Reservoir Properties Prediction Using Combination of Seismic Inversion and

Geostatistical Approach

Dyah Tribuanawati

Acoustic Impedancevolume

Porosity volume

Seismic InversionSeismic Inversion

•Improve the definition of lithology boundaries by the resolution of the interpretation. •The seismic data is now a rock property.

Acoustic Impedance from seismic data :Acoustic Impedance from seismic data :

Inverse processInverse process Remove wavelet and add low-frequency Remove wavelet and add low-frequency

componentcomponent Interval property rather than boundary propertyInterval property rather than boundary property Inversion itself does not deliver petrophysical Inversion itself does not deliver petrophysical

propertiesproperties

Seismic InversionSeismic Inversion

The object of using inversion is to convert the seismic section to more accurately represent the properties of the earth’s layers.

In reflection seismology, the seismic trace is the result of convolving a reflectivity series with a wavelet.

In seismic inverse modeling, the process is reversed

Geophysical inversion involves mapping the Geophysical inversion involves mapping the physical structure and physical structure and propertiesproperties of the subsurface of the earth using measurements of the subsurface of the earth using measurements made on the surface of the earth possibly constrained by made on the surface of the earth possibly constrained by well log well log measurementsmeasurements

Workflow of Seismic InversionWorkflow of Seismic Inversion

Beginning with the trace, essentially de-convolve it and end up with the reflectivity series.

This reflectivity series is then displayed side-by-side as a set of pseudo-acoustic logs, which we can then interpret as a cross-section of the subsurface in terms of its acoustic impedance distribution.

Forward ModelingForward Modeling Inverse ModelingInverse Modeling

Earth Model

Model Algorithm

Seismic Response

Seismic Response

Model Algorithm

Earth Model

ForwardModelling convolution

De-convolution

InverseModelling

Earth Wavelet Seismic*

Seismic / Wavelet AI

Seismic Inversion for Reservoir Characterization

Seismic Inversion : what is it ?Seismic Inversion : what is it ?

Inversion is the process of extracting, from the seismic data, the underlying geology which gave rise to that seismic.

Inversion is a non-unique process and there is not one method which is the best in all cases.

Types of inversion:•Band limited inversion•Model-based inversion•Sparse-spike inversion

Model-based and sparse-spike inversion gave the most detailed results.

Inversion is the process of extracting, from the seismic data, the underlying geology which gave rise to that seismic.

Traditionally, inversion has been applied to post-stack seismic data, with the aim of extracting acoustic impedance volumes.

Another recent development is to use inversion results to directly predict lithology parameters such as porosity and water saturation

Workflow for Acoustic Impedance Workflow for Acoustic Impedance (P-Impedance)(P-Impedance)

Seismic

P-Impedances

Wavelet

Constrains

Low frequency modelor initial model

Logs (Density & Velocity)

Seismic Horizons

Sparse spike Inversion workflow

Full Stack

Horizons

Calibrated Logs

ConstrainedSparse spike

inversion

P-Impedance

Porosity Distribution

Full Stack

Angle Stack

Existing Horizon

Well Logs

Shear Logs

Shear Modeling

Calibrated Logs

CSSI workflow

SADI workflow

SI workflow

Simultaneous Inversion WorkflowSimultaneous Inversion Workflow

Full Stack

CSSI (constrained Sparse Spike

Inversion

Calibrated Logs

Shear Synthetics

Horizons

IntegratedHorizons,Logs andSeismic

SimultaneousInversion

Angle Stack

SADI Property

Rock Properties

Simultaneous – SADI workflowSimultaneous – SADI workflow

Seismic0-10deg

Seismic10-20 deg

Seismic20-32 deg

Wavelet Wavelet Wavelet

EI logs EI logs EI logs

P-impedanceS-impedance

DensityVp/Vs

Poissonratio

Lambda-Rho

MuRho

Logs

Constrains &Low Frequency

Horizons

StatMod workflow using AIStatMod workflow using AI

CSSIimpedance

Revisedhorizons

LithologyClassification

Detailed earthmodel

Probability model

SISLithology

Histogram &Variogram

Pay sandprobability

WaveletsSyntheticVp/Vs

Vp/Vscube

Logs

Subsurface PropertiesSubsurface Properties

Estimate from seismic :Estimate from seismic :• LithofaciesLithofacies• PorosityPorosity• Depth, age, diagenesisDepth, age, diagenesis• Pressure Pressure • Fluid type (oil, gas, water)Fluid type (oil, gas, water)• SaturationSaturation• PermeabilityPermeability

