upscaling slides may 2012
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Upscaling Tutorial
Gillian E. Pickup
May 2012
Purpose
• Ideally, upscaling tutorial should be part of
the Res Sim tutorials
• But,
– there is little time
– PE students do not know how to use Petrel
• However
– many students ask about upscaling during the
FDP or IP, so some training required
Outline
• Quick reminder of upscaling methods
– single-phase
• When to Upscale
• Upscaling in Petrel
• Exercises
Outline
• Quick reminder of upscaling methods
– single-phase
• When to Upscale
• Upscaling in Petrel
• Exercises
Flow Parallel to Uniform Layers
• Use the arithmetic average,
Dx
P1 P2
ki, ti Qi
n
i ii 1
eff a n
ii 1
t k
k k
t
Flow Across Uniform Layers
• Use the harmonic average,
Dx
Q
ki, ti
DPi
n
ii 1
eff h ni
i 1 i
t
k kt
k
Flow through Correlated Random
Fields
• Use the geometric average,
– assumes perm in each cell is different
correlation length
n
ii 1
g
ln(k )
k expn
Summary of Averaging Methods
• Flow along parallel layers
– Arithmetic average
• Flow across parallel layers
– Harmonic average
• Flow through a random model
– Geometric average
• Can apply these averages to models which are
approximately layered, or random
Numerical Methods
• Usually permeability distribution will not be so simple
• Need to use numerical methods
• Assume incompressible rock and fluids
• Also, assume steady-state linear flow
Boundary Conditions
• We need to specify the pressure or flows at the edge
of the model
– i.e. boundary conditions
• The resulting pressure distribution will depend on the
boundary conditions
Boundary Conditions
a) Constant Pressure, or No-flow boundary conditions
• Most common type of boundary conditions
• Use when there is little cross-flow
P1 P2
- - - - no flow through the sides - - - -
- - - - no flow through the sides - - - -
Effective Permeability Calculation
Pressure = P1
on left face Pressure= P2
on right face
L
Area, A Flow Rate, Q
x
y
z
Effective Permeability Calculation
P1 P2
L
A Q
x
y
z
1. Solve equations to give pressures, Pij for each block
2. Calculate inter-block flows in x-dir, using Darcy’s Law
3. Calculate total flow, Q, by summing individual flows
between any 2 planes.
4. Calculate keff using the equation:
5. Repeat for y-dir and z-dir.
eff,xk A P1 P2Q
L
c) Linear pressure BCs
– similar to fixed pressure boundaries, but
pressure gradient is linear along the sides
– keff from linear BCs > keff from Periodic BCs > keff
from No-Flow BCs
P1 P2
P1 P2
P1 P2
d) Flow jacket, or skin
– can be used to avoid the effects of boundary conditions
keff calculated for
this block
boundary conditions applied
to outer edges of model
Awkward Cases
• Cases with large permeability contrasts
• May get large errors
– Low perm shales in a high perm sandstone
– High perm channels in a low net/gross region
– High perm fractures in a low perm region
– Low perm faults in a high perm region
Summary of Single-Phase Flow
• Can use averaging for simple models
• For more complex models use numerical simulation
– various boundary conditions
What about Two-Phase Flow?
• We often have two-phase flow – water flood
– gas flood
• Heterogeneity affects the flood front
• Two opposing effects occur when upscaling
– loss of physical dispersion due to permeability
homogenisation
– increase of numerical dispersion due to larger grid size
• Should upscale for two-phase flow
– pseudo rel perms
Heterogeneous Permeability
Distribution
•PERMX
Oil Saturation
Soil
What about Two-Phase Flow?
• Schlumberger no longer supports the Pseudo
Package
– Kyte and Berry etc
– difficult to apply
– not robust
• Most people just use single phase upscaling
– but this can give wrong answers
• “Smart” single-phase upscaling helps
– see notes for details
Outline
• Quick reminder of upscaling methods
– single-phase
• When to Upscale
• Upscaling in Petrel
• Exercises
When to Upscale?
• First, what size of cells will you use in
your model?
• What factors should you consider?
When to Upscale?
• First, what size of cells will you use in
your model?
• What factors should you consider?
– what is required for decision to be made?
– how soon do you need the results?
– how much data is available?
– what is the large-scale geological structure
Some Factors to Consider
• What is required for the decision being made?
– when are the results required?
• How much data is there?
• What is the large-scale geological structure?
– make sure large-scale connectivity is adequately
represented
Some Factors to Consider
• Are small-scale structures likely to have an
effect?
– strong Pc contrasts?
– connectivity of small-scale heterogeneities?
• What is the recovery process?
– miscible processes may require finer grid
When to Upscale?
• Conventional approach developed during
1990s
– make detailed geological models (106 cells)
– upscale (1-phase) for simulation
– then history-match model
• Is this a good idea?
Alternative Approach
• Start with a coarse model
– test range of models for history-matching
– constrain major uncertainties
– refine model later
• as more data obtained
• if necessary
• Do we still need upscaling?
Problems with Coarse Models
• Miss out fine-scale detail
– under-estimate physical dispersion
– ignore interaction between heterogeneity and
two-phase flow
• capillary and gravity forces
• Numerical errors
– numerical dispersion
What Should You Do?
• Consider each model individually
– what decision are you trying to make?
• level of detail required?
– how much data is available?
• Remember you are dealing with a model
– always has limitations
Outline
• Quick reminder of upscaling methods
– single-phase
• When to Upscale
• Upscaling in Petrel
• Exercises
Upscaling Permeability in Petrel
• Simple averaging methods
– arithmetic, harmonic, geometric
• Numerical methods
– different boundary conditions
• open and closed
– diagonal tensors or full tensors
xx xy xz
yx yy yz
zx zy zz
k k k
k k k
k k k
x y zk k k
Upscaling in Petrel
• Upscales other properties
– porosity
– water saturation
– N/G
• weighted arithmetic average
• Also upscales well logs
– with simple averages
Outline
• Quick reminder of upscaling methods
– single-phase
• When to Upscale
• Upscaling in Petrel
• Exercises
Exercises
• Tutorial explained in notes
– easy stages
• 2D horizontal stochastic model
• 2D vertical layered model
Files in T:\Res Sim\Petrel Upscaling Tutorial
Model A Results
• Fine – sigma = 2, lamda = 40 m
Model A Results
• Coarse, upscaled by 20 x 20
Model A Results
• In this case upscaling did not make
much difference!
fine
coarse
Watercut
Model B Results
• The layering affects the vertical sweep
through the model
Model B Results
• The layering can be preserved using
non-uniform upscaling
– each colour represents one layer
Model B Results
• The coarse model with the zones
preserved give better recovery
upsx10
upsx6
fine, zones
Cumulative Oil Production
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