volume shift

User Guide 107 1990-2014 Petroleum Experts Limited Page. See also The Equation of State Model The Acentric Factor Volume Shift 2.2.2.3 Volume Shift Volume Shift arises from an inherent weakness in the 2 parameter (a and b) Equations of State in estimating liquid densities. The Peng Robinson equation of state can be written as: ) ( ) ( ) ( b v b b v v T a b v RT P In the 3 parameter version ν is replaced by a corrected version Vs where Vs = V + cV c is the third parameter and is the sum of the individual xi ci . This third parameter volume shifts the equation. Since this correction is done after the flash equilibrium calculations, the component K values, saturation pressure and phase envelope are not affected. What is changed is the compressibility Z and anything derived from it i.e. Density, GOR, FVF, Relative Volume etc. The use of Volume Shift seems to be very attractive, since it corrects a known problem. However there are potentially significant problems in using this method e.g.: 1) The Equation of State is non-predictive model. Matching must be carried out in order to model real fluid behaviour. Volume Shift can be used to make up for bad data or inadequacies in the matching methods. However, large Volume Shift corrections can lead to incorrect results (for example, unphysical profiles of densities or FVF). That is why when matching on Volume Shift it is necessary to make sure the EOS gives consistent results for a wide range of pressures and temperatures and this can be achieved by running sensitivity calculations in PVTP, for example CCE, CVD, separator, etc. This potentially negative effect of the Volume Shift can be mitigated by introducing the Volume Shift at the end of the final EOS matching process. 2) The Volume Shift approach is a correction factor which solves the difficulty of matching density. It does, however, introduce other problems with regards to the continuity of the original equation. It is not a temperature dependent function. Matching a c at one elevated temperature may cause difficulties with matching and the material balance at another lower temperature. This can potentially introduce mass imbalance when going from high to low temperatures, which may significantly affect calculations like pressure drop estimation in the wellbore. 99 101 107 99

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User Guide 107

1990-2014 Petroleum Experts Limited

Page.

See also The Equation of State Model The Acentric Factor Volume Shift

2.2.2.3 Volume ShiftVolume Shift arises from an inherent weakness in the 2 parameter (a and b) Equations of Statein estimating liquid densities.The Peng Robinson equation of state can be written as:

)()()(

bvbbvvTa

bvRTP

In the 3 parameter version is replaced by a corrected version Vs where

Vs = V + cV

c is the third parameter and is the sum of the individual xi ci . This third parameter volumeshifts the equation.Since this correction is done after the flash equilibrium calculations, the component K values,saturation pressure and phase envelope are not affected. What is changed is thecompressibility Z and anything derived from it i.e. Density, GOR, FVF, Relative Volume etc.The use of Volume Shift seems to be very attractive, since it corrects a known problem.

However there are potentially significant problems in using this method e.g.:

1) The Equation of State is non-predictive model. Matching must be carried out in order tomodel real fluid behaviour. Volume Shift can be used to make up for bad data or inadequaciesin the matching methods. However, large Volume Shift corrections can lead to incorrect results (for example, unphysicalprofiles of densities or FVF). That is why when matching on Volume Shift it is necessary to make sure the EOS givesconsistent results for a wide range of pressures and temperatures and this can be achieved byrunning sensitivity calculations in PVTP, for example CCE, CVD, separator, etc.This potentially negative effect of the Volume Shift can be mitigated by introducing the VolumeShift at the end of the final EOS matching process.

2) The Volume Shift approach is a correction factor which solves the difficulty of matchingdensity. It does, however, introduce other problems with regards to the continuity of the originalequation. It is not a temperature dependent function. Matching a c at one elevated temperaturemay cause difficulties with matching and the material balance at another lower temperature.This can potentially introduce mass imbalance when going from high to low temperatures,which may significantly affect calculations like pressure drop estimation in the wellbore.

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