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Heavy-End PR Interaction Parameter PVT Fit Calculator

Fit one methane/heavy-cut interaction parameter to fixed-temperature pressure and vapor-mole-fraction observations, with sensitivity and residual checks.

Inputs

PVT measurements
Pressure (MPa(a))Vapor mole fractionRemove
6 / 40
Paste CSV measurements

Results

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

Learn, compare and practice

Worked explanations, controlled studies and printable exercises connected to this calculation.

Calibrating heavy end PVT parameters without hiding residuals

Calculation sequence

  1. Supply 4-40 unique absolute-pressure observations at one measured temperature and the same recombined feed composition. Use equilibrium vapor mole fraction strictly between 0.001 and 0.999. Do not mix production gas-oil ratios, mass quality or data from different feeds into this fit. Example observations are synthetic independent-engine data, not a laboratory sample.
  2. Hold the conditional gamma distribution, shared cut SG, critical-property correlation and all other interaction pairs fixed. Evaluate a coarse bounded kij grid, then minimize the vapor-mole-fraction residuals with SciPy's bounded least-squares solver. This narrow one-parameter fit does not silently optimize molecular distribution, density correction or a caloric curve.
  3. Reject a bound-active or insensitive solution, failed phase audits, or vapor-fraction RMSE above 0.1. The sensitivity norm describes local responsiveness, not a statistical confidence interval. Inspect individual residuals and test pressures excluded from the fit before using the fitted kij for predictions; a good residual on training points is not a validation data set.
  4. At every returned state independently re-evaluate classical PR pressure, log fugacity and residual enthalpy/entropy. Require component balance <=2e-7, log-fugacity mismatch <=2e-5 and relative pressure residual <=2e-6. Reject vanishing phase fractions below 1e-6 and density separation below 1.1 for ordinary splits. These are numerical checks, not measured-PVT validation.
  5. Calculations run locally in a dedicated WebAssembly worker. The advanced Python/scientific engine is a roughly 33 MB first download, separate from ordinary calculators; it is self-hosted and version pinned. No composition or measurements are sent to a calculation server. Save and file backups retain canonical inputs, while CSV/PDF include returned tables and source notes. The worker is released after idle time and failures never return partial results.

Worked check

The default observations are a synthetic 350 K six-pressure isotherm generated by the independent NeqSim 3.26 engine with kij=0.07. Holdout pressures of 1.5, 3.5 and 5.5 MPa are kept separate from fitting. The resulting parameter is close to 0.07, subject to the two libraries' documented rounded PR-constant differences; no experimental accuracy is implied.

Synthetic examples for reproducibility, not measured field results.

Assumptions and limitations

  • A deliberately bounded four-cut approximation over 100-300 g/mol, not a complete Whitson C7-to-C80 assay. Every cut uses the same supplied 60/60 F SG. Reject an unbracketed mean, retained gamma probability below 1e-6, Tb>=Tc or omega outside 0-1. Shape does not determine aromaticity or a measured carbon-number distribution.
  • MW=100-300 g/mol, SG=0.65-0.90, shape=0.5-10; the conditional mean must also be achievable at that shape. At least two feed fractions >=0.001; C7+ is 0.004-0.99. T=180-450 K and p=0.1-10 MPa(a) are software bounds, not a validated accuracy envelope. No water, N2, CO2, H2S, solids, multiple liquids, volume shifts or density matching.
  • Only methane/heavy-cut pairs share the user k_heavy (-0.2 to 0.4). All other pairs are zero. Properties use the pinned NeqSim Riazi-Daubert MW-SG variant plus explicit Edmister omega, not a silent Pedersen or Kesler-Lee fallback. Neither a solved flash nor a fitted parameter is proof of physical accuracy.
  • One isotherm and one kij only; no uncertainty model, weighting, multi-temperature regression, automatic outlier deletion or guarantee of global identifiability. Input rows remain in the user's browser and exported backup. A synthetic demonstration fit is never presented as a field calibration.

Implemented equations

Conditional gamma moments and four equal-probability cuts

f(M)∝g(M)e−(M−100)/bg(M)=(M−100)α−1100≤M≤300Mˉj=∫ajaj+1Mf(M) dM∫ajaj+1f(M) dM∫ajaj+1f(M) dM=1/4\begin{aligned}f(M)&\propto g(M)e^{-(M-100)/b}\\g(M)&=(M-100)^{\alpha-1}\\100&\le M\le300\\\bar M_j&=\frac{\int_{a_j}^{a_{j+1}}M f(M)\,dM}{\int_{a_j}^{a_{j+1}}f(M)\,dM}\\\int_{a_j}^{a_{j+1}}f(M)\,dM&=1/4\end{aligned}

PR attraction with a disclosed interaction matrix

a=∑i∑jxixjaiaj(1−kij)kij=kji,kii=0\begin{aligned}a&=\sum_i\sum_j x_ix_j\sqrt{a_ia_j}(1-k_{ij})\\k_{ij}&=k_{ji},\quad k_{ii}=0\end{aligned}

Bounded one-parameter nonlinear least squares

k^=argmin⁡−0.2≤k≤0.4∑j[βPR(pj,T;k)−βj]2\hat k=\underset{-0.2\le k\le0.4}{\operatorname{argmin}}\sum_j[\beta_{\rm PR}(p_j,T;k)-\beta_j]^2

Sources and maintenance

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

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