The popular method of Burnett (1936) ranks as one of the most precise methods for taking PVT data that produce accurate compressibility factors without the need for direct mass or volume measurements. The Burnett method consists of making a series of isothermal expansions of the experimental fluid from a primary volume into a previously evacuated secondary volume with the pressure being measured after each expansion. A series of such measurements makes up a run, and an analysis of the pressure sequence for each isotherm yields the densities, compressibility factors, and virial coefficients.The method has been utilized by numerous investigators over a wide range of temperatures and pressures. Recent experimental investigations are those reported by Scheloske (1981), Patel (1986, and H o k e et al. (1987).Data reduction techniques to determine compressibility factors and virial coefficients from Burnett PVT data range from simple graphical techniques to more elaborate computer techniques. Among the latter are the parameter optimization methods of Canfield (1967,1970a) and the maximum likelihood algorithm of Britt and Luecke (1973), which has been adapted by Embry (1980). Both these methods, although accurate, require extensive iterative computer calculations in their minimization procedures. In addition, Ewing and Marsh (1979) performed a series inversion on the Berlin (pressure) virial form of the compressibility factors to obtain a polynomial expression for the Burnett pressure ratios.Here, we present a simple and elegant method that provides accurate estimates of the second and third virial coefficients directly from an experimental Burnett pressure sequence. The method is fast, requires no extensive calculations, and makes use of the pressure-ratio graphs routinely prepared during such experiments.
Development of the MethodFor an apparatus configuration of the type shown in Figure 1, the general equations of state prior to and at the ith expansion are: pi-1 (VAi-1 = W i -I Z -I RT (1) and pt( v, 4 + vB)i = (nAB)iZiRT (2) (3) For nonadsorbing gases, as the number of moles before and after the expansion are conserved, (nA)i-l = (nAB),. The equation for the pressure ratio for pressures before and after an expansion is thus obtained by dividing Eq. 2 by Eq. 1 as To feedvacuum system To presrure measurement system MRP M "4 Figure 1. Burnett apparatus. V,-V,, Valves HT/DPI, High-temperature V,, Primary cell volume V . , Secondary cell volume MRP, Magnetic recirculation pump differential pressure indicator