fefelvn:
Natural gas is generally a mixture of several components, mostly methane but also containing ethane, propane and at least some butanes. There would be some computational error if you assume that constants for pure methane apply to such a mixture.
To answer your specific query, I found Beattie-Bridgeman constants for methane in Professor S. M. Walas' excellent book: "Phase Equilibria in Chemical Engineering" (Butterworth, 1985) on page 598:
A0=2.2769, a=0.01855, B0=0.05587, b=-0.01587, C=128300. Here, the units are P[atm], V[liter/gmol], T[K], and R=0.08206[liter.atm/gmol/K]
For the other hydrocarbons, you would need to back-calculate the Beattie-Bridgeman constants from published P-V-T data.
However, I would suggest that you look instead at using a cubic equation of state (Peng-Robinson or Soave-Redlich-Kwong). Either of these can be used to do the computation of the J-T coefficient accurately for light hydrocarbon systems. Both options require pure-component properties (Tc, Pc, omega, and ideal gas enthalpy coefficients) plus readily available binary interaction parameters. When dealing with a single phase, all binary interaction parameters can be set to zero without significant loss of accuracy (these are normally used only in phase equilibrium computations).
Finally, most modern process simulators do isenthalpic flash calculations very efficeintly, so you can compute the required J-T coefficients very quickly using any of them.