Research -- Reports

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Numerical Solution of the Buckley-Leverett Equation with a general fractional flow function, Report no. 76, Dept. of Mathematics, Univ. of Bergen, Norway
Abstract
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Simulating Flow in Fractures and Fracture Closure on a Generic Valhall Model, Unifob / CIPR Report UP 03 / 2006 (w. Standnes, Dag) (confidential)
Abstract
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An Improved Compaction Model for Reservoir Simulating and Coupled Flow -- Stress Simulation, Unifob / CIPR Report UP 05 / 2007
Abstract
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Benefits and Drawbacks of Horizontal vs. Geological Based Simulation Grids -- a study based on a Troll Segment Model,
Unifob / CIPR Report UP 03 / 2008 (confidential)
Abstract
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Two-phase Upscaling in Homogeneous Reservoir Examples. IFRA PASF JIP WP3 Phase 0 Simulation Study,
Uni CIPR Report UC 20/2014
Abstract
A dispersion-free numerical procedure for the solution of
nonlinear conservation equations based on exact solutions of
the Riemann Problem by the Random Choice Method is
reviewed. This paper is concentrated on the displacement of
oil by water in a onedimensional porous rock, however, the
technique applies equally well to a variety of physical
problems where accurate modelling of the evolution of
discontinuities / shock waves is imperative.
For immiscible displacement, the nonlinear part of the
conservation equation is an empirical function with error
bounds. The effect of representing the (unknown) smooth
nonlinearity function by a tabulated version is studied,
accompanied by a proof for the structural stability of the
problem with respect to small perturbations in the nonlinear
function.

The mechanisms of fluid flow in fractures in a chalk and
fracture closure were studied both by pure flow simulation,
and by coupled flow and rock mechanics simulation.
Simulated fracture flow as such, and different ways to model
the closure are discussed. Since the fractures are basically one-
dimensional objects, they are only to a small degree affected
by boundary conditions, and the closure can equally well be
modelled as a function of fluid pressure as of strain – a
considerable simplification. Explicit fracture modelling does
not seem to be necessary to obtain reliable simulated results.
Key words: Chalk, fractures, fracture closure, coupled
simulation

Based on exact strain calculations from a simplified coupled flow –
stress simulation run, the reservoir is subdivided into a number of
“pseudo soil regions” such that in each sub-region compaction is a
function of fluid pressure only, while still honouring the original soil
properties. This revised compaction model is tailored for the flow
simulator framework, and when used in that setting the flow
simulator computes a compaction state which is as good as identical
to the “exact” state computed from strain, in (almost) every grid cell.
The construction process is always possible, and an error tolerance
can be set such that coupled simulations can be guaranteed to run in
explicit mode (no pore volume iterations needed) without loss of
accuracy. The overall gain is a flow simulator computed compaction
field which is accurate at all times (not only at stress steps), and
which can be computed with significantly less computer effort than
with the standard approach
Key words: Compaction, Reservoir simulation, coupled simulation,
computational mechanics

In simulation models for reservoirs containing a thin oil zone, an alternative to the established approach of aligning the simulation
grid layers with geological layers (“geo-grid”), is to use a model with horizontal grid layers, at least covering the oil zone, and
possibly also all or parts of the gas cap and water zone. The motivation for this approach is that as the high resolution part of the
grid can be concentrated to regions of fluid contact movement, an improved representation of contact movement and cusping /
coning into horizontal wells can be expected. The main drawback is obviously that the geological description and petrophysics will
be poorer resolved than on a traditional grid, which is built in a manner tailored to honour these features. The aim of this study has
been to classify the benefits and drawbacks of using horizontal grids in thin-oil-zone reservoir models, and in the cases where such
grids actually are used, to identify some recommended practice.
The main conclusions from the study can be summarized as,
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True horizontal wells are better represented on a horizontal grid. In a geo-grid all well completions are approximated to the
nearest cell centre, which is an error source which may be significant.
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Using the same areal resolution, comparable results were obtained with geo-grids and horizontal grids. Gas production and
partly also water production was better resolved on the horizontal grid.
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For comparable grids the computer processing time was about 30-50% lower for the horizontal grid than the geo-grid.
Results from a geo-grid with local grid refinement near the horizontal wells were almost identical to the horizontal grid case,
but very costly in terms of computer time.
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Recommended strategies for the horizontal grid
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In the oil zone it was found that one meter thick layers was the best compromise between accuracy and computing time
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The use of horizontal layers in the gas cap and water zone depends on the process. In general, high resolution
horizontal layers should be used to capture contact movement.
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In this study the gas cap was in expansion mode, while the water zone was an active aquifer.
o
Almost identical results were achieved with only two horizontal layers in the gas cap, with a high resolution horizontal
grid in the gas cap, and using geo-layers in the gas cap. Hence, as the gas is in expansion mode, the resolution or
gridding strategy for the gas zone does not seem to be important.
o
During production, the oil-water contact moves upwards and downwards in a complex manner. This was best captured
by using a horizontal grid with slowly increasing layer thicknesses from the oil-water contact downwards, covering
about 20% of the water zone thickness, and geo-layers below.
Key words: Reservoir simulation, thin oil zone, horizontal wells, horizontal grid

The impact of simulation grid size and dimension has been studied for two-phase flow with
varying relative permeability, using three different reservoir simulator
Key words: Upscaling, homogeneous, two-phase, ECLIPSE, IMEX, STARS