part 6 upscaling ứng dụng địa thống kê trong tìm kiếm thăm dò dầu khí

bài giảng ứng dụng địa thống kê trong tìm kiếm thăm dò dầu khí. giúp sinh viên hiểu biết sâu hơn về những phương pháp như mô phỏng ngẫu nhiên, tất định, gauss . Từ đó làm cơ sở trong việc xây dựng mô hình địa chất 3D trong phần mềm petrel

Upscaling and Upgridding for

Reservoir Simulation

What is Upscaling?

block cell due to the fine scale local variation of rock properties with a

block cell due to the fine scale local variation of rock properties with a

homogeneous single value for that property across the cell

single property value for a given volume of interest, usually a fluid flow simulation

grid block

flow-based simulation experiments

The Position of Upscaling in

Reservoir Modelling Disciplines

Upscaling

Upscaling of Geological Properties

Example: Upscaling permeability by a factor of twenty five

Upscaling

Upscaling converts a set of fine scale geological properties into a

representative single block value for a given volume of interest.

The Danger of Arithmetic Averaging

of Permeability

Impermeable Gridblocks Permeable

Gridblocks

What is a Simulation Grid?

Unstructured Grid

Features that Govern the Design of a

Simulation Grid

as reservoir boundaries and faults

model assumptions were incorrect

often subject to change

Static Model to Dynamic Model

Workflow

Reservoir Data

Store (RDS)

Map Route 3D Geological Model

Route Import

Maps, Faults, Wells

Import, visualize and classify data

Import Wells

Structural

Model

Gridder

Property Model Create 3D

Gelogical Model

Create Structured Grid

Construct 3D Structural Model

Create Unstructured Grid

Upscale

Define boundary, create units from structural maps,

Assign prop maps to structural units, visualize, create properties or import 3D geological model

Create simulation grid from the 3D geological model

Import 3D Geological Model (RESCUE)

GeoModel in RESCUE format contains both structure and fine scale properties

Upscaler

3D Viewer

Upscale Properties

Import/

Visualize Data

Upscale properties for simulation grid

Generate time dependent and other data and perform simulation Visualize any imported

or generated data including simulation results

Export to Eclipse/

Schedule

Corner Point Geometry Grid

hexahedrons of varying dimensions

Rectangular Grid

hexahedrons with the same row or column dimensions within an X or Y row for a

rectangular grid boundary only

PEBI Grid

shapes and sizes; the shapes and sizes of which adapt to match grid features such as

boundaries, faults, and wells

boundaries, faults, and wells

Tetrahedral Grid

tetrahedrons of various sizes Tetrahedrons are used to match the grid to features such as

boundaries, faults, and wells; otherwise, rectangular hexahedrons are used for gridding

boundaries, faults, and wells; otherwise, rectangular hexahedrons are used for gridding

Gridding to Sloping Faults

upper-most fault trace and lower most fault trace used to deviate the grid to match the fault)

or segmented coordinate lines (intermediate fault traces used to deviate the grid to match

or segmented coordinate lines (intermediate fault traces used to deviate the grid to match

the fault)

LAYER 1

LAYER 2 LAYER 1 FAULT TRACES

LAYER 2

LAYER 3

Upscaling Effective Properties

Impact of Upscaling Method on

Effective Properties

1x1

10 10 10 10 10 10 10 10 100 100 100 100 100 100 100 100

10 10 10 10 10 10 10 100 100 100 100 100 100 100 100 10

10 10 10 10 10 10 100 100 100 100 100 100 100 100 10 10

10 10 10 10 10 100 100 100 100 100 100 100 100 10 10 10

10 10 10 10 100 100 100 100 100 100 100 100 10 10 10 10

16x16

32.8

Upscaling Method Effective Permeability

sampling

10 10 10 10 100 100 100 100 100 100 100 100 10 10 10 10

10 10 10 100 100 100 100 100 100 100 100 10 10 10 10 10

10 10 100 100 100 100 100 100 100 100 10 10 10 10 10 10

10 100 100 100 100 100 100 100 100 10 10 10 10 10 10 10

100 100 100 100 100 100 100 100 10 10 10 10 10 10 10 10

100 100 100 100 100 100 100 10 10 10 10 10 10 10 10 100

100 100 100 100 100 100 10 10 10 10 10 10 10 10 100 100

100 100 100 100 100 10 10 10 10 10 10 10 10 100 100 100

100 100 100 100 10 10 10 10 10 10 10 10 100 100 100 100

100 100 100 10 10 10 10 10 10 10 10 100 100 100 100 100

100 100 10 10 10 10 10 10 10 10 100 100 100 100 100 100

100 10 10 10 10 10 10 10 10 100 100 100 100 100 100 100

sampling

“an exact science”, it will always depend

on the type of reservoir and on engineering judgement

Upscaling Non-dimensional Real

Properties

dimensionless real numbers

average over the fine cells:

