Generating Seismicly

8/2/2019 Generating Seismicly

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ABSTRACT

The classic integration of seismically-derived attributes into

geocellular models by collocated cokriging is revisited, leading

to improved geocellular modeling results above the seismic

bandwidth between wells. This article shows a practical ap-

proach to the challenge of downscaling and the integration of

the seismic acoustic impedance (seismic AI) attribute by cali-

brating it to the heterogeneity defined by the log-derived

acoustic impedance (log AI). The approach is a reduction of

the downscaling method by full cokriging to a simpler stepwise

sequential kriging to estimate the required parameters for sto-

chastic simulation. A downscaled model AI is created by com-

bining the low-frequency seismic attribute with a predicted

high-frequency component before it is integrated into the

porosity model using log data. The current tools of preference,

collocated cokriging and/or collocated co-simulation, assume

proportionality between the variogram structures for both the

synthetic log AI and the seismic AI. The problem with this as-

sumption is that the modeled attribute may closely resemble

the original low-resolution data. If the correlation between at-tributes is significant, then the resulting downscaled realiza-

tions by collocated methods look diffuse, so they are unsatis-

factory for use in high-resolution geocellular models. The

downscaling approach is redefined in this study by performing

analytical computations and verifications with real reservoir

data. A proper second order downscaling approach for seismic

AI must be based on full cokriging and non-collocated co-sim-

ulation using both the logs and seismic. A complete integration

should also reproduce the higher order geological heterogene-

ity, which is contained in the high-resolution well logs but not

normally shown in the seismic attributes. The numerical com-

plications of cokriging and the lack of robust tools in most ex-

isting software have motivated the development of practical

collocated solutions that can be implemented with less effort.

The contribution of this study is that it provides an alternative

non-collocated approach for better representation of the verti-

cal heterogeneity in geocellular models by downscaling the

seismic AI prior to integration.

INTRODUCTION

One of the challenges for integrating 3D seismic impedance

(seismic AI) datasets into 3D static geocellular models is the

limited vertical resolution of the original seismic data from

which the seismic AI is derived. The question of how to amal-

gamate the different resolutions between the vertically detailed

3D static models, predicted from well logs, and the lower reso-

lution seismic data has been identified as one of the major

challenges for integration of seismic data1 into geocellular

models. The essence of the problem is that correlations be-

tween rock properties are scale dependent2. Estimating pat-

terns of rock bodies and their properties (e.g., porosity andpermeability) in the high vertical resolution geocellular models

utilized for the reservoir development is in part limited by the

vertical resolution of the input seismic data. Note that seismic

data is usually imported to the modeling software as voxet

thick cells similar to pixels in images, and not nodes. The seis-

mic AI contains the low-frequency components of heterogene-

ity; however, the high-frequency components are unknown.

The physical reasons for the resolution limitations of seismic

data, which include the temporal frequency based on the two-

way time sample rate, are described in the literature3. To gain

information about the high-frequency heterogeneity of the

rocks, one has to resort to the synthetic acoustic impedance

(log AI) from the wells. The information in the log AI can be

considered as the convolution of the low-frequency seismic and

the high frequency impedance signal only available from logs.

Therefore, it is natural to conclude that the high-frequency

AI component at inter-well locations of the geocellular

model should be predicted from the well data before any

further integration of the seismic data into porosity models

using high-resolution logs is performed. The purpose is to

gain signal consistency with other logs (i.e., porosity) sam-

pled at high resolution.

If a geocellular model is constructed at high resolution (i.e.,from 0.5 to 1 ft average thickness), then direct integration of

the acoustic impedance seismic volume by collocated cokrig-

ing4 may not provide a consistent model because the collo-

cated correlations between the coarse resolution seismic AI and

the porosity well data may not be constant, even within a sin-

gle voxet cell. The reason for this is nonstationarity (i.e., the

covariance is a function of spatial location), and it involves the

missing high-frequency components. For example, the well

data may contain stringers of permeable sandstones sur-

rounded by impermeable shale dominating a voxet cell. Seis-

mic acoustic impedance voxet cells have a typical resolution of

Generating Seismicly-Derived High-ResolutionRock Properties for Horizontal DrillingOptimization in the Arabian Gulf

