Evaluating Constant-Volume Depletion Data
Authors: Whitson Curtis H. , Torp Stein B. 
Published: December 2007

Abstract
This paper presents methods for evaluating constant volume depletion (CVD) data obtained from experimental analyses of gas condensates and volatile oils. Theoretical and practical developments are supported by experimental data from a North Sea gas-condensate fluid.
The three major contributions of the work are:presentation of material-balance equations to calculate fluid properties from measured CVD data,a simple method for calculating black-oil formation volume factors and solution GOR's using material-balance results and a separator flash program, andinvestigation of the Peng-Robinson (PR) equation of state (EOS) as a tool for matching measured PVT data and studying vapor/liquid phase behavior during CVD.

Introduction
CVD experiments are performed on gas condensates and volatile oils to simulate reservoir depletion performance and compositional variation. Measured data can be used in a variety of reservoir engineering calculations, among the most useful being material-balance calculations, generating black-oil PVT properties and, more recently, the tuning of empirical EOS. All these applications are addressed in this paper.
Few engineers are aware of useful fluid properties that can be derived from CVD data--e.g., liquid composition (and therefrom K-values), density, and molecular mass of the C7+ fraction, vapor density, and total system molecular mass. Only experimental CVD data and simple material-balance equations are used to calculate these data. A procedure outlining these calculations was first presented by Reudelhuber and Hinds. Their description, however, is somewhat difficult to follow and not extensively known or used by petroleum engineers. The material-balance relations are presented here in equation form using current SPE nomenclature.
Based on material-balance-derived properties, a method is proposed for calculating black-oil PVT properties--i.e., FVF's and solution GOR's used in two- phase flow equations and reservoir material balances. The method was first suggested by Dodson et al. in 1953 for solution-gas/crude-oil systems. Their method, however, requires expensive and time-consuming liquid sample removals and experimental flash separations. The proposed method follows the Dodson et al. procedure but uses experimentally determined vapor corp. positions and material-balance-derived liquid compositions together with a multistage separator flash program. PVT properties calculated using this method are compared with those predicted by the PR EOS.
Though more complicated, empirical equations of state are also used to evaluate CVD data. Several investigators have used the PR EOS to simulate PVT studies of light gas condensates and crude oils. Unfortunately most studies have emphasized K-value predictions instead of volumetric predictions, and most have avoided systems operating near the critical point. Results have varied considerably, depending on which properties are compared. Conrad and Gravier propose a method to improve liquid-density estimations by adjusting properties of the heaviest-plus fraction (boiling point and methane interaction coefficient). Firoozabadi et al. studied another lean gas condensate and found that by adjusting only the methane-heavy fraction interaction coefficient, the PR EOS highly overestimated liquid volumes.
About 30 CVD studies performed by commercial and private laboratories were analyzed using the material- balance approach.
JPT
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