Summary
This paper presents a transient wellbore simulator coupled with a
semianalytic temperature model for computing wellbore-fluid-temperature
profiles in flowing and shut-in wells. Either an analytic or a numeric
reservoir model can be combined with the transient wellbore model for rapid
computations of pressure, temperature, and velocity. We verified the simulator
with transient data from gas and oil wells, where both surface and downhole
data were available. The accuracy of the heat-transfer calculations improved
with a variable-earth-temperature model and a newly developed
numerical-differentiation scheme. This approach improved the calculated
wellbore fluid-temperature profile, which, in turn, increased the accuracy of
pressure calculations at both bottomhole and wellhead.
The proposed simulator accurately mimics afterflow during surface shut-in by
computing the velocity profile at each timestep and its consequent impact on
temperature and density profiles in the wellbore. Surrounding formation
temperature is updated in every timestep to account for changes in
heat-transfer rate between the hotter wellbore fluid and the cooler formation.
The optional hybrid numerical-differentiation routine removes the limitations
imposed by the constant relaxation-parameter assumption used in previous
analytic-temperature models.
Both forward and reverse simulations are feasible. Forward simulations
entail computing pressure, temperature, and velocity profiles at each wellbore
node to allow matching field data gathered at any point in the wellbore. In
contrast, reverse simulation allows translating pressures from one point to
another in the wellbore, such as wellhead to bottomhole condition.
Introduction
Modeling of the changing pressure, temperature, and density profiles in the
wellbore as a function of time is crucial for the design and analysis of
pressure-transient tests, particularly when data are gathered off-bottom or in
a deepwater setting, and the identification of potential flow-assurance issues.
Other applications of this modeling approach include improving the design of
production tubulars and artificial-lift systems, gathering pressure data for
continuous reservoir management, and estimating flow rates from multiple
producing horizons.
A coupled wellbore/reservoir simulator entails simultaneous solution of
mass, momentum, and energy balance equations, providing pressure and
temperature as a function of depth and time for a predetermined surface flow
rate. Almehaideb et al. (1989) studied the effects of multiphase flow and
wellbore phase segregation during well testing. They used a fully implicit
scheme to couple the wellbore and an isothermal black-oil reservoir model. The
wellbore model accounts only for mass and momentum changes with time.
Similarly, Winterfeld (1989) showed the simulations of buildup tests for both
single and two-phase flows in relation to wellbore storage and phase
redistribution. The Fairuzov et al. (2002) model formulation also falls into
this category.
Miller (1980) developed one of the earliest transient wellbore simulators,
which accounts for changes in geothermal-fluid energy while flowing up the
wellbore. In this model, mass and momentum equations are combined with the
energy equation to yield an expression for pressure. After solving for
pressure, density, energy, and velocity are calculated for the new timestep at
a well gridblock. Hasan and his coworkers presented wellbore/reservoir
simulators for gas (Kabir et al. 1996), oil (Hasan et al. 1997), and two-phase
(Hasan et al. 1998) flows. Their formulation consists of a solution of coupled
mass, momentum, and energy equations, all written in finite-difference form,
and requires time-consuming separate matrix operations. In all cases, the
wellbore model is coupled with an analytic reservoir model. Fan et al. (2000)
developed a wellbore simulator for analyzing gas-well buildup tests. Their
model uses a finite-difference scheme for heat transfer in the vertical
direction. The heat loss from the fluid to the surroundings in the radial
direction is represented by an analytical model.
© 2007. Society of Petroleum Engineers
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History
- Original manuscript received:
28 June 2006
- Revised manuscript received:
25 February 2007
- Manuscript approved:
4 March 2007
- Version of record:
20 June 2007
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