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

Case Studies

„ Case Studies: Marathon Oil

„ Case Study: Statfjord Formation in the Statfjord Field

„ Case Study: Major Arabian Carbonate

„ Stochastic Modeling of Surfaces

Case Study:

3-D Reservoir Characterization for

Improved Reservoir Management

SPE 37699

M J Uland, S W Tinker, D H Caldwell,

Marathon Oil

Permeability Cross-Section

North Brae Field

Permeability Cross-Section using the 2D maps from the original 13-layer Simulation

Model

Net-to-Gross Maps

North Brae Field

Three of the original 13-layer model net-to-gross 2D maps used as

aerial templates for both the deterministic and stochastic 3D

models

Permeability Cross-Section

North Brae Field

Permeability cross-section for the 140 layer deterministic 3D model

Note the increased reservoir heterogeneity as compared to the

homogeneous 13 layer simulation model

Permeability Cross-Section

North Brae Field

Permeability cross-section for the 120 layer stochastic 3D model

Note the difference in the permeability distribution between this

model and the deterministic 140 layer model

Permeability Cross-Section

North Brae Field

Permeability cross-section for the 27 layer simulation 3D model

that was upscaled from the 120 layer geostatistical model

Net Pay Map and Model

Lawrence Field

Original 2D waterflood netpay map

showing one continuous grainstone

reservoir

Stratigraphic 3D model showing individual grainstone bars that had different waterflood responses

Connected Geobodies

Lawrence Field

Connected geobodies from the 3D model The small red colored geobodies represent infill drilling targets

Simulation Models

Anonymous Field

The original 5-layer simulation

model using 2D maps

Upscaled porosity for the 21 units used in the secondary recovery 3D model

flow-Geobody Analysis

Anonymous Field

Geobody analysis from the 3D model indicates that a minimum of 20

flow-units would be needed to capture the higher permeability intervals

for use in a secondary recovery simulation model

Flow Unit Cross-Sections

porosity-transmissibility grids (shown in red) at the interface of each flow unit

Cross-Sections

Yates Field

Cross sections showing stratigraphic

framework used to construct the 3D

framework used to construct the 3D

geologic model (top) and the porosity

distribution within the 3D model

Stratigraphic grids and lithofacies

regions are superimposed on bottom

right section

Fence Diagram of Permeability

Yates Field

Fence diagram of permeability Permeability was calculated in every cell as a function

of porosity, lithology, pore type, texture and calcite cement White boxes indicate

actual permeability from core analysis

Structural Cross-Section

Yates Field

Structural cross section showing porosity

distribution in upper figure with well control

distribution in upper figure with well control

(vertical white lines) Porosity from the

stratigraphic model was extracted and used to

populate a 3D elevation slice model composed of

140 five-foot thick layers The figure on the right

is porosity from the elevations slice model Note

how the porosity structure is preserved

Turbidite Lobe GeoBodies

Ewing Bank 873 Field

Pre-development wells Five turbidite lobes based on seismic and welllobes based on seismic and well control that were used to constrain the reservoir porosity distribution in the initial 3D model (left)

Post-development wells Eight

turbidite lobes based on seismic and

well control that were used to

constrain the reservoir porosity

distribution in the current 3D model

(right)

Porosity Distribution

Ewing Bank 873 Field

Porosity distribution for the current 3D model using the 8 turbidite lobes as

constraints

Case Study:

Stochastic Modeling of Incised

Stochastic Modeling of Incised

Valley Geometries

Statfjord Field

AAPG Bulletin V 82 No 6 (June 1998)

A C MacDonald, L M Falt, A Hekton

Conceptual Framework for

Bounding Surfaces

Conceptual Framework for bounding surface development driven by cyclic base-level

fluctuations 1 base-level fall leads to the development of a regional erosion surface with incised

fluctuations 1, base level fall leads to the development of a regional erosion surface with incised

valleys, sequence boundary(SB1) 2, low rates of base-level rise/aggradation and confinement of

rivers within the valley produce a sand-rich valley fill that can be capped by a significant

base-level rise or flooding surface (FS1) 3, higher rates of base-base-level rise/aggradation and a wide,

nonconfined alluvial plain leads to the preservation of isolated channels within mudstone-rich

overbank deposits 4, renewed base-level fall causes the development of the next regional

erosion surface (SB2)

Sequence Boundaries Composed

of Incised Valleys, Terraces and

Interfluve

Sequence boundaries are composed of incised regions (valleys) and flatter regions