Authors: Dr. J.A. Vargas-Guzman, William L. Weibel, Idam Mustika and Qadria Anbar

60 WINTER 2011 SAUDI ARAMCO JOURNAL OF TECHNOLOGY


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SAUDI ARAMCO JOURNAL OF TECHNOLOGY WINTER 2011 61

a few milliseconds in the time domain, and depending on the

rock propagation velocity, which is equivalent to a thickness

that may be 30 times greater than the average cell in a high

vertical resolution 3D geocellular reservoir model. The prob-

lem can be quite severe due to the stringer sand bodies, with

high porosity and high permeability, may be diluted by averag-

ing in thick voxet cells of high acoustic impedance, which may

translate to false low porosity. The reverse phenomenon may

also be observed, and low porosity rocks (e.g., low permeabil-

ity barriers) may disappear after blending into the thick voxet

cells of low acoustic impedance.

The most popular integration approach, as is proposed in

the literature, is to predict a detailed resolution rock property

using collocated cokriging and associated co-simulation tools5;

however, as is argued in this study, collocated cokriging should

not be used for downscaling (i.e., predicting the high-frequency

AI) at the inter-well locations. Collocated cokriging assumes

the variogram structures for seismic and log data are propor-

tional for all lag distances. This is analogous to proposing that

the power spectra for seismic AI and well log derived AI in the

vertical direction should be proportional for every frequency.The Fourier transform provides the relation between spectra

and covariances or variograms, i.e., Bochners theorem6. The

missing high frequencies truncate the power spectrum of the

seismic AI; therefore, the variograms (or covariances) cannot

be proportional because the high-frequency component from

the log AI spectrum will add to the shape of the seismic AI

spectrum in the frequency domain. As a result, the high-fre-

quency component of the seismic, which is correlated to its

equivalent high-resolution porosity, needs to be incorporated

into the AI before the integration of the seismic data in such a

way that missing components are avoided. This convolution ofthe high-frequency and the low-frequency AI components must

be done in the spatial domain with geostatistics to achieve the

conditioning to the log AI data in the modeling results. At-

tempting the integration in the frequency domain will entail an

unconditional stochastic simulation of the high frequency com-

ponents7. In addition, a more detailed or higher resolution AI

model requires prior stratigraphic conditioning to the fine res-

olution, complex spatial geometry of rock bodies in the physi-

cal space8.

One data integration approach is to downscale the seismic

by incorporating the high-frequency component to match the

resolution of the well log data in such a way that spurious cor-relations (due to resolution differences and non-stationary co-

variances) are avoided. Another approach is direct simulation

based on parameters constrained by block kriging9; upscaling

of the log data instead of downscaling the seismic attributes

could help to match the seismic resolution. The weakness of

this latter approach is that it does not allow the construction

of the desired high-resolution geocellular models by integrating

well log porosity data because the high-frequency log AI infor-

mation is lost. An additional uncertainty is that the complex

geometries of the rocks may represent stringer sands or good

reservoir rock bodies that are strongly anisotropic and so lack

uniform lateral continuity. Therefore, the prediction of the

model may show a pixel with high porosity at the wellbore

while all surrounding cells do not conform to the expected

geobody. Some techniques have been devised that use seismic

amplitude vs. offset (AVO) analysis to come up with solutions

for detecting rock bodies using seismic anisotropy of the veloc-

ity field10. Such techniques are destined to fail if the limitations

of resolution are severe. A review of the state-of-the-art use of

rock physics and geostatistics is available11. It is evident that

the high-frequency variations in impedance and other seismic

properties cannot be measured in practice; therefore, after re-

visiting the theory required for a sound downscaling, this

study proposes a simple and practical methodology that re-

laxes the hard assumptions imposed in conventional collocated

methods. The theoretical principles for downscaling correlated

variables are detailed12. Enhancing the vertical resolution of

seismic is not a unique process, as the results are still stochastic

predictions; a sound downscaling strives to avoid unrealistic

results due to spurious correlations during the integration of

the data.A similar scaling situation is the use of prior low-resolution

numerical cellular models, of porosity and permeability, which

need to be locally updated to higher resolution with more de-

tailed data for single platform flow simulations. Another exam-

ple is the use of gamma ray or density rock property models

downscaled for geosteering operations. In this study, these types

of high-resolution models are named sector models and are

used to guide the drilling from offshore platforms. The real lim-

itation is not only the limited vertical resolution, but horizontal

resolution as well, as both resolutions are not independent of

each other. History matching is performed in sector models us-ing boundary flux conditions extracted from the whole reser-