Upscaling Porosity

Simple Upscaling of Permeability

approximate flow solution

geometric factors This amounts to taking into consideration the cross-sectional area

and length of each fine scale grid block This is equivalent to using the volume and

squared length

because they cancel out

directions have the same form

Simple Upscaling of Permeability

Harmonic-Arithmetic Upscaling of

Permeability

tube (j,k) over j and k

Harmonic-Arithmetic Upscaling of

Permeability

„ The harmonic averages are

first calculated along 1D

stacks of cells in the x,y,z

directions

„ Followed by an arithmetic

means of the harmonic

averages

Arithmetic-Harmonic Upscaling of

Permeability

flux through each slab must be the same, the flux is given by the equation:

permeability, we obtain the final expression

permeability, we obtain the final expression

Arithmetic-Harmonic Upscaling of

Permeability

„ The arithmetic means are

first calculated in the selected

x,y,z plane.

„ Followed by a harmonic

average of the arithmetic

means

Validation of Upscaled Geological

Properties

Example: Validation of Upscaled Permeability

An “accurately” upscaled simulation grid has similar:

- Breakthrough time of displacement front

- Shape of displacement front

- Recovery

Completing the Reservoir

Simulation Model

Production History

Saturation Functions (Kr, Pc) Well Completions

Geometry, Rock Properties

Completing a Reservoir Simulation

Model

fluid and rock properties, initial distribution of phases in equilibrium, saturation functions for

fluid and rock properties, initial distribution of phases in equilibrium, saturation functions for

every rock type, and a set of time-dependent well completions and production history

and these components’ composition is constant except for changes in dissolved gas

individual components change with time, such as gas condensate dropout, depending on

the nature of the reservoir and injected fluids

Completing a Reservoir Simulation

Model

reservoir simulation, the system is initialized statically in a first step

based on the equilibrium data (initial pressure at reference depth, water-oil

contact or WOC, gas-oil contact or GOC, fluid densities, model geometry

and capillary pressure

from the geological model

significant coarsening of the reservoir model for the purpose of reservoir

simulation further investigations and possible modifications to the reservoir

simulation, further investigations and possible modifications to the reservoir

model are required

geometry and/or modifications to properties such as the pore volumes, in the

form of pore volume multipliers

Completing a Reservoir Simulation

Model

satisfactorily under static conditions, then the reservoir simulation model is operated under

the constraint of the historically observed production data, such as fluid production and

injection rates A history match of the reservoir simulation model with the observed data is

performed

reservoir simulation model that requires few model changes to achieve a static match

possibly the geophysical model

Completing a Reservoir Simulation

Model

that the simulation model gives a similar response to the behavior observed in the field

Typical parameters that are used to model response evaluation include:

response include:

Completing a Reservoir Simulation

Model

engineers make changes to the reservoir model parameters on a simulation block basis,

allowing a quick update of the simulation model and observation of the model response

allowing a quick update of the simulation model and observation of the model response

onto the changes

depending on the size and complexity of the reservoir

simulation model from the geological model and causes them to get out of sync

Completing a Reservoir Simulation

Model

achieve a history match on the geological model itself, keeping the geological model

consistent with the reservoir simulation model

simulation model, but as soon as the required changes are known, they should be

re-applied to the geological model and verified

at later stages of the modeling process to update the simulation model with updated or

improved geological data such as new development wells or updated fault locations seen

in reprocessed or higher-quality seismic surveys

Completing a Reservoir Simulation

Model

matching, you can then assume that you can use the model to make predictions

of reservoir operations in the future and then run multiple model scenarios to

of reservoir operations in the future and then run multiple model scenarios to

optimize field development and recovery of reserves Scenarios include

‰ artificial lift methods

by using, for example, polymer flooding or solvents) recovery mechanisms

modeling environment and then comparing the time-dependent fluid distribution

with those observed in 4D seismic results will close the loop between seismic,

geological modeling and reservoir simulation

Static Model to Dynamic Model

Workflow using GeoQuest Software

Property 3D CPS3/F3D

Struct & Prop.

Maps, Faults 3D Geol Model

(RESCUE)

Schedule

FloGrid - Generating 3D coarse simulation grid - Upscaling fine scale geol properties

- Generating well to grid connections

Grid Geometry &

Well Trajectory File

Preparing & combining time dependent data:

- Production data

- Well completions

Well Production &

Completion Data Schedule Section Include File

Well Deviations

GeoFrame

OilField

Manager

Finder

Eclipse Office SCAL

PVTi

VFPi

Saturation Funct.

PVT Functions

VFP tables

Gradients Sensitivity study during history matching

Eclipse Simulators

FloViz

GRAF

SimOpt

Eclipse Data

Sim Results

Sim Results

Black Oil or Comp.

Fluid Flow Simulation

3D Visualization Line Plots