Velocity-Rock Property General RelationsVelocity-Rock Property General Relations

Geological implication of Vp - PorosityGeological implication of Vp - Porosity

AI-Vp/Vs relation of sandstone

Well Seismic TieWell Seismic Tie

Stochastic Inversion provides resolution comparable to well logs

Top Reservoir

Seismicdata

Acoustic Impedance

Well Logdata

Well Data Preparation Well Data Preparation WorkflowWorkflow

Data Loading, QC and Selection

To load and QC well log data for availability, quality and consistency.

To compensate for borehole rugosity (washouts), remove invalid values, spikes, fill gaps, log editing, depth alignment and normalize if necessary.

Log Conditioning

To produce Vclay, Porosity and Saturation for the input of rock physics. Petrophysical analysis are doing to get best correlation of synthesis well data to seismic data.

Petrophysical Analysis

Improve data quality for Density, P-Sonic, S-Sonic and Vp/Vs value. Re-build P-Sonic and S-Sonic data at the missing area. Compensate for fluid invasion for the well data.

Rock Physics Modeling

Petrophysics / Rockphysics OverviewPetrophysics / Rockphysics Overview

Well log data play a critical role in quantitative seismic Well log data play a critical role in quantitative seismic reservoir characterizationreservoir characterization

Some usage of well log data:Some usage of well log data:

Wavelet estimationWavelet estimation Low frequency model buildingLow frequency model building Deriving relationship between rock properties (elastic) and Deriving relationship between rock properties (elastic) and

reservoir (petrophysical) propertiesreservoir (petrophysical) properties

Log ConditioningLog Conditioning Normally in washout/rugose area and missing data.Normally in washout/rugose area and missing data. No conditioning in reservoir or sand unless too No conditioning in reservoir or sand unless too

obvious/spike.obvious/spike. Create synthetic curve using Neutron, Deep Resistivity, Create synthetic curve using Neutron, Deep Resistivity,

Gamma Ray and density or P-Sonic.Gamma Ray and density or P-Sonic.

PetrophysicsPetrophysics

VCL, PHIT, PHIE and Sw calculation only reservoir VCL, PHIT, PHIE and Sw calculation only reservoir interval (generate synthetic-seismic correlation for interval (generate synthetic-seismic correlation for wavelet extraction)wavelet extraction)

To improve the definition of lithologic To improve the definition of lithologic boundaries by doubling the resolution of the boundaries by doubling the resolution of the interpretation. The seismic data is now a rock interpretation. The seismic data is now a rock property. property.

To return the rock properties of Acoustic To return the rock properties of Acoustic Impedances, Shear Impedance and Density.Impedances, Shear Impedance and Density.

BenefitBenefit

Inversion of seismic data to impedance improves exploration and reservoir Inversion of seismic data to impedance improves exploration and reservoir management success, producing more hydrocarbons with fewer, more management success, producing more hydrocarbons with fewer, more highly productive wells. highly productive wells.

Among the improvements are:Among the improvements are:– Higher resolution through reduction of the wavelet effects, tuning and Higher resolution through reduction of the wavelet effects, tuning and

side lobes. side lobes. – Incorporation of low frequencies not contained in the seismic data.Incorporation of low frequencies not contained in the seismic data.– Increase asset team interaction through the use of layer based (versus Increase asset team interaction through the use of layer based (versus

interface) acoustic impedance models that are readily understood by interface) acoustic impedance models that are readily understood by all asset team members.all asset team members.