voir model. Therefore, consistency between a sector model and

the prior model is a prerequisite for downscaling. The practical

importance of downscaling for nonconventional resources was

discussed13 presenting an example from the Athabasca oil

Fig. 1. Clastic reservoir schematic showing stratigraphy and sand-shale facies

(above) and porosity and permeability (High=Red) in a faulted sector model

(below). MRC well paths are also shown.


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sands. A simple approach is to perform a stochastic downscal-

ing that yields results that are conditional to the prior coarse

resolution model, assuming second order correlations only, and

very abundant local well data. Practical implementation of

commercially available tools suggests that proper data integra-

tion requires a detailed workflow to avoid the introduction of

spurious correlations. A sound integration of the seismic to

other higher vertical resolution data (e.g., porosity logs) is criti-

cal for improving the drilling and completion practices formaximum reservoir contact (MRC) multilateral wells, Fig. 1,

used in field development.

CROSS-CORRELATION: THE FUNDAMENTAL LAW OF

DATA INTEGRATION

Acoustic impedance in a voxet cell is equivalent to the combi-

nation of impedances of higher resolution elements (i.e., logs)

as follows: I-

= 1n where vj is the velocity and r j is the density ofeach element. Note that AI is noted as I for simplicity in

the mathematical formulations. The averaged computation is

I

-

=-rv-+ cov(p,v). The covariance cov(p,v) is the second order

similarity between the attributes, and -r and -v are the arithmetic(first order) averages. Therefore, not only the mean values

need to be known, but the associated covariance values have

to be included for exact upscaling. In statistical terms, the co-

variance is the entire average of all cross-covariances within

the cell. A concept a bit less popular than the classic Pearson

correlation coefficient is the cross-correlation coefficient14.

Two distinct rock properties can have nonproportional

covariance functions, or nonproportional variograms, Fig. 2.

This is common to all data integration exercises, and the cross-

covariance function is therefore nonproportional to either one

of the individual covariance or variogram functions. At least in

theory, if the synthetic log is correctly scaled to the seismic vol-

ume voxet, the spectra for the same low-frequency components

of acoustic impedance data should be proportional. Therefore,

a lack of good correlation between a synthetic acoustic imped-

ance log AI and the seismic AI after depth matching is really an

issue of resolution.

The negative Pearsons correlation coefficient between

porosity() and acoustic impedance Iis Eq. 1.

If you have numerous realizations of a simulated porosity

field (x) and an acoustic impedance field I(x) at high resolu-

tion following the well resolution log AI data resolution, then

it is evident that numerous realizations of the simulated field

are made of one random variable (xj) at each cell or location

(e.g., point node or volume element). The variable xj represents

the 3D coordinates x of each cells j center. The numerous

realizations are conditional to the same input data values (i.e.,

core porosity well data and unique coarse resolution seismic

AI). Therefore, the high-resolution model AI has to yield the

coarser seismic AI after upscaling (i.e., averaging of smallercells should yield the coarser cell data). The correlation coeffi-

cient for two random variables of porosity at locations x i and

xj is abbreviated as r(j, k). The correlation for the acoustic

impedance at those two locations is r(Ij, Ik ), and the correla-

tion between acoustic impedance and porosity is r(Ij, k). This

last term is called the cross-correlation and is usually com-

puted from an extension of Eqn. 1, using the cross-covariance

instead of the covariance, and using lag distances to represent

pairs of variables separated in different cells. Therefore, strictly

speaking, cross-covariance is just covariance between two at-

tribute random variables placed at two separated locations,j

and k. The cross correlation is related to the cross-covariance

as follows:

(1)

Since the pair-wise covariance for all pairs of cells cannot be

known as a priori, geostatistics uses a functional covariance es-

timated from stationary assumptions in the data. Such a co-

variance is directly related to variograms. The variogram for

the finer resolution shows the low range of variability, and the

variogram for the coarse resolution shows the long range of

variability only, Fig. 2. Cross-covariance is also represented by

functional forms, and the procedures of this type of modeling

are described in the literature14

. The cokriging and sequentialcokriging approaches utilized for downscaling require analyti-

cal models of cross-covariance, which are obtained using an

ambi-rotational technique generalized from Min/Max Autocor-

relation Factors (A-MAF), which is a spatial extension of the

Principal Component Analysis (PCA). A numerical example of

this approach is available15, and it is suitable for multivariate

models with up to two nested variogram structures.

