Summary
A physically and mathematically rigorous transient-state equilibrium
diffusion model is applied for simultaneous determination of the gas-diffusion
and interface-mass-transfer coefficients from pressure de-cline by dissolution
of gas in quiescent liquids involving petroleum reservoirs. The short- and
long-time analytical solutions of this model are reformulated to enable direct
determination of the best-estimate values of these parameters by regression of
experimental data. Typi-cal experimental data are then analyzed by means of the
present im-proved methods, and the values obtained are compared with the
re-ported values. The present methodology is proven practical and yields unique
and accurate parameter values.
Introduction
Gas-diffusivity and interface-mass-transfer coefficients are important
parameters determining the rate of dissolution of the injection gases in oil
during secondary recovery, and the rate of dissolution and sepa-ration of light
gases in reservoir oil and brine, water tables associated with
depleted-reservoir gas storage, drilling mud, and completion fluids (Hill and
Lacey 1934; O’Bryan et al. 1988; O’Bryan and Bourgoyne 1990; Bodwadkar and
Chenevert 1997; Bradley et al. 2002; Liu and Civan 2005). In order to develop
proper gas-injection strategies, accurate values of these parameters are
required for reser-voir simulation and prediction of oil recovery by miscible
flooding and the optimization of miscibility for best recovery.
Laboratory measurement of gas diffusivity in quiescent liquids is usually
accomplished through the measurement of the pressure of gas in contact with
certain liquids, such as oil, brine, drilling mud, and completion fluids in a
closed PVT cell (see Fig. 1 ) during gas dissolution in the liquid phase. The
accuracies of the available models, including those by Riazi (1996), Sachs
(1997, 1998), and Zhang et al. (2000), are limited by the inherent simplifying
assumptions involved in the analytic treatment and the subsequent
interpretation of such experimental data. As judged by the reported studies,
there appears to be no consensus among the available analytical approaches used
for diffusivity measurement. In addition, the previous studies focused mostly
on the determination of gas diffusivity and did not account for
interface-mass-transfer effects. The methodology offered by Civan and Rasmussen
(2001, 2002, 2003), and further elaborated in the present paper, allows for
both interface mass-transfer effects and for bulk diffusivity. It is a novel
and practical approach that determines parameters describing both effects from
a given set of pressure-decline data.
The best estimate of the coefficient of diffusion of gas species (solute) in
a given liquid medium (solvent) is usually inferred indirectly by matching the
prediction of a suitable mathematical model involving the species transfer by
diffusion to experimental data under prescribed conditions. For this purpose,
Sachs (1998) resorts to the numerical solution of the nonlinear model equations
incorporating the dependency of the diffusion coefficient on concentration
without clearly describing the boundary conditions used in the solution.
© 2006. Society of Petroleum Engineers
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History
- Original manuscript received:
11 February 2004
- Revised manuscript received:
24 August 2005
- Manuscript approved:
11 September 2005
- Version of record:
20 March 2006
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