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Four-Cut Gamma C7+ Characterization and PR Flash Calculator

Split a measured C7+ mean into four bounded gamma cuts and inspect the PR phase split, cut properties and molecular-weight closure.

Inputs

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.

What a heavier C7 plus assumption changes in a synthetic flash

Calculation sequence

  1. Enter the C7+ fraction's measured molar-average molecular weight and petroleum SG at 60/60 F. Enter six light-component mole fractions and C7+ on one recombined molar basis; they must sum to one. Choose a gamma shape as a distribution assumption, not a hidden fit to an assay that has not been supplied.
  2. Solve the conditional mean for the shifted gamma scale over 100-300 g/mol. Integrate four equal-probability quantile intervals and calculate each interval's exact first-moment representative MW. This application-specific truncation is disclosed: it cannot represent a heavy tail beyond 300 g/mol. Reject a requested mean that cannot be attained at the selected shape.
  3. Estimate each cut's critical and boiling properties using the same SG and pinned MW-SG/Edmister procedure as the single-lump baseline. Apply the common methane/heavy interaction parameter and flash all ten components together. PT-only heavy reference gauges cancel at fixed temperature and are not a physical heat-capacity model; caloric calculations require the separate explicit-Cp tool.
  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 synthetic M=200 g/mol, SG=0.85, alpha=2 case gives gamma scale 74.404780 g/mol and retains 0.749154 of the unconditioned distribution. Four cut MWs are approximately 136.442335, 177.812721, 217.856210 and 267.888735 g/mol; their equal-mole average is 200. At 350 K, 2 MPa and the default feed, kij=0 gives vapor mole fraction 0.821171 and bulk density 39.684753 kg/m3. This is a model comparison, not a measured assay.

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.

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}

MW-SG normal boiling and critical temperatures

Tb=97.58M0.3323SG0.04609Tc=59(554.4)eETM0.2998SG1.0555ET=−1.3478×10−4M−0.61641SG\begin{aligned}T_b&=97.58M^{0.3323}SG^{0.04609}\\T_c&=\tfrac59(554.4)e^{E_T}M^{0.2998}SG^{1.0555}\\E_T&=-1.3478\times10^{-4}M-0.61641SG\end{aligned}

Estimated critical pressure

Pc[bar]=0.068947(45203)eEP⋅M−0.8063SG1.6015EP=−0.0018078M−0.3084SG\begin{aligned}P_c[\mathrm{bar}]&=0.068947(45203)e^{E_P}\\&\quad\cdot M^{-0.8063}SG^{1.6015}\\E_P&=-0.0018078M-0.3084SG\end{aligned}

Edmister acentric estimate and Watson factor

ω=37log⁡10(Pc/101325)Tc/Tb−1−1KW=(1.8Tb)1/3/SG\begin{aligned}\omega&=\frac37\frac{\log_{10}(P_c/101325)}{T_c/T_b-1}-1\\K_W&=(1.8T_b)^{1/3}/SG\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}

Sources and maintenance

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

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