Measurement and Prediction of the Phase Behaviour of Carbon Dioxide, Alkane and Water Mixtures at Reservoir Conditions
Author(s)
Forte, Esther
Type
Thesis
Abstract
Knowledge of the phase behaviour of mixtures of oil with carbon dioxide and water
is essential for reservoir engineering, especially in the processes of enhanced oil recovery
and geological storage of carbon dioxide. Both processes require versatile tools able
to describe the global phase behaviour at reservoir conditions, which may include the
critical region of the mixtures involved. For a comprehensive understanding however
the study of simpler systems needs to be completed. In this work two ternary systems
have been studied as models for (oil + carbon dioxide + water) mixtures. The first one
consists of (n-decane + carbon dioxide + water); the second is a mixture of (propane
+ carbon dioxide + water). To measure phase equilibria at representative reservoir
conditions, a new analytical apparatus has been designed with maximum operating
temperature and pressure of 423K and 45MPa, respectively. The equipment relies
on recirculation of two coexisting phases using a two-channel magnetically-operated
micro-pump designed during this work, sampling and on-line compositional analysis
by gas chromatography. The apparatus has been validated by comparison with
published isothermal vapour-liquid equilibrium data for the binary system (n-decane
+ carbon dioxide). New experimental data have been measured for the systems (ndecane
+ carbon dioxide + water) and (propane + carbon dioxide + water) under
conditions of three-phase equilibria. Data for the three coexisting phases in the mixture
of (n-decane + carbon dioxide + water) have been obtained on five isotherms
at temperatures from (323 to 413)K and at pressures up to the point at which two
of the phases become critical. Similarly, for the mixture (propane + carbon dioxide
+ water), data for the three coexisting phases on four isotherms at temperatures
from (311 to 353)K and pressures up to the same point are reported. The experimental
work has been complemented here with a theoretical effort in which models
for these molecules are developed within the framework of the statistical associating
fluid theory for potentials of variable range (SAFT-VR). The phase behaviour of the
three binary subsystems has been calculated using this theory and, where applicable,
a modification of the Hudson and McCoubrey combining rules has been used to treat
the systems predictively. The experimental data obtained for the ternary mixture are
compared to the predictions of the theory. Furthermore, a detailed analysis of the
ternary mixture is carried out based on comparison with available data for the constituent
binary subsystems. In this way, the observed effects on the solubility when
the third component is added are analysed.
An accurate prediction of phase behaviour at conditions far and close to criticality
cannot be accomplished by mean-field based theories, such as the SAFT-VR equation
of state, that do not incorporate long-range density fluctuations. A treatment based
on renormalisation-group (RG) theory as developed by White and co-workers has
proven very successful in improving the predictions of the critical region with different
equations of state. The basis of the method is an iterative procedure to account for
contributions to the free energy of density fluctuations of increasing wavelengths. The
RG method has been combined with a number of versions of the statistical associating
fluid theory (SAFT), by implementing White’s earliest ideas with the improvements
of Prausnitz and co-workers. Typically, this treatment involves two adjustable parameters:
a cut-off wavelength L for density fluctuations and an average gradient of the
wavelet function Φ. In this work, the SAFT-VR equation of state has been extended
with a similar crossover treatment which however follows closer the most recent improvements
introduced by White. The interpretation of White’s latter developments
allows one to establish a straightforward method which enables Φ to be evaluated; only
the cut-off wavelength L needs then be adjusted. The approach used here begins with
an initial free energy incorporating only contributions from short-wavelength fluctuations,
which are treated locally. The contribution from long-wavelength fluctuations
is incorporated through an iterative procedure based on attractive interactions which
incorporate the structure of the fluid following the ideas of perturbation theories and
using a mapping that allows integration of the radial distribution function. Good
agreement close and far from the critical region is obtained using a unique fitted parameter
L that can be easily related to the range of the potential. In this way the
thermodynamic properties of a square-well (SW) fluid are given by the same number
of independent intermolecular model parameters as in the classical equation. Far from
the critical region the approach provides the correct limiting behaviour reducing to
the classical equation (SAFT-VR). In the critical region the β critical exponent is calculated
and is found to take values close to the universal value. In SAFT-VR the free
energy of an associating chain fluid is obtained following the thermodynamic perturbation
theory of Wertheim from knowledge of the free energy and radial distribution
function of a reference monomer fluid. By determining L for SW fluids of varying
well width a unique equation of state is obtained for chain and associating systems
without further adjustment of critical parameters. Computer simulation data of the
phase behaviour of chain and associating SW fluids are used to test the accuracy of
the new equation. Furthermore the treatment is here extended to model pure fluids
and results are presented for a number of alkanes, carbon dioxide and water.