– Accurate rock property modeling, as impedance can be related to Accurate rock property modeling, as impedance can be related to several key rock / petrophysical properties such as porosity, lithology several key rock / petrophysical properties such as porosity, lithology and water saturation.and water saturation.

BenefitBenefit

Better understanding of the accuracy of seismic data, well Better understanding of the accuracy of seismic data, well log data. quality and quality of input interpretations. log data. quality and quality of input interpretations. Through rigorous tying of the wells to the seismic and Through rigorous tying of the wells to the seismic and estimation of the waveform that is in the earth and the estimation of the waveform that is in the earth and the seismic inversion of the data back to well control, the seismic inversion of the data back to well control, the asset team can better understand accuracy and asset team can better understand accuracy and consistency of their input data.consistency of their input data.

Since drilling costs account for the majority of the total Since drilling costs account for the majority of the total E&P costs, reducing the number of wells required to E&P costs, reducing the number of wells required to exploit a field will have a significant impact on profitability.exploit a field will have a significant impact on profitability.

Example and Case Study

Seismic vs Acoustic ImpedanceSeismic vs Acoustic Impedance

Lithology ImpedanceSelatan A-6

0

5

10

15

20

25

30

35

40

45

50

P Impedance

Cou

nt

coal

carb. shale

shale

sand

SAND AREA

Lithology vs Acoustic ImpedanceLithology vs Acoustic Impedance

27000-280005000-9000 21000-2200016000-17000

Lithology Impedance

Acoustic Impedance sectionAcoustic Impedance section

Line Section

AI anomaly

A

B

A B A B

A B

A

B

channels

Line sectionGita Channel ?

C D

D

C

B

A B

A B

??

Line Section

E

F

E F

X

Y

X Y

Acoustic Impedance map below TAF window 10-20msAcoustic Impedance map below TAF window 10-20ms

Distributary channel

Tidal channels

GR (gAPI)0.0 150.0

SP (mV)-80.0 20.0

DEPTH_15

3200

3250

3300

3350

3400

3450

3500

3550

3600

TVDSS

3150

3200

3250

3300

3350

3400

3450

3500

3550

ILD (ohm.m)

0.2 20.0

NPHI (pu)60.0 0.0

RHOB (g/cm3)1.7 2.7

TOP_15

SES_TAF

Shaly sand

Introduction

Petrophysics and Rockphysics

Seismic Inversion Analysis

Tim

e =

0T

ime

= 0

Phase = 0Phase = 0

+90ﾟ+90ﾟ

-90ﾟ-90ﾟ

Tim

e =

0T

ime

= 0

Phase = 0Phase = 0

+90ﾟ+90ﾟ

-90ﾟ-90ﾟ

Tim

e =

0T

ime

= 0

Phase = 0Phase = 0

+90ﾟ+90ﾟ

-90ﾟ-90ﾟ

Tim

e =

0T

ime

= 0

Phase = 0Phase = 0

+90ﾟ+90ﾟ

-90ﾟ-90ﾟ

EI(08)

EI(13)

EI(18)

EI(20)T

ime

= 0

Tim

e =

0T

ime

= 0

Tim

e =

0T

ime

= 0

Tim

e =

0T

ime

= 0

Tim

e =

0

EI(08)

EI(13)

EI(18)

EI(20)

Phase = 0Phase = 0

+90ﾟ+90ﾟ

-90ﾟ-90ﾟ

Phase = 0Phase = 0

+90ﾟ+90ﾟ

-90ﾟ-90ﾟ

Phase = 0Phase = 0

+90ﾟ+90ﾟ

-90ﾟ-90ﾟ

Phase = 0Phase = 0

+90ﾟ+90ﾟ

-90ﾟ-90ﾟ

Corr.= 0.8994

Corr.= 0.8899

Corr.= 0.8915

Corr.= 0.8715

Corr.= 0.8657

Corr.= 0.4745

Corr.= 0.7755

Corr.= 0.7750

Wavelet Extraction

Preliminary Wavelet Estimation Preliminary Wavelet Estimation

Angle Stack

Amplitude Spectrumof the extracted Wavelet

Phase Spectrumof the extracted Wavelet

Extracted Wavelet

Near-upperNear- lower

P-impedance

Vp/Vs

Upper

Lower

Preliminary Seismic Well tiesPreliminary Seismic Well ties

Synthetic Seismogram(near = 8deg.) Near

Preliminary Seismic Well tiesPreliminary Seismic Well ties

P-impedance

Vp/Vs

Sw

Time correlation of Sonic D-Tto VSP D-T

Synthetic-Seismic CorrelationVersus moving time gate/location

Seismic Trace(Angle Stack 5-

11deg.)

