I agree with Girirajan sir. GC is always the first choice for fatty acid analysis. However some of the publications for biodiesel analysis are available for HPLC analysis.
With C18 column you can have a look at Agilent's manual for HPLC in Food Analysis. Methanol, toluene and ethyl acetate are some of the mobile phases usually used...
Dedetection VFAs could be performed by HPLC using the AQUASIL C18, 5 μm, 250 x 4.6 mm column; eluent: 1% acetonitrile, 99% 0.05M KH2PO4; pH = 2.8; Flow Rate (FR) = 1.25 mL/min and UV detection at 210 nm. Before performing any liquid measurements, samples subjected to filtration using a 0.22 μm membrane.