Regression to Experimental PVT Data
Authors: Christensen P.L. 
Published: March 2010

Abstract
A procedure is presented for regression of equation of state parameters to experimental PVT-data. The starting point is a predictive C7+ characterization based on the available analytical data. If the agreement between the experimental and calculated PVT data is unsatisfactory, the first step is to critically evaluate the analytical data. If this still does not lead to satisfactory results, an adjustment of the equation of state volume translation parameter is performed. This parameter is chosen because it influences the liquid phase densities without having any influence on the phase equilibrium results. Any additional parameter regression needed is performed by adjustment of the two most sensitive coefficients in the expressions used to determine the equation of state parameters. It is shown that the applied procedure may be used to match experimental PVT data without having a major influence on properties which may be derived from an equation of state, but for which no experimental data exist for the actual composition. Also it is shown that reasonable results are obtained for the measured PVT properties at conditions not used in the regression.

Introduction
The requirements to a PVT simulation program are not limited to prediction of volumetric properties, phase fractions and saturation points at reservoir conditions. PVT simulation software is also expected to be able to predict the phase behaviour at process plant and transport conditions. Not only saturation points and volumetric properties need to be calculated but also derived properties as for example enthalpies, entropies, heat capacities, Joule- Thomson coefficients and sound velocities. This has to do with the frequent use of PVT simulation packages to generate the PVT property tables needed as input to reservoir and flow simulation programs.
Petroleum reservoir fluids consist of thousands of different hydrocarbon constituents. The diversity in chemical structure of the individual components increases with carbon number. It is, therefore, unpractical to analyse for all C7+ components. A standard composition analysis most often stops at either C7+, C10+ or C20+. In PVT simulations the C7+ fraction is usually represented through a number of pseudo-components. Previously the detailed composition of the plus-fraction was not given much attention when selecting the pseudo-components. Though different in their detailed approach, the formerly used characterization procedures had in common that experimental PVT data were needed to be able to assign equation of state parameters to the pseudocomponents. The applied experimental data most often originated from PVT experiments (constant mass expansion, constant volume depletion and differential liberation) carried out at reservoir temperature. One of the most extensive works on how to perform a component pseudorization without estimating the composition of the plus-fraction has been presented by Coats(1).
One reason for previously making no attempt to estimate the detailed composition of the plus-fraction was lack of high quality analytical data. Composition analyses to above C7+ were rare and often the information available about the C7+ fraction was limited to its mole fraction. New analytical techniques have made it possible to develop C7+ characterization procedures based on fairly accurate estimations of the molar composition of the plus fraction.