Transport properties

Evidence class: validation, calibration, and application. This report compares torch-flash viscosity and thermal-conductivity predictions with three real petroleum-fluid datasets and demonstrates the surface/interfacial-tension and liquid-diffusion APIs on physically resolved states. The reservoir-gas and thermal-conductivity curves are predictive. The Heavy Oil 5 figure distinguishes the default prediction from a simultaneous two-parameter calibration to all displayed heavy-oil observations.

The implementation follows K. S. Pedersen, P. L. Christensen, and J. A. Shaikh, Phase Behavior of Petroleum Reservoir Fluids, 3rd ed. (2024), chapter 10, doi:10.1201/9780429457418, with the primary model papers cited below. Calculations use float64 on CPU and SI API inputs; axes show conventional petroleum units after explicit conversion.

Reservoir-gas viscosity

The validation fluid contains eight named light components and fourteen measured C7-C20+ cuts. The plotted 28 measurements cover 50-200 °C and 415-1381 bar and were reported by Kashefi et al., doi:10.1016/j.petrol.2013.10.021. Measured heavy-cut masses and densities are mapped to PR properties before the four viscosity routes are evaluated.

Pedersen corresponding states gives the lowest aggregate error at 3.62% MAPE, followed by Lee-Gonzalez-Eakin at 5.02%. The published one-parameter PR76 friction-theory form gives 16.16% MAPE, and untuned LBC gives 34.61%. The corresponding-states formulation is from Pedersen et al., doi:10.1016/0009-2509(84)87009-8; LBC is from Lohrenz, Bray, and Clark, doi:10.2118/915-PA; and the friction model is the one-parameter form of Quiñones-Cisneros, Zéberg-Mikkelsen, and Stenby, doi:10.1016/S0378-3812(00)00474-X.

Heavy-oil viscosity

Heavy Oil 5 uses the measured whole C7+ mass and standard density from Pedersen Tables 10.8-10.9. The C7+ fraction is expanded through C200 with the Pedersen-Milter-Sørensen heavy-aromatic parameter set: C7-C9 remain individual fractions and C10-C200 are reduced to nine approximately equal-weight pseudocomponents. The phase model is PR78 with the published polar-component interactions. A bubble point is solved once at each temperature; all sub-bubble states at that temperature are then flashed in one batch, and the viscosity correlation receives the equilibrium liquid composition. This phase preparation converged at every displayed state with a maximum log-fugacity residual below \(10^{-8}\).

The solid curve is the source-parameter prediction with both dimensionless CSP factors equal to one. The dashed curve is a joint calibration of the third and fourth CSP factors to all 21 observations at 38, 49, and 60 °C. The full-batch objective is the mean squared logarithmic viscosity ratio. Bounded PyTorch LBFGS stopped by the loss tolerance after 34 iterations, below the 200-iteration limit and with 30-iterate no-improvement patience.

The PR78 source-factor prediction gives 63.74% MAPE. The simultaneous fit selects a third CSP factor of 1.38412 and a fourth CSP factor of 2.10535, reducing MAPE to 15.57% while retaining the low-pressure upturn and the temperature-dependent curve shapes. The log-viscosity sensitivity matrix is full rank \(2/2\), with condition number 35.7. This is calibration evidence only: there is no Heavy Oil 5 holdout, and visible state-dependent deviations remain.

The heavy-oil viscosity formulation is from Lindeloff et al., The Corresponding States Viscosity Model Applied to Heavy Oil Systems, J. Can. Pet. Technol. 43 (2004), 47-53. The C200 PR characterization is from Pedersen, Milter, and Sørensen, doi:10.2118/88364-PA.

CO2/methane thermal conductivity

The six homogeneous-gas measurements contain 49.39 mol% CO2 and 50.61 mol% methane. They originate with Christensen and Fredenslund, doi:10.1021/je60083a034. The mixture model maps each state to the Hanley methane reference correlation; the right-hand panel separately exposes the complete pure-methane model at three molar densities. The methane correlation is defined by Hanley, McCarty, and Haynes, doi:10.1016/0011-2275(75)90010-7.

The Christensen-Fredenslund mixture prediction gives 1.02% MAPE and a 2.76% maximum absolute deviation over the six experimental states. No mixture conductivity parameter is adjusted.

Surface and interfacial tension

The application first solves a PR76 methane/n-butane \(P\)-\(x\)-\(y\) isotherm at 270 K. Of 33 attempted continuation points, 32 pass the equilibrium-residual, phase-separation, and liquid-volume-below-vapor-volume gates; their maximum fugacity residual is \(7.61\times10^{-9}\). Weinaug-Katz and Lee-Chien then receive the same coexisting compositions and molar densities. Brock-Bird is evaluated independently for subcritical n-butane; its defining source is doi:10.1002/aic.690010208.

Both gas-oil interfacial models decrease smoothly toward zero as the phase compositions coalesce. The Brock-Bird curve also decreases toward the n-butane critical temperature. These are application checks of physical trend and API orchestration, not comparisons with interfacial-tension measurements.

Kinematic viscosity and n-paraffin diffusion

The final application uses PR78 liquid density and LBC dynamic viscosity for n-decane at 10 MPa. Kinematic viscosity is the direct SI ratio \(\nu=\eta/\rho\). Hayduk-Minhas uses the same bulk viscosity together with an explicit illustrative n-paraffin solute normal-boiling molar volume of 200 cm³/mol. The infinite-dilution correlation is defined by Hayduk and Minhas, doi:10.1002/cjce.5450600213.

Dynamic and kinematic viscosity decrease smoothly from 290 to 450 K, while the calculated diffusion coefficient increases. Every displayed value is finite and positive. The diffusion curve is an application of the stated solute descriptor, not an experimental n-decane self-diffusion validation.

Conclusion and limitations

The experimental evidence supports the Pedersen corresponding-states viscosity for the selected reservoir gas and the Christensen-Fredenslund thermal-conductivity model for the selected CO2/methane gas. For Heavy Oil 5, the default heavy-oil factors remain substantially biased, while one joint two-factor calibration captures the pressure and temperature trends with a 15.57% MAPE. This result does not establish transferability to another oil. LBC and the published one-parameter PR76 friction model show larger model-form deviations in the dense reservoir-gas case.

Transport correlations consume a specified homogeneous state or an already resolved pair of coexisting phases; they do not perform stability analysis, flash calculations, or phase identification. Their empirical validity ranges, required critical volumes or component parameters, and phase-root selection remain part of the scientific configuration.