THE COLLOCATED SIMPLIFICATION OF COKRIGING

Cokriging is an essential tool to generate co-simulation param-

eters, and the approach is described in various publications14,

16. Before the advent of sequential kriging, difficulties in invert-

ing large matrices and handling cumbersome unstable systems

of equations, to solve full cokriging systems, pushed geostatis-

ticians to consider a simplification termed collocated cokrig-

ing4. The result is that collocated cokriging is currently the

most widely used approach for data integration, and it is avail-

able in commercial software throughout the industry. A char-

acteristic of collocated cokriging is that the weight numbers

used to estimate porosity from acoustic impedance become

constant. If the acoustic impedance data is standardized (i.e.,

centered with mean zero and variance one), the collocated ap-

Fig. 2. Nonproportional variogram components for coarse and fine resolution

acoustic impedance.


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proach for standardized data can be written as:

(2)

where wj are the sequential kriging weights to update the

porosity estimates with data residuals after the acoustic imped-

ance has been projected to the space of porosity. Note that col-

located cokriging is formulated here as a stepwise approach to

avoid a simultaneous solution7. The collocation allows the use

of the correlation coefficient in the weight, and this correlation

can be made spatially variable. In addition, the seismic AI data

I is not sparse, and therefore represents constant values within

thick voxet cells. The geostatistical theory shows that the model

is valid if the functional cross-covariance and the individual

covariances are proportional (i.e., intrinsic co-regionalization).

Practical applications of collocated methods show that the

porosity in the collocation behaves as a projection of the

acoustic impedance following a linear regression type of

model. The end results show that such projections look

blocky, or resemble the original coarse resolution data, re-

gardless of the detailed grid utilized for the geocellular model-

ing. If the correlation coefficient is very high, the collocation

gives a projected copy of the coarse seismic AI data, which iscalled secondary input data in the geostatistical theory of cok-

riging. This problem was observed during the integration of

acoustic impedance in the construction of high-resolution

models to determine platform placement for offshore drilling

using petrophysical properties. The use of a constant correla-

tion may also lead to spurious local correlations between the

primary well AI data and the secondary seismic AI.

Oz and Deutsch (2002)1 examined the scale dependent cor-

relation theory that was developed2, and concluded that cross

correlations for properties (e.g., seismic and well log data) are

not independent of the resolution; therefore, the cross correlationcannot be ignored during the integration of data. The artifacts

observed in practice may disappear if the correct nonpropor-

tional cross-covariance and covariance are utilized with full

cokriging estimation of the co-simulation parameters. In this

article, analysis and testing suggests that collocated cokriging

should not be used for spatial estimation of properties that are

at different resolutions. The main reason is that properties at

different resolutions have nonproportional variograms. If the

properties have proportional variograms, they respond to in-

trinsic co-regionalization in geostatistics14.

STOCHASTIC SIMULATION AND ESTIMATION MADE

SIMPLE

The simulation operation requires drawing numbers from a

parametric conditional cumulative probability distribution at

each location. The simulation process uses a random number

generator to draw property values from a Gaussian distribu-

tion N(m j,s j) of values. The required parameters are the meanm j, and the standard deviation s j at each location, j. These pa-rameters are usually estimated by kriging. The most efficient

approach for cokriging estimation of a rock property (e.g.,

porosity) is called sequential cokriging. Successive or sequen-

tial cokriging uses one data value at a time, and does not reuse

already incorporated samples, (not to be confused with kriging

within the sequential Gaussian simulation). For example, as-

sume you have high resolution acoustic impedance at many

locations and porosity at fewer locations. If you take a single

porosity data point

and one acoustic impedance data point

Iat each step of the estimation process, then, the estimated

porosity is:

(3)