Extracted Wavelet

Calculated fromRHOB-conditionedVp_sonic-logVs_sonic-log

Seismic Reservoir Characterization work in 2004

Well-logs

Core Data

3D Seismic Data(Angle Stacks)

Seismic Inversion(Elastic Impedance ; EI)

Petrophysical Analysis Rock Physics ModelingRock Physics Modeling

3D Lithofacies Prediction (PHIT, IND-SH)

Seismic Inversion Pilot Study in 2006

Well-logs

Core Data

3D Seismic Data3D Seismic Data(Angle Stacks)(Angle Stacks)

PGS 2001PGS 2001

Seismic InversionSeismic Inversion(Elastic Impedance ; EI)(Elastic Impedance ; EI)

Petrophysical AnalysisRock Physics ModelingRock Physics Modeling

3D Seismic Data3D Seismic Data(Angle Stacks)(Angle Stacks)

Petrophysical AnalysisPetrophysical AnalysisRock Physics ModelingRock Physics Modeling

Seismic InversionSeismic Inversion(Simultaneous Inversion – Ip, Is, Vp/Vs)(Simultaneous Inversion – Ip, Is, Vp/Vs)

3D Lithofacies Prediction (PHIT, IND-SH)3D Lithofacies Prediction (PHIT, IND-SH)3D Lithofacies Prediction (PHIT, VCL, PHIE)3D Lithofacies Prediction (PHIT, VCL, PHIE)

Petrophysical AnalysisRock Physics ModelingRock Physics Modeling

Seismic Inversion Pilot Study in 2006

Well-logs

Core Data

3D Seismic Data3D Seismic Data(Angle Stacks)(Angle Stacks)

PGS 2001PGS 2001

Seismic InversionSeismic Inversion(Elastic Impedance ; EI)(Elastic Impedance ; EI)

3D Seismic Data3D Seismic Data(Angle Stacks)(Angle Stacks)

Seismic InversionSeismic Inversion(Simultaneous Inversion – Ip, Is, Vp/Vs)(Simultaneous Inversion – Ip, Is, Vp/Vs)

3D Lithofacies Prediction (PHIT, IND-SH)3D Lithofacies Prediction (PHIT, IND-SH)3D Lithofacies Prediction (PHIT, VCL, PHIE)3D Lithofacies Prediction (PHIT, VCL, PHIE)

Petrophysical AnalysisPetrophysical AnalysisRock Physics ModelingRock Physics Modeling

INPEX

EI-16deg.

EI-22deg.

PHIT(Total Porosity)

IND_SH(Shale Indicator)

Rock Physics Modeling

EI-6deg.

Reservoir Characterization work

ρgas

Vpgas

Vsgas

ρwet

Vpwet

Vswet

ρdry

Vpdry

Vsdry

Work-flow of the Rock Physics Modeling

(INPUT)

VOLUME Fraction (from Petrophysics)Density(ρ), Velocity(Vp,Vs).

Pore Fluids (Gas, water etc.)

(OUTPUT)

“Modeled” - VpVp, , VsVs, ρbρb

ρma

Vpma

Vsma

Matrix(Solid Mineral Mixture)

Matrix + Dry Pore

Gas Saturated Rock

Water Saturated Rock

Xu and White (1995)

of

(Theoretical Formula)(Experimental Relations)

PETROPHYSICS RESULT Caliper

Gamma Ray Deep Rest.

Shallow Neutron.

