Summary
An accurate well-modeling capability is important for both production- and
reservoir-engineering calculations. Ideally, the models used for these two
applications should be related in a logical manner. Multiscale methods allow
varying degrees of resolution and can, therefore, provide a natural link
between production and reservoir models. In this paper, we present a coupled
wellbore-/reservoir-flow model that is based on a multiscale
mixed-finite-element formulation for reservoir flow linked to a drift/flux
wellbore-flow representation. The model is able to capture efficiently the
effects of near-well heterogeneity in the reservoir and phase holdup and
pressure variation in the wellbore. The formulation presented here is for
oil/water systems. The basic reservoir/wellbore linkage is described and
validated through comparison to results from an existing simulator. The
multiscale method is then applied to a heterogeneous-reservoir model. Both
vertical and deviated wells are considered. Comparisons of the multiscale
solution to the fully resolved (fine-scale) solution demonstrate the efficiency
and high degree of accuracy of the method for both reservoir and wellbore
quantities.
Introduction
The accurate modeling of near-well flow effects is essential for large-scale
reservoir simulation and detailed production-engineering calculations.
Near-well models ideally should include wellbore- and reservoir-flow effects
and should be suitable both as standalone well-production applications and as
modules in reservoir simulators. Multiscale-finite-element methods, in concept,
are well-suited for this type of modeling because they allow varying resolution
and provide a systematic procedure for coarsening and refining. Thus, they can
provide the basis for a modeling framework that maintains consistency between
reservoir- and production-engineering models. To our knowledge, however,
multiscale methods have not yet been applied for this problem.
In this work, we develop a multiscale mixed-finite-element method (MsMFEM)
for modeling coupled wellbore and near-well flow. The MsMFEM solves the
pressure equation (in the reservoir domain) on a coarse grid but captures
fine-scale effects through basis functions determined from numerical solutions
of local single-phase-flow problems on the underlying fine-scale geological
grid. We fully resolve the well trajectory on the fine scale using a flexible
grid, which is close to radial around the well but logically Cartesian away
from the well. The flow within the wellbore is represented using a drift/flux
model. This model captures the slip between phases and provides the in-situ
phase fractions (holdup), which provide a means for computing the pressure
profile within the wellbore. Pressure variation within the wellbore is
important in many settings because it affects the local inflow from the
reservoir into the well (in the case of a production well).
Multiscale methods for reservoir simulation have been introduced as an
alternative to standard upscaling as a tool for more fully incorporating
fine-scale features at low computational cost. Among the relevant approaches
are the multiscale finite-element methods (e.g., Hou and Wu 1997; Efendiev et
al. 2006), the multiscale finite-volume method (Jenny et al. 2003) and the
MsMFEM (Chen and Hou 2003). The variational multiscale approach of Arbogast
(2000), also formulated within a mixed-finite-element context, represents
another related methodology. Here, we consider a version of the MsMFEM
introduced by Aarnes (2004) and extended in later publications (Aarnes et al.
2006, 2008).
© 2009. Society of Petroleum Engineers
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History
- Original manuscript received:
4 December 2006
- Meeting paper published:
26 February 2007
- Revised manuscript received:
18 July 2008
- Manuscript approved:
5 August 2008
- Published online:
16 March 2009
- Version of record:
1 March 2009
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