In the first step, sparse acoustic impedance data Ii is used to

estimate porosity at all locations (without using the porosity

data). The weight wI

, is used to convert the acoustic imped-

ance to porosity estimates at sample locations, and the weight,wI

j, is used to convert acoustic impedance into porosity at

non-sample locations. The partial result is an estimated poros-

ity that does not honor the log data. The weight w,sj

is then

applied to match the log data using the residual of the porosity

data minus the prior estimate, which is

-wI,i I. The weights

must come from ratios of conditional cross-covariances and

conditional variances17. The approach was derived using

Bayesian partitions of data sets, and it has been demonstratedthat the approach is as numerically exact as full cokriging. The

weights for acoustic impedance in sequential cokriging are not

constant, as used in the collocated version, Eqn. 2. The advan-

tage of sequential kriging is that it avoids the inversion of ma-

trices or the cumbersome solutions of large systems of equa-

tions that were initially proposed in the matrix form of

cokriging16.

PRACTICAL DOWNSCALING AND SIGNAL

EQUALIZATION

The seismic AI contains the low-frequency components of het-erogeneity; however, the high-frequency components are un-

known. To gain information about the high frequency hetero-

geneity of the rocks, one has to resort to the log AI at the

wells. The information in the log AI is equivalent to the convo-

lution of the low-frequency seismic and the high-frequency log

component, which is unknown outside the wellbores. There-

fore, the high-frequency component should be predicted from

the well data at the inter-well locations to gain modeling con-

sistency before further integration of the seismic data into the

porosity models, using the high-resolution logs, is performed.

The prediction of the high-frequency component can be madein the spatial domain using the sequential kriging and simula-

tion tools described above.

If a point set, extracted from the voxet cell centers, is painted

with seismic and well log AI data, the observed Pearson correla-

tion in a standard data cross-plot corresponds to the correlation

of voxet cell size (blocks), or averages, and the finer resolution

log AI. Estimation of properties (e.g., hydrocarbon in place)

with upscaling requires correct block averaging of porosity as

provided by block cokriging. This is equivalent to estimating

blocks using finer resolution data. Moreover, the downscaling

problem requires the corresponding enhancement of local vari-


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1. The seismic AI is sampled at the centers of the voxet cells as

a point set. The seismic AI power spectrum in the vertical

direction is compared to a set of validated wells to make

sure the low-frequency components are properly equalized

to the voxet size, upscaled synthetic well log AI.

2. The low-frequency component (seismic AI) is estimated at

all high-resolution cells in the geocellular model following

the stratigraphic system of coordinates. Due to the large

amount of data in the point set, stochastic simulation was

not necessary to generate this low-frequency component.

3. The high-frequency data is constructed at the wells by sub-

tracting the seismic AI model (step 2) from the synthetic log

AI. The residuals are treated as conditional components7.

The high-frequency component is simulated in the geocellu-

lar grid constrained to stratigraphy and rock regions.

4. The high and low AI models are combined and the results

are quality controlled.

5. The integration step can be handled in various ways:

a. If the variograms of porosity and the model AI are non-

proportional, cokriging should be used, which requires

the cross-covariance.b. A faster approach is to use the cross-correlation between the

model AI and the well porosity data. The model AI is

projected in porosity space with the collocated correlation

for each rock type and stratigraphic zone, and the residual

between the actual well porosity data and the projected

porosity component is simulated using a conditional

covariance function created from a conditional spectrum.

c. If the downscaled seismic AI is highly correlated to the

porosity, using collocated co-simulation works well for

data at the same resolution.

d. In the examples that follow, the authors decided to avoidthe use of collocated methods and cross-covariance struc-

tures; this allowed a full range of automated vendor soft-

ware to be used. The model AI (which contains the high-

frequency simulated component) was re-sampled follow-

ing the initial seismic AI point set, and then projected to

the porosity space using a linear model. The resulting

data was merged with the well log porosity, and a simple

stochastic simulation, honoring the statistics of the poros-

ity log conditional to the merged data, was applied using

the statistical parameters of the log porosity as the cell

size support. The clastic reservoir example includes prior

knowledge of the permeability from the coarse resolutionflow simulation models.