Density RHOBCN

RHOB InpexModel

VCL-1 Sw-Jason

VCL-2

Low Frequency Velocity Model Low Frequency Velocity Model (Initial Model for Seismic Inversion) (Initial Model for Seismic Inversion)

Well-2Well-1

Petrophysical AnalysisRock Physics ModelingRock Physics Modeling

Seismic Inversion Pilot Study in 2006

Well-logs

Core Data

3D Seismic Data3D Seismic Data(Angle Stacks)(Angle Stacks)

PGS 2001PGS 2001

Seismic InversionSeismic Inversion(Elastic Impedance ; EI)(Elastic Impedance ; EI)

3D Seismic Data3D Seismic Data(Angle Stacks)(Angle Stacks)

Seismic InversionSeismic Inversion(Simultaneous Inversion – Ip, Is, Vp/Vs)(Simultaneous Inversion – Ip, Is, Vp/Vs)

3D Lithofacies Prediction (PHIT, IND-SH)3D Lithofacies Prediction (PHIT, IND-SH)3D Lithofacies Prediction (PHIT, VCL, PHIE)3D Lithofacies Prediction (PHIT, VCL, PHIE)

Petrophysical AnalysisPetrophysical AnalysisRock Physics ModelingRock Physics Modeling

VCL predicted from Inverted Ip and Vp/Vs

PHIT predicted from Inverted

Well-1 Well-1

PHIE predicted from PHIE=PHIT-0.157*VCL

Well-1 Well-1

Overview Reservoir Overview Reservoir CharacterizationCharacterization

Seismic to Reservoir PropertySeismic to Reservoir Property

Geoscientist vs Geostatistician Geoscientist vs Geostatistician

Geoscientist– Creates a map that is assumed to be correct until Creates a map that is assumed to be correct until

additional information becomes availableadditional information becomes available

Geostatistician– Creates an expected value or average map and has a Creates an expected value or average map and has a

quantitative estimate of its accuracyquantitative estimate of its accuracy

INTRODUCTIONINTRODUCTION

“Geo” clearly links geostatistics to the earth sciences.

The application of statistical methods in the earth sciences, particularly in geology.

Geostatistics provides a toolbox for the geologist to use in analyzing data and transferring such analysis and interpretation to the task of reservoir forecasting.

A tool can never replace data, but it can help build an interpretation and the corresponding numerical model.

Geostatistics

To be applied to quantitatively relate well and seismic data, assess the quality of the resulting map, estimate the probability of success from the available data

Fundamentals of Semivariogram Estimation, Fundamentals of Semivariogram Estimation, Modeling and UsageModeling and Usage

Semivariogram is a measure of the rate of change with distance for attributes that vary in space.

Semivariogram is required any geostatistical procedure for prediction away from well controls.

4 step procedures for Statistical tools4 step procedures for Statistical tools

To quantify the spatial continuity of the well data To quantify the spatial continuity of the well data using using Variogram AnalysisVariogram Analysis

To find and quantify a relationship between To find and quantify a relationship between well and well and seismic dataseismic data

To use what has been learned to grid the well data To use what has been learned to grid the well data using the seismic data as a guide via Kriging with using the seismic data as a guide via Kriging with external driftexternal drift

To assess the accuracy of the map just madeTo assess the accuracy of the map just made

Overview of geostatisticsOverview of geostatistics

VariogramVariogram KrigingKriging Kriging with external driftKriging with external drift CokrigingCokriging

The geostatistical method give the methodology for The geostatistical method give the methodology for quantitatively determining the spatial characteristics or quantitatively determining the spatial characteristics or geologic variables prior to countouringgeologic variables prior to countouring

Geostatistical MethodGeostatistical Method

Learn from the data through simple statistical data Learn from the data through simple statistical data analysis (mean, variances, min and max values, analysis (mean, variances, min and max values, histogram plot) and variogram analysis.histogram plot) and variogram analysis.

Find relationship between data sets through crossplot, Find relationship between data sets through crossplot, geophysics trying to find relationship between sparse geophysics trying to find relationship between sparse well data and relatively dense seismic data.well data and relatively dense seismic data.

