam while pressure and saturation temperature fall. The predicted outlet vapor mass fraction is about 0.07606; the result is not a measured geothermal-well benchmark.

Synthetic examples for reproducibility, not measured field results.

Assumptions and limitations

Steady one-dimensional pure-water homogeneous equilibrium screening model: equal phase velocities and instantaneous thermal/phase equilibrium. No hydrocarbon composition flash, salts/brine, dissolved/noncondensable gas, slip/holdup correlation, metastable nucleation delay, severe slugging, countercurrent flow or reservoir coupling. This is not a general petroleum PVT/production-well simulator.
The complete traverse must stay at 0.1-10 MPa absolute and 273.16-700 K in IF97 regions 1, 2 or 4. Supercritical water is excluded. A coupled acceleration determinant >=0.5 and velocity <=150 m/s are conservative software conditioning gates, not a critical-flow prediction or field-accuracy guarantee. Invalid intermediate states cause rejection, not phase-fraction clipping.
Constant surrounding temperature, prescribed constant Darcy fD (0-0.1) and nonnegative U. No transient wall/formation heat storage, automatic boiling heat-transfer closure, roughness-to-friction calculation, changing area, pumps, fittings, work extraction or heat-source calibration. Numerical conservation and agreement with independent EOS calculations do not replace measured well validation.

Implemented equations

Equilibrium flash and mixture volume

\begin{aligned}G&=\dot m/(\pi D^2/4),\quad u=Gv\\x&=\frac{h-h_f(p)}{h_g(p)-h_f(p)}\\v&=(1-x)v_f+xv_g\\T&=T_{\rm sat}(p)\end{aligned}

Coupled steady momentum and total energy

\begin{aligned}F&=f_DG^2v/(2D)\\\frac{dp}{ds}+G^2\frac{dv}{ds}&=-F-\frac{g\sin\theta}{v}\\\frac{d}{ds}\left(h+\frac{G^2v^2}{2}\right)&=q_m-g\sin\theta\\q_m&=\frac{\pi D U}{\dot m}(T_e-T)\end{aligned}

Sources and maintenance

Published by PetroCalcHub Team. Implementation and source checks: 2026-10-21. This does not claim independent expert review.

Report a correction

Related tools and references

Ramey single-phase liquid temperature Local inclined Beggs-Brill segment Constant-calibrated vertical drift profile Gas formation volume factor Petroleum PVT guide Peng-Robinson hydrocarbon flash (not water)SRK hydrocarbon flash