Carbonate Reservoir Example

This carbonate case study is from the middle Jurassic Lower

Fadhili formation. The target reservoir is strongly affected by

diagenesis on one of the flanks of a structural anticline. This

reservoir heterogeneity is critical for the optimal placement of

water injector wells, used to maintain the reservoir pressure. In

addition, the reservoir rocks follow a complex progradation

depositional sequence. The rocks are permeable grainstones,

A second order downscaling is performed with stepwise se-

quential cokriging of the seismic and log AI and simulation us-

ing covariances; however, a more advanced approach has been

introduced18 that uses cumulants to add the higher order sta-

tistical information. Downscaling in practice requires addi-

tional information in the geocellular model to guide the spatial

estimations and stochastic simulations. The downscaling ap-

proach should also consider nonstationary stratigraphic mod-

els of rock types and regions constructed using a priori low-

frequency seismic, analogs and/or categorical data.

The final result of combining the low- and high-frequency

seismic and well AI is a downscaled model AI that can be

transformed to the frequency domain. It contains all the fre-

quencies and spectra in the synthetic log AI, and it should yield

the coarse resolution voxet after back vertical upscaling. The

downscaled acoustic impedance is unique only at the centers of

each voxet cell and at the wells. The rest of the domain is sim-

ulated, but looks strongly constrained to the seismic because it

is using as many samples (centers of voxet cells) as there are in

the seismic volumes zone of interest.

Most software packages contain univariate simulation toolsto perform modeling by using data sets A and B stepwise with-

out major complications. In addition, the proposed approach

considers that adding posterior data on top of the smooth

prior can still honor the statistics of the posterior conditioning

to the data, Eqn. 3. A word of caution: You cannot assume a

priori the independence between the seismic AI and the high-

frequency residual from the log AI. If some amount of correla-

tion remains, you may have to remove the redundancy before

constructing the high-frequency component.

INTEGRATION OF DATA AFTER SPATIALDOWNSCALING

The integration of downscaled acoustic impedance to porosity

logs is straightforward, provided that correlations are consis-

tent. Such consistency is achieved by spatial downscaling and

integration. The collocated approach may not produce strong

artifacts when both variables (e.g., porosity and acoustic im-

pedance) are at the same high resolution and the specified cor-

relations are locally valid; however, local departures due to

nonstationary covariance can cause problems and instability.

Therefore, the practical recommendation is to resort to co-sim-

ulation with sequential cokriging if non-stationary covariancebecomes a problem. Note that Eqns. 2 and 3 provide the dif-

ference or information lost by not using sequential cokriging to

evaluate the probability distribution parameters for simulation

of porosity conditional to the downscaled model AI.

CARBONATE AND CLASTIC RESERVOIR EXAMPLES

Workflow Followed in the Studies

The steps used in the downscaling and integration workflow

are summarized:



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passing to wakestones and mudstones towards the south. The

overall trends of the rocks can be seen in the seismic attributes.

The reservoir coarsens upwards to the north and becomes fine

textured towards the south. Dolomitization and other diage-

netic effects have caused the reservoir to become less perme-

able on the flanks. The formation facies vary from peloidal

skeletal mudstones to packstones. Variography was performed

and the direction of anisotropy (i.e., trend) of the carbonate

platform bodies was identified following a general 120 az-

imuth. The extensive variability of the reservoir rocks and the

diagenetic effects required a careful nonstationary model. The

seismic AI data was incorporated to handle this otherwise un-

predictable heterogeneity.A seismic AI volume is of fairly low resolution, Fig. 3. The

objective of the study was to improve the high-resolution spatial

model distribution of porosity by integrating the negatively

correlated seismic AI. Downscaling and integration were applied

after the sampled point set (as previously explained) was com-

bined with the synthetic log AI from the wells. Figure 4 shows

the downscaled acoustic impedance. The initial porosity model

without the seismic acoustic impedance data is too continuous

laterally, and could not represent the diagenesis effect. The

downscaling prior to integration methodology allowed for a

more realistic porosity model to be generated. A secondary

trend is extracted at the crest of the anticline from the acoustic

impedance. This trend cannot be explained by carbonate depo-

sition, but may be due to deterioration of the rock quality at

the flanks of the anticline due to diagenesis, Fig. 5. Figure 6

shows examples of the coarse and fine resolution acoustic im-

pedance followed by the porosity model from the integration

of data. The results were checked to ensure the data was prop-

erly matching the spatial location and first and second order

parameters. In addition, history matching was performed (not

shown here) in which the contribution of the integration of

data was absolutely necessary.