Derived map based on Derived map based on Kriging and CokrigingKriging and Cokriging Assess the accuracy/error/risk of the map step 3. The Assess the accuracy/error/risk of the map step 3. The

assessment of risk is perhaps the greatest leap forward assessment of risk is perhaps the greatest leap forward that geostatistics provides in solving mapping problems.that geostatistics provides in solving mapping problems.

VariogramVariogram

* **

* *

Map distance between data points

Variance Best fit line =Variogram Model

A Variogram is a graph that is used to express the spatial continuity of a regionalized (mappable) variable. It is a crossplot of the average squared difference of the variable of interest between all data pairs a given distance apart (variance) versus distance apart.

*

*

*

*

**

Range

Semivariogram modelSemivariogram model

Semivariogram

0.50 1 1.50

0.5

1

1.5

Spherical

Exponential

Linear

Lag

Variogram

The key parameters that describe the variogram are :The key parameters that describe the variogram are :

– Nugget effect Nugget effect or the value of the model at zero or the value of the model at zero distancedistance

– SillSill or the variance of the dataor the variance of the data– RangeRange, or the breakover point from the correlated to , or the breakover point from the correlated to

uncorrelated zone of the variogramuncorrelated zone of the variogram

Variogram AnalysisVariogram Analysis

The Nugget is a gauge of measurement uncertainty. If it zero The Nugget is a gauge of measurement uncertainty. If it zero then the data would be honored exactly, the grid values then the data would be honored exactly, the grid values would not honor the well data.would not honor the well data.

Variogram analysis Variogram analysis can be used to can be used to identify and quantity identify and quantity the the fact that fact that spatial continuity spatial continuity can be longer in one direction can be longer in one direction than another (anisotropic) in the than another (anisotropic) in the control points via control points via directional variograms.directional variograms.

The direction and magnitude of the isotropy/anisotropy can The direction and magnitude of the isotropy/anisotropy can be used in subsequent steps of the geostatistical methodbe used in subsequent steps of the geostatistical method

Finding relationshipFinding relationship

Find the relationship between Find the relationship between seismic (soft seismic (soft data) and well data (hard data).data) and well data (hard data).

Crossploting of the well variable and the seismic Crossploting of the well variable and the seismic variable at the well location will sometimes lead variable at the well location will sometimes lead to finding usable relationship for to finding usable relationship for co-kriging.co-kriging.

C1

C2Nugget

Distance

Range

Variogram model

Calculated fromData points

Sill* * *

*

*

*

Parts of Variogram model. The Nugget quantifies measurement inconsistencyand the range is the break point between correlated and uncorrelated data

*

* *

Well data(Hard data)

Cross variogram model

Seismic data(Soft data)

Variogrammodel

Cokriging

Variogram model

Cokriged map

Cokriging using well and seismic data. Note theCross-variogram model in addition to variogram models.

Well data(Hard data)

Seismic data(Soft data)

Variogram model

Kriging withExternal

Drift

KED Map

Kriging with External Drift (KED) uses well dataand its variogram with seismic data

3 km

7000 7100

2 km

7400

1 km

Point tobe kriged

* *

*

Variance

Variogram model

1 2 3 km

Kriging vs Cokriging

KrigingKriging is a gridding algorithm that estimates a grid is a gridding algorithm that estimates a grid value such that for the parameter of interest, the value such that for the parameter of interest, the squared difference between the grid node value and the squared difference between the grid node value and the surrounding control points is consistentsurrounding control points is consistent

Co-krigingCo-kriging looks at not only spatial relationship in the looks at not only spatial relationship in the data to be gridded data to be gridded (porosity data as a hard data) (porosity data as a hard data) but but also spatial relationship in a second denser data set also spatial relationship in a second denser data set (Seismic as a soft data)(Seismic as a soft data)

is mathematically achieved by calculating the grid value as a is mathematically achieved by calculating the grid value as a weighted average of the surrounding control pointsweighted average of the surrounding control points. .

