Sorry this is such a late response but I never check this site. The premier source for what you're looking for is AGA8 (American Gas Association Report No. 8). I attached a compressibility chart and also a paper you might like...
Here's a spreadsheet that calculates a variety of properties for natural gas using the Redlich-Kwong-Soave EoS that you can use to find the Joule-Thompson coefficient as well as many other things. My AGA8 spreadsheet is 19MB and it wouldn't upload. I have another spreadsheet that uses the...
The best source for natural gas properties is the American Gas Association Report 8 (AGA8). I have posted a free Excel AddIn that provides such properties in a spreadsheet. The composition of natural gas varies considerably depending on the source so the JT coefficient varies with mole fractions...
While not clearly stated, it looks like the solution presumes you are going to use the specific heat of the ideal gas (from some source like NASA Glenn) plus the Nelson-Obert generalized compressibility chart to obtain an estimate of the real gas specific heat at some given conditions. There...