Clastic Reservoir Example

In the second example, an offshore clastic reservoir model was

initially constructed conditional to hundreds of wells. The

rocks consist of a thicker main sand zone overlain by sand-

stone stringers intercalated with shales. Intermediate rock

qualities are shaley sands and sandy shales, which are part of

fining upward sequences in tidal and distributary channels.

The main sand is made up of staked fining upward sands.

Some coarsening upward features appear as isolated sand bars.

The challenge in this reservoir is to develop production in the

upper stringer sands, which are less likely to be intercepted by

vertical wells. The development strategy is therefore to drill de-viated wells to intersect the sand stringers, then plug back and

drill a horizontal production section along the stringers, with

completion at MRC.

Additional production drilling required the placement of

platforms selected from the global reservoir model. The initial

areal resolution of cells was 125 x 125 m2, and the vertical res-

olution was approximately 2 ft on average. The goal was to

construct a detailed reservoir model with a 50 x 50 m2 cell size.

The model should contain the same heterogeneities as in the

prior coarser well only model, including faults and stratigraphy.

The initial efforts showed that downscaling using collocated

techniques was disappointing; the final model showed blocky

artifacts (i.e., too similar properties in neighboring cells) con-

forming to the coarse voxet and ignoring the new higher reso-

lution grid. One of the reasons for the artifacts was that the

correlation between the prior and the posterior models had to

be kept significant (as shown in the data) to assure that the

flux boundary conditions from the coarser resolution model,

to be applied during dynamic forecast, would still be valid for

the downscaled versions of the model.

After the construction of high-resolution grids, the rock

properties were downscaled from the original coarse resolution

Fig. 4. Coarse initial (left) and higher resolution (right) acoustic impedance models

for the carbonate reservoir (High=Blue; Low=Red).

Fig. 5. Coarse (left) and downscaled (center) acoustic impedance models, and a high resolution (right) porosity models (High=Reddish) for the carbonate reservoir.

Fig. 6. Coarse (left) and downscaled (center) acoustic impedance models

(High=Blue; Low=Red) and a porosity model (right) for the carbonate reservoir

(High=Reddish/Yellow).



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model with additional new wells already existing at the plat-

form. The end results for the sector static models, including the

new, successfully completed wells, are shown in Fig. 1. The

statistics of the variability (i.e., moments) of heterogeneity

show valid results, which are consistent with the second order

expectances. These models are being used to place new wells

after the flow simulations provided a positive match and the

expected flow rates without water encroachment.

CONCLUSIONS

The methodology for the integration of seismic AI data into

porosity models has been revisited with a proposal to generate

a model AI that combines the low-frequency seismic AI with a

predicted high-frequency well AI. Since seismic AI contains only

the low-frequency components (i.e., within the seismic band-

width), the high-frequency components have been extracted from

the synthetic well log AI as residuals, or the difference between

the seismic AI and the log AI, after careful depth matching. The

log AI predicted at inter-well locations is equivalent to the con-

volution of the seismic AI and the high frequency unknown ge-

ologic component. Predictions of the higher frequency AI may

not have significant correlations with the seismic in practice,

but they were performed incorporating the known stratigra-

phy, facies and/or rock regions to create a nonstationary model

AI. The search for a different integration method is motivated

by some of the current drawbacks in traditional downscaling

with collocated cokriging, mainly the spurious correlations

that may occur between collocated seismic AI and log AI. The

correlations may be spurious in areas where the seismic AI val-

ues are less representative of the true geology due to a low sig-

nal-to-noise ratio. Non-stationarity issues also encouraged

searching for better ways to downscale seismic AI. Downscalingwith signal equalization is implemented in the frequency do-

main, and conditioning to the wells leads to geostatistical esti-

mates of the high-frequency component in the final spatial

model. An advantage of using the approach outlined here is

that it does not require solving systems of equations and re-

solving the stability complications found in full cokriging. There-

fore, the proposed parameter estimation via sequential cokrig-

ing for stochastic simulation is a practical tool for downscaling

and integration of seismic attributes into geocellular models.

