Two-Phase Isentropic Compressibility and Two-Phase Sonic Velocity for Multicomponent-Hydrocarbon Mixtures
Authors: Firoozabadi Abbas , Pan Huanquan 
Published: December 2007

Abstract
Two-phase compressibility and two-phase sonic velocity of hydrocarbon mixtures are needed for variety of applications in well testing, metering, and seismic exploration. In this work, a thermodynamic model is presented to estimate the two-phase is entropic compressibility and two-phase sonic velocity. The model accounts for the mass transfer between the equilibrium phases and the effect of capillary pressure. The results reveal that isothermal and is entropic compressibilities can be different by a factor of 20 in the two-phase near the retrograde dewpoint With the exception of the retrograde dewpoint the difference between the is entropic compressibility in the single-phase and two-phase is less than the corresponding difference for the isothermal compressibility. The sonic velocity in the two-phase can be either less or more than the single phase. For the mixtures that the sonic velocity decreases in the two-phase. the decrease is much less pronounced than in nonhydrocarbon systems such as water-steam and water-air.

Introduction
Fluid compressibility and sonic velocity are used for a wide range of problems in production and exploration of hydrocarbon reservoirs. These include well testing, metering, and seismic exploration. Various methods are available for the estimation of compressibility and sonic velocity in the single-phase - both gas and liquid states. For hydrocarbon mixtures in the two-phase state, the available methods are unreliable.
Compressibility is often defined on the basis of the thermodynamic path. For an isothermal process, the compressibility relates volume change to pressure change at constant temperature. In an is entropic path, the volume and pressure changes are given by is entropic compressibility. These two compressibilities in the single-phase state are related by,
(1)
where CT is the isothermal compressibility and CS is the is entropic compressibility; CP and CV are the heat capacity at constant pressure and volume, respectively. Since CP CV, then CT CS. The difference between CT and CS depends on pressure, temperature and composition and may be from 10 to 20%, to 200 to 300% in the single phase for pure hydrocarbons. Available techniques are adequate for reliable estimation of CT and CS for hydrocarbon mixtures in the single-phase state. For reservoir engineering applications, CT represents the fluid compressibility in the reservoir away from the wellbore In the wellbore, due to expansion, the fluid may undergo heating or cooling and the process may become nonisothermal. If the heat loss can be neglected, the is entropic compressibility may better represent the pressure and volume changes. In many real applications, the compressibility is perhaps between the two limits.
Fluid compressibility in the two-phase gas-liquid state can be very different from the single-phase gas and liquid states. While the gas phase compressibility is higher than the liquid phase, the two-phase gas-liquid compressibility could be higher than the gas-phase compressibility. The procedure for the calculation of the isothermal two-phase compressibility of hydrocarbon mixtures has been presented in Ref. 2. It is clear from the work of Ref. 2 that any averaging technique based on individual phase compressibilities is unacceptable, and may lead to an order of magnitude error. The results presented in Ref. 2 are based on the assumption that the interface between the gas and liquid phases is flat. In porous media, the interface is curved and therefore capillary pressure may affect the two- phase compressibility One purpose of this work is to account for the effect of capillary pressure on two-phase compressibility. Similar to single phase, where two types of compressibility - is entropic and isothermal - are defined, in the two-phase, one can also define isothermal and is entropic compressibilities. P. 41^