Summary
Geologists often generate highly heterogeneous descriptions of reservoirs,
containing complex structures which are likely to give rise to very tortuous
flow paths. However, these models contain too many grid cells for multiphase
flow simulation, and the number of cells must be reduced by upscaling for
reservoir simulation. Conventional upscaling methods often have difficulty in
the representation of tortuous flow paths, mainly because of the inappropriate
assumptions concerning the boundary conditions. An accurate and practical
upscaling method is therefore required to preserve the flow features caused by
highly heterogeneous fine scale geological description.
In this paper, the problems encountered in routinely used upscaling
approaches are outlined, and a more accurate and practical way of performing
upscaling is proposed. The new upscaling method, Well Drive Upscaling (WDU),
employs the wells and the actual reservoir boundary conditions (e.g., faults
and physical boundaries of the geological model). The main advantage of this
method is that the dominant flow paths can be preserved, and thus the
geological knowledge can be assimilated appropriately. The new method has
firstly been applied to a synthetic model with a tortuous channel, and is shown
to have significant improvement over the traditional approach. The sensitivity
study on the scale-up factor using a benchmark model shows the advantage of the
method with various scale-up factors. The method was then applied to a model of
a field in the central North Sea, which involves three-phase flow. In the cases
studied, the WDU method produced a comparable result to the dynamic Pore Volume
Weighted approach, which involves running the fine grid simulation and
computing appropriate relative permeabilities and interblock
transmissibilities. The new method makes the upscaling process practical, and
our tests show it to be more accurate than traditional methods.
Introduction
The heterogeneity observed in a field is generally high and the geological
structures therein can be complex. From a geological point of view, it would be
ideal to represent each facies boundary, both vertically and horizontally, by a
gridblock boundary (Mallet 1997; Deutsch and Tran 2002). Also, if distinct
layering exists within a genetic unit, a further split into subunits is also
desirable. In practice, reservoir models are usually created at the scale of
meters or less vertically and 100 meters or less areally [and each block itself
may have involved small-scale upscaling (Pickup et al. 2005)]. In many cases,
detailed reservoir modeling for a highly heterogeneous reservoir may result in
a large number of grid cells (e.g., 106 grid cells or more). This large number
of grid cells prohibits direct simulation of the reservoir, especially for a
very heterogeneous reservoir model. This is because, apart from the limitation
of computational power, the high level of heterogeneity often makes it
difficult to obtain a converged solution. The problem becomes more severe when
simulations involve three-phase flow. In order to perform reservoir simulation
on a highly heterogeneous geological model within a reasonable time frame, we
have to apply appropriate upscaling techniques to reduce the number of grid
cells so as to speed up the reservoir simulation and thus field development
planning process.
Although a number of upscaling methods have been developed in the past a few
decades (Pickup et al. 2005; Christie 1996, 2001), they are often not
satisfactory and have been discussed in a number of critical reviews (Barker
and Thibeau 1997; Farmer 2002). The main conflict in the application of the
current upscaling techniques lies in the balance of the accuracy and
practicality of the methods. There are two main problems that cause the
conflict. The first is the problem of using inappropriate boundary conditions
in single-phase upscaling, which is likely to reduce the accuracy, and the
second problem is the impracticality of the dynamic two-phase upscaling which
should (in theory) be more accurate. Details of the these methods have been
discussed in a number of reviews on upscaling (Christie 1996, 2001; Barker and
Thibeau 1997; Farmer 2002; Renard and de Marsily 1997), so a complete review of
upscaling methods will not be presented here. However, we outline one of the
commonly used methods: the pressure solution method for upscaling single-phase
flow. In this method, a single-phase pressure solve is carried out in each
coarse cell in turn, and Darcy’s law is used to calculate the effective
permeability tensor (Christie 1996). In order to solve the pressure equation,
boundary conditions must be applied to each cell. (This is referred to as the
local upscaling method.) A typical example is the no-flow, or constant pressure
boundary condition, where the pressure is fixed at either end of the region of
a coarse block, and no flow is allowed through the sides. Other boundary
conditions include linear pressure and periodic boundary conditions (Farmer
2002). Such boundary conditions, however, may differ significantly from the
actual boundary conditions within a heterogeneous fine-scale model (Chen et al.
2003; Zhang 2006). A highly heterogeneous reservoir model often produces
tortuous flow paths, and it is difficult to generalize a flow pattern on the
boundaries of a coarse block and apply to all the coarse blocks in a reservoir
model. The flow paths for a coarse model may be completely different from the
original fine-scale geological model response when inappropriate boundary
conditions are applied (i.e., the effect of geological structure may be lost).
A multiphase flow simulation from such a coarse model will not honor the
small-scale geological structure either, even if we ignore the error caused by
multiphase flow effects in the upscaling process.
© 2008. Society of Petroleum Engineers
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History
- Original manuscript received:
21 August 2006
- Meeting paper published:
5 December 2006
- Revised manuscript received:
10 May 2007
- Manuscript approved:
10 May 2007
- Version of record:
20 March 2008
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