Upscaling Slides May 2012

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