Kriging takes into account the Kriging takes into account the distance between control points distance between control points and the grid note to be calculated and how close the control and the grid note to be calculated and how close the control points are to each other (declustering) and maintains the points are to each other (declustering) and maintains the spatial relationship given by the variogram model. spatial relationship given by the variogram model.

The weights are assigned in such a way as to minimize the The weights are assigned in such a way as to minimize the variance in the least squares sense, thus eliminating variance in the least squares sense, thus eliminating systematic systematic overestimation or underestimation overestimation or underestimation error.error.

Kriging

Co-kriging

Co-kriging calculates a grid value as Co-kriging calculates a grid value as a weighted average a weighted average of control and guide points. of control and guide points.

Co-kriging takes into account Co-kriging takes into account how far the control how far the control and and guide points are from the grid point to be computed and guide points are from the grid point to be computed and how close control and guide datahow close control and guide data

Co-kriging also honors Co-kriging also honors spatial relationships found in the spatial relationships found in the variogram for the control data and guide data and in the variogram for the control data and guide data and in the cross variogram between control data and guide dacross variogram between control data and guide datata

ABSTRACT: Reservoir characterization in Kaji-Semoga Field, South Sumatra, Indonesia, using seismic inversion and geostatistical approach

Tribuanawati, Dyah , P.T. Exspan Sumatera, Jakarta, Indonesia

An integrated reservoir modeling study of the Baturaja Limestone has been conducted using 2-D seismic data from Kaji-Semoga Field, South Sumatra, Indonesia.

The work was designed to aid prediction of the lateral extent of the reservoir, to build a porosity model for use in flow simulation and reserve assessment and to evaluate uncertainty in reserve estimation. The method involved study of seismic attributes, followed by geological interpretation and Seismic Inversion modeling using wavelet estimation from a number of wells near the build-up.

Several geo-statistical techniques for integrating well log porosity with quantitative average porosity derived from a constrained sparse spike inversion method were applied in the reservoir modeling.

The spatial distribution of porosity in inter-well regions has been estimated based on variogram ranges and azimuth. Continuous petrophysical properties within each facies type were determined by application of kriging and co-kriging mapping simulation methods.

Co-kriging was initially tested on a numerically simulated reservoir model and compared with kriging, then a conventional least squares product technique relying only on local correlation between porosity and acoustic impedance was applied.

As compared to kriging, the seismically assisted geo-statistical method detects subtle lateral variations in porosity that cannot be mapped from sparse well data alone.

The result of the study shows that if a reservoir is seismically resolved and properly imaged, sparse spike inversion can be used in conjunction with geo-statistical methods to obtain a more complete reservoir description.

AAPG Search and Discovery Article #90913©2000 AAPG International Conference and Exhibition, Bali, Indonesia

ConclusionConclusion Reservoir scenarios representative of late exploration/appraisal, Reservoir scenarios representative of late exploration/appraisal,

development and mature field development phases were development and mature field development phases were designed to illustrate the impact of using seismic data as a designed to illustrate the impact of using seismic data as a secondary variable to constrain a reservoir description. secondary variable to constrain a reservoir description.

The integration of secondary data sets, such as Acoustic The integration of secondary data sets, such as Acoustic Impedance from Seismic data can significantly Impedance from Seismic data can significantly reduce inter-well reduce inter-well estimation uncertainty.estimation uncertainty.

Geostatistical methods are available that provide the Geostatistical methods are available that provide the fundamental framework for fundamental framework for quantitative data integrationquantitative data integration

ConclusionConclusion

The most important benefits of geostatistical The most important benefits of geostatistical methods is the availability to assess uncertainty methods is the availability to assess uncertainty associated with associated with kriging and cokriging using kriging and cokriging using stochastic methods.stochastic methods.

Example and Sample Case

Variogram model to derived sand package

Function Sill X-Range Y-Range Z-RangeSpherical 0.4 400 ft 400 ft 30 ft

Exponential 0.6 2000 ft 2000 ft 30 ft

Rock Fluid Index Sand probability

Sand probability

Vp/Vs

Paysand probability

Thickness Map

Thickness Map