ACKNOWLEDGMENTS

The thoughtful review of Saudi Aramco and SPE colleagues is

deeply appreciated. The authors would like to thank Saudi

Aramco management for granting permission to publish this

article.

This article was presented at the SPE Reservoir Characteri-

zation and Simulation Conference and Exhibition, Abu Dhabi,

U.A.E., October 9-11, 2011.

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William L. (Bill) Weibel is a Geophysi-

cist with more than 30 years of oil in-

dustry experience, the last 10 years be-

ing with the Reservoir Characterization

Department (RCD) of Saudi Aramcos

Exploration organization. Since joining

Saudi Aramco in 2000, he has con-

tributed seismic interpretations that have defined the struc-

ture and provided reservoir quality estimation of several

fields, including Berri, Qatif, Abu Safah, Dammam, Khur-saniyah, Hawtah, Manifa and Shaybah.

He has authored and coauthored two technical papers

for conferences held by the European Association of

Geoscientists & Engineers (EAGE) and the Society of

Petroleum Engineers (SPE).

In 1981, Bill received his M.S. degree from the

University of Arizona, Tucson, AZ.

Idam Mustika joined Saudi Aramco in

2008 as a Geologist Geomodeler in the

Reservoir Characterization Department,

Geological Modeling Division, and has

been a geological modeler at the EventSolution also. He has modeled numer-

ous gigantic reservoirs and worked in

various seismic integration projects, improving models for

history matching. Before joining Saudi Aramco, Idam

worked for Schlumberger, YPF, Maxus, Repsol CNOOC SES

and Petronas Carigali Sdn Bhd as a Geomodeler and Devel-

opment Geologist, residing in various countries.

In 2000, Idam received his B.S. degree in Geology from

Padjadjaran University, Bandung, Indonesia.

Qadria Al-Anbar is a Geological Con-

sultant working with the Geological

Modeling Division. Since joining Saudi

Aramco in June 1980, she has worked

in several different divisions, including

the Exploration Division, Reservoir

Geology Division, Hydrology Division,

Biostratigraphy Division and Northern Reservoir Geology

Division. Qadria is the second female Geologist in Saudi

Aramco and the first one to work in building 3D geological

models. Her work has had a big impact on development

plans for oil fields and the increase of natural reserves.

In 2002, Qadria received the 1st Annual Technical

Achievement Award as a member of the Geological

Modeling Group for her major role in facilitating theconsiderable reserves increase.

She received her B.S. degree in Geology from Damascus

University, Damascus, Syria.

BIOGRAPHIES

Dr. Jose Antonio Vargas-Guzmn joined

Saudi Aramco in 2002 and works as a Con-

sultant with the Reservoir Characterization

Department, Geological Modeling Division.

During his career, he has been involved in

mathematical applications to 3D geological

modeling and evaluation, and he is the sen-

ior author of many journal papers, book reviews and book

chapters; he and has received numerous literature citations. The

International Association for Mathematical Geology (IAMG)

conferred on him the Best Paper Award from the Mathematical

Geology journal for his peer-reviewed paper on successive esti-mation of spatial conditional distributions in 2003. The IAMG

also bestowed on him the Best Reviewer Award from the Jour-

nal of Mathematical Geosciences in 2007.

Jose Antonio is a former Fulbright and DAAD Scholar. In

1998, he received his Ph.D. degree from the University of

Arizona, Tucson, AZ, where he has also served as a research

associate, instructor and full time faculty member. He was

granted a graduate scholarship and a post-doctoral fellowship

with funding provided by the U.S. Nuclear Regulatory

Commission (NRC) and the Department of Energy (DOE),

respectively. Also, he was a research fellow in advanced

geostatistics at the University of Queensland, Australia. In the

1980s, he served as a Chief Geologist for Socit Gnrale deSurveillance (SGS).

Jose Antonios most outstanding inventions are 3D

geological modeling algorithms, such as sequential-kriging,

stochastic simulation by successive residuals, conditional

decompositions, transitive modeling of facies, spatial up-scaling

of the lognormal distribution, downscaling methods for seismic

data with derivatives of the variogram, scale effect of principal

component analysis, power random fields, and cumulants for

higher-order spatial statistics of complex rock systems and

heavy tailed distributions of permeability fields.


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