(terraces and interfluves) Significant flooding surfaces can occur within the valley

(FS1), at the top of the valley (FS2), or within the nonconfined alluvial plain (FS3)

Stochastic realizations of

Sequence Boundaries

Realizations of 2D gaussian functions in map view and in cross section The two surfaces

are simulated with identical parameters (and random seed numbers), except that

realization (1) uses and exponential variogram and realization (2) uses a gaussian

variogram Note the anisotropy that is oriented 45 degrees with respect to the x-axis

Scale is in meters

Parameterization of Valley Geometry

These figures illustrate the various steps involved in describing a single valley

associated with a single sequence boundary

Well Control and Sequence

Stratigraphic Correlations

Flooding Surface (FS4) Map View

and Cross Section Realizations

Sequence Boundary Realizations

Realizations of sequence boundary 5 in map and cross-section The

average depth map (lower right) is based on 100 simulations

Cross-Sections through two 3D

Realizations of Reservoir Stratigraphy

Gamma ray logs are at well locations Sandstone-rich valley-fill units (VF1-5) are in reds,

yellows and greens; mudstone-rich units (HS0-4) are in blues and purples

Stochastic Realizations of 3D Model

3D reservoir architecture

of realizations 58 and 86

The valley fills are y

illustrated consecutively

from the base and

upward The thickness of

each new valley fill is

illustrated with rainbow

colors where the reds and

yellow illustrate areas with

relatively thick valley fills,

and blues and illustrate

Statfjord Field Study Results

„ The simulated geometry's provided an improved description of reservoir distribution,

connectivity and barrier distribution

„ The improved reservoir description provided a better basis for predicting reservoir

performance and for designing well locations in complex fluvial reservoirs

„ Uncertainty in the reservoir architecture was accounted for by generating multiple

realizations

Statfjord Field Study

One Final Comment

„ “The main drawback to developing flexible, realistic models is that the number of

parameters that need to be estimated increases dramatically The danger is that

overestimating these parameters will become overly tedious Although there is clearly

a trade-off, this problem cannot be avoided totally, thus, geologists must equip

themselves with the analog data and develop appropriate procedures to simplify the

complex parameter estimation”

Integrated Reservoir Modelling of

a Major Arabian Carbonate

Major Arabian Carbonate Reservoir

„ Oil production from wells on a one

„ Oil production from wells on a

one-kilometer spacing with flank water

injection There has been significant

production and injection during the last

20 years

„ This has had rapid and erratic water

movement uncharacteristic of the rest

of the field and reason for building a

new geological and flow simulation

models

Modeling Process

„ Novel aspect was modeling

„ Novel aspect was modeling

permeability as the sum of a

matrix permeability and a

„ Typical modeling procedure

that could be applied to other

carbonates and to clastic

reservoirs

Indicator Simulation of Lithology

„ Presence / absence of limestone / dolomite was modeled with indicator simulation

on a by-layer basis

Gaussian Simulation of Porosity

„ Variogram model for porosity in limestone:

„ Variogram model for porosity in dolomite:

Gaussian Simulation of Porosity

„ Porosity models for limestone and dolomite were built on a by-layer basis then

put together according to the layer and lithology template

Indicator Simulation of Matrix

Permeability

Gaussian Simulation of

Large-Scale Permeability

„ Matrix permeability at each well location yields a K•h matrix

„ Well test-derived permeability at each well location yields a K•total

„ Subtraction yields a K•h large

„ Vertical distribution of K•h large scaleon a foot-by-foot basis is done by considering

multiple CFM data

Gaussian Simulation of

Large-Scale Permeability

„ Large-scale permeability models were built on a by-layer basis with SGSIM

„ Matrix permeability and large-scale permeability models were added together to yield

a geological model of permeability

„ A calibrated power average was considered to scale the geological model to the

resolution for flow simulation

Flow Simulation: First History

Match

Flow Simulation: Fourth History

Match

Stochastic Modeling of Surfaces

Stochastic Modeling of Surfaces

„ To assess uncertainty in pore volume or reservoir performance predictions requires

adding uncertainty to the gridded surface elevations

„ Characteristics of the uncertainty

… essentially zero at the well locations

… varies smoothly away from the wells

… variance depends on the quality of the seismic and the distance from the wells

Uncertainty at wells is 0

Uncertainty increases away from wells