Summary
The modeling of rapid flow of multiphase reservoir fluids in wells involving
nonequilibrium partial separation of dissolved gases from the metastable oil
and water phases is reviewed and formulated. The multiphase-fluid flow is
described by means of the differential mass, momentum, and energy-balance
equations along the well. The rate of gas transfer from the metastable liquid
phases to the gas phase is expressed in terms of the relaxation time determined
by the prevailing gas-phase volume fraction and the pressure and temperature
conditions. The differential equations are solved numerically under a typical
scenario involving the constant gas-, oil-, and water-production rates at the
wellhead. It is demonstrated that the nonequilibrium saturation and pressure
distributions in wells deviate from the equilibrium results, depending on the
variation of the local relaxation time along the well. It is concluded that
inclusion of nonequilibrium relaxation effects in models for rapid multiphase
flow in wells is required.
Introduction
When the reservoir fluid system invades the wellbore, it is usually at an
equilibrium state at the prevailing pressure and temperature conditions. As
this fluid system moves along the well from the bottom hole toward the
wellhead, the pressure of the fluid system decreases owing to the decline of
the hydrostatic pressure and the loss of mechanical energy by wall shear.
Simultaneously, an exchange of heat may take place between the fluid system
flowing through the well and the surrounding geological formation. A fraction
of the dissolved gas separates from the liquid phases to form and/or join the
gas phase.
The separation of the dissolved gas from the liquid phases (oil and water)
occurs under nonequilibrium conditions when the flow of the multiphase-fluid
system is sufficiently rapid. This is because the separation of the gas
component from the liquid phases involves the transport of the gas to the
interface located between the liquid and gas phases by diffusion, which is a
much slower process than the transport of the well fluids by convection (Civan
1994; Civan and Rasmussen 2003). Such conditions may not allow enough time for
the fluid system to attain a local equilibrium state, referred to as the
saturation condition, along the well. Therefore, as described in Fig. 1, the
equilibrium gas saturation of the multiphase-fluid system may be higher than
the actual gas saturation, the difference of which constitutes the driving
force for the interface gas transfer between the liquid and gas phases.
As stated by Bilicki and Kestin (1990) and Downar-Zapolski et al. (1996)
about a similar process concerning the phenomenon of vapor production
associated with the flashing (rapid evaporation) of liquid flows, the liquid
system attains a metastable condition and, therefore, the flushing of the
liquid phase at saturation delays. The retardation depends on the local fluid
conditions (including the vapor fraction in the multiphase-fluid system) and
the pressure and temperature conditions. Consequently, the prevailing
metastable condition creates nonequilibrium between the liquid and vapor phases
and causes the interface transfer of the gas from the liquid phases to the
vapor phase to occur gradually at a finite rate. Bilicki and Kestin (1990) and
Downar-Zapolski et al. (1996) describe the nonequilibrium interface mass
transfer by means of a first-order relaxation equation, similar to Einstein
(1920). Badur and Banaszkiewicz (1998) modified the conventional relaxation
equation to include the capillary effects based on the Ginzburg-Landau model.
In contrast, the frequently used equilibrium-state models assume an infinitely
fast interface mass transfer and, therefore, an instantaneous gas separation at
saturation. Inherently, such equilibrium models, including the popular OLGA
model [an extended mechanistic two-fluid equilibrium model by Bendiksen et al.
(1991)], are not adequate for describing the rapid fluid flow in wells
experiencing an incomplete interface gas transfer.
In this paper, the relevant modeling approaches for description of rapid
multiphase flow of reservoir fluids in wells from the bottom hole to the
wellhead, by considering the effect of the nonequilibrium incomplete separation
of dissolved gases from the oil and water phases, are reviewed and discussed.
The multiphase-fluid flow is described by means of the differential mass,
momentum, and energy-balance equations along the well. The mathematical
modeling considers transient-state phase transition and partitioning of the gas
between the gas and liquid (oil and water) phases. The partitioning occurs
partially depending on the multiphase-flow rates and the relaxation time,
determined by the prevailing local gas-phase fraction, and the multiphase-fluid
pressure, temperature, and mixing conditions.
The model is simplified for flow under steady-state production conditions
and applied for a typical case involving the well operation at constant gas-,
oil-, and water-production rates at the wellhead. A solution of the governing
differential equations is obtained numerically, and the simulation results are
presented. The extent of the nonequilibrium effect on the deviation of the
pressure distribution along the wells from the equilibrium-model predictions is
delineated. The results obtained for nonequilibrium conditions are compared
with those obtained under equilibrium conditions, the latter of which is based
on conventional modeling assuming equilibrium between the various fluid phases.
This study demonstrates that the nonequilibrium gas saturation and
multiphase-fluid-pressure profiles along the well deviate from the equilibrium
results depending on the relaxation time involving the rate of gas transfer
from the metastable liquid phases to the gas phase.
© 2006. Society of Petroleum Engineers
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History
- Original manuscript received:
5 June 2004
- Revised manuscript received:
29 July 2005
- Manuscript approved:
2 August 2005
- Version of record:
20 February 2006
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