The determining of chemical compositions in biodiesel depends on kind of properties of biodiesel that you want to check. There are some biodiesel properties that you only use normal analysis methods, not need GC. GC-MS, NMR,... But all of these properties are based on ASTM standards. And of course, GC is an important method for your testing. For more details, you can get from the following reference
check the technical literature and depending on the depth of your curiosity you can use a variety of instruments, but in essence biodiesel is a mix of fatty acid-methyl esters to an extent of at least 98.5% GC-FID is enough, to deeper extent you might use GC-MS and further down GC-IR, HPLC, etc.
The biodiesel chemical formula is a combination of alkyl C12-C22 Fatty Acid Methyl Esters. Its Molecular weight is ~292(q). As to biodiesel chemical composition, carbon, hydrogen and oxygen weigh 77 grams, 12 grams and 11 grams. Its density at 60‹ F is 11g. The most common forms of biodiesel are Ethyl Stearate and Methyl Linoleate. The chemical formula for Methyl Linolaeate is C19H34O2 and for Ethyl Stearate is C20H40O2. Biodieselsf oxidative stability and melting point are a major concern. It is difficult to use palm oil in cold seasons because it solidifies.
I suggest that you consult ASTM 6751 fist to find out what property you want to determine in order to get the right equipment. For particular properties are determined. Using particular equipment.