Automated Method For Smoothing ExperiInental Flash Liberation PVT Data
Authors: Al-Yousef H.Y. , Al-Marhoun M.A. 
Published: March 2010

Abstract
The present method used by petroleum engineers to smooth experimental flash liberation data involves graphical technique to abram the bubblepoint volume. A trial-and-error procedure that utilizes the Y-correlation is then used to obtain the bubblepoint pressure and smooth the data below the bubblepoint pressure_ The data points above the bubblepoint pressure are smoothed using a graphical technique or least-squares regression.
The smoothing technique presented in this study is a nonlinear parameter estimation approach. It smooths the data points above and below the bubblepoint pressure and determines the bubblepoint volume and bubblepoint pressure simultaneously. Other advantages of this approach are that it avoids trial-underror procedure and provides a quantitative measure of the results by calculating confidence limits on the estimated parameters. It was also demonstrated that the new correlation introduced (X-correlation) is more sensitive to the bubblepoint volume while the Y-correlation is more sensitive to the bubblepoint pressure.

Introduction
Pressure volume relationships are needed for many reservoir engineering calculations. One of the methods to obtain such data is to conduct a flash liberation on constant composition expansion experiment on a gas-oil mixture at a constant temperature. The analysis of the data obtained will define the bubblepoint volume, the bubblepoint pressure, the single-phase volumetric behavior at pressure above the bubble and the two-phase volumetric behavior at pressures below the bubbleprint.
The experimental smoothing procedure used by petroleum engineers consist of three steps. First, the experimental data of volume versus pressure ate plotted. The bubble point volume is obtained from the intersection of the two curves of the data above and below the bubblepoint pressure. The pressure at the intersection point is considered as an initial estimated of the intersection point is considered as an initial estimate of the bubblepoint pressure which is usually refined during the smoothing process of the data below the bubblepoint pressure. The second step is to smooth the experimented data at pressures above the bubblepoint. This can be accomplished either graphically (1) or using regression techniques by fitting the relative volume versus pressure to a quadratic equation.
The third step is to smooth the data at pressures below the bubblepoint. The most popular method of smoothing such data is by use of an empirical relation termed the Y -correlation2. The Y-correlation is defined as:
Equation. (Available In Full Paper)
Where Y is calculated from the regression line:
Equation. (Available In Full Paper)
In Equation (3), a 1 and a2 are the regression parameters.
The properties of the Y-correlation were summarized by Standing(2) System composed almost entirely of hydrocarbons show a linear relation of Y and pressure, while systems that contain appreciable quantities of non-hydrocarbons usually give curved relation of Y and pressure. The sensitivity of the Y-correlation of Y and pressure. The sensitivity of the Y-correlation is greatest close to the bubblepoint of the system.
The smoothing method outlined above has several disadvantages:Only the experimental data at pressure below the bubblepoint pressure are utilized to obtain the bubblepoint pressure.