is essential for reservoir engineering, especially in the processes of enhanced oil recovery
and geological storage of carbon dioxide. Both processes require versatile tools able
to describe the global phase behaviour at reservoir conditions, which may include the
critical region of the mixtures involved. For a comprehensive understanding however
the study of simpler systems needs to be completed. In this work two ternary systems
have been studied as models for (oil + carbon dioxide + water) mixtures. The first one
consists of (n-decane + carbon dioxide + water); the second is a mixture of (propane
+ carbon dioxide + water). To measure phase equilibria at representative reservoir
conditions, a new analytical apparatus has been designed with maximum operating
temperature and pressure of 423K and 45MPa, respectively. The equipment relies
on recirculation of two coexisting phases using a two-channel magnetically-operated
micro-pump designed during this work, sampling and on-line compositional analysis
by gas chromatography. The apparatus has been validated by comparison with
published isothermal vapour-liquid equilibrium data for the binary system (n-decane
+ carbon dioxide). New experimental data have been measured for the systems (ndecane
+ carbon dioxide + water) and (propane + carbon dioxide + water) under
conditions of three-phase equilibria. Data for the three coexisting phases in the mixture
of (n-decane + carbon dioxide + water) have been obtained on five isotherms
at temperatures from (323 to 413)K and at pressures up to the point at which two
of the phases become critical. Similarly, for the mixture (propane + carbon dioxide
+ water), data for the three coexisting phases on four isotherms at temperatures
from (311 to 353)K and pressures up to the same point are reported. The experimental
work has been complemented here with a theoretical effort in which models
for these molecules are developed within the framework of the statistical associating
fluid theory for potentials of variable range (SAFT-VR). The phase behaviour of the
three binary subsystems has been calculated using this theory and, where applicable,
a modification of the Hudson and McCoubrey combining rules has been used to treat
the systems predictively. The experimental data obtained for the ternary mixture are
compared to the predictions of the theory. Furthermore, a detailed analysis of the
ternary mixture is carried out based on comparison with available data for the constituent
binary subsystems. In this way, the observed effects on the solubility when
the third component is added are analysed.
An accurate prediction of phase behaviour at conditions far and close to criticality
cannot be accomplished by mean-field based theories, such as the SAFT-VR equation
of state, that do not incorporate long-range density fluctuations. A treatment based
on renormalisation-group (RG) theory as developed by White and co-workers has
proven very successful in improving the predictions of the critical region with different
equations of state. The basis of the method is an iterative procedure to account for
contributions to the free energy of density fluctuations of increasing wavelengths. The
RG method has been combined with a number of versions of the statistical associating
fluid theory (SAFT), by implementing White’s earliest ideas with the improvements
of Prausnitz and co-workers. Typically, this treatment involves two adjustable parameters:
a cut-off wavelength L for density fluctuations and an average gradient of the
wavelet function Φ. In this work, the SAFT-VR equation of state has been extended
with a similar crossover treatment which however follows closer the most recent improvements
introduced by White. The interpretation of White’s latter developments
allows one to establish a straightforward method which enables Φ to be evaluated; only
the cut-off wavelength L needs then be adjusted. The approach used here begins with
an initial free energy incorporating only contributions from short-wavelength fluctuations,
which are treated locally. The contribution from long-wavelength fluctuations
is incorporated through an iterative procedure based on attractive interactions which
incorporate the structure of the fluid following the ideas of perturbation theories and
using a mapping that allows integration of the radial distribution function. Good
agreement close and far from the critical region is obtained using a unique fitted parameter
L that can be easily related to the range of the potential. In this way the
thermodynamic properties of a square-well (SW) fluid are given by the same number
of independent intermolecular model parameters as in the classical equation. Far from
the critical region the approach provides the correct limiting behaviour reducing to
the classical equation (SAFT-VR). In the critical region the β critical exponent is calculated
and is found to take values close to the universal value. In SAFT-VR the free
energy of an associating chain fluid is obtained following the thermodynamic perturbation
theory of Wertheim from knowledge of the free energy and radial distribution
function of a reference monomer fluid. By determining L for SW fluids of varying
well width a unique equation of state is obtained for chain and associating systems
without further adjustment of critical parameters. Computer simulation data of the
phase behaviour of chain and associating SW fluids are used to test the accuracy of
the new equation. Furthermore the treatment is here extended to model pure fluids
and results are presented for a number of alkanes, carbon dioxide and water.
Date Issued
2011-09
Date Awarded
2011-12
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
License URL
Advisor
Galindo, Amparo
Trusler, Martin
Sponsor
Shell International Exploration and Production BV
Creator
Forte, Esther
Publisher Department
Chemical Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)