breaking of a paradigm: geology can provide 3d complex … · 2018-12-27 · geological inversion...

Copyright 1999, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the 1999 SPE Annual Technical Conference andExhibition held in Houston, Texas, 3–6 October 1999.

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AbstractStationarity of the random function is the key property of

stochastic models to the extent that wrong hypotheses couldlead to very unrealistic reservoir modeling for flowsimulations.

When non stationarity is suspected at the scale of thedomain to be modeled, geologists usually propose eithergeological drift or seismic attributes to constrain stochasticmodels.However, in both cases, confidence in the soft data is limitedby the rough aspect of the trends from geological input, thescale problem, and the quality of correlations between therandom function and the variables from seismic data.

This paper presents an original approach for buildingcomplex 3D prior probability fields of geological facies. Itconstitutes a very challenging way of integrating two majoradvances in geosciences in recent years: geostatistics andsequence stratigraphy.

From facies descriptions on cores and logs,palaeobathymetry curves of deposits are constructed for eachwell. Logs of the accommodation potential (increment of spaceavailable for sediment accumulation) are then produced fromthose curves and deposit thicknesses in the wells.A Principal Components Analysis of data in all wells makes itpossible to separate the signal into two components: a commonfactor which represents the tectono-eustatic activity at fieldscale (easily extrapolated), and residuals which correspond tolocal variations in subsidence. 3D grids of accommodationpotential and palaeobathymetry can then be modeled, withrespect to the time intervals within each layer.Geological inversion is therefore possible and leads to theproposal of a complex 3D prior probability field for facies

modeling, with different organizations in both thetransgressive and the prograding parts of the sequence.When constrained by such trends, stochastic modeling (objectbased or SIS) can render very realistic images of reservoirheterogeneity.This method was applied successfully in carbonate and mixed(silici-clastic and carbonate) platform reservoirs, in whichproperties are highly variable and non stationary.

IntroductionThe recent development of stochastic simulation of

reservoir heterogeneity was conducted in a balanced waybetween the two persistent and yet opposing concerns:• the quest for objectivity1, that has led to abuses in

principles such as parsimony, indifference and moreovermaximum entropy –any model should introduce minimumartifacts of its own– ;

• the quest for reality, motivated by the needs of gettinggeologically realistic 3D distribution of sedimentological,and therefore petrophysical, features.The quest for objectivity leads to favoring hard data –

usually well data in reservoir modeling– whereas the quest forreality leads to integrating additional information available onthe spatial distribution, through concepts or soft data.

The realistic or non realistic aspect of geological imagesgenerated by stochastic simulations is a consequence of twostochastic model input parameters, stationarity (explicitparameter) and the constancy of the sedimentation rate(implicit parameter):• Stationarity: it has been demonstrated as a key parameter

on both the evaluation of Original Hydrocarbons In Placeand flow simulation results 2,3.For a given random function (RF), stationarity can be anacceptable hypothesis at a given scale, but unacceptable atother scales. Equally, this hypothesis can be valid for sometypes of reservoirs, but could be impossible to apply forother types.Usually, due to the low density of hard data in the oilindustry, stationarity is a hypothesis which is not tested. Itis therefore a choice, a decision, which has a major effecton the results.When modeling geological facies –a categorical RF– usingsequential simulation, the local conditional

SPE 56652

Breaking of a Paradigm: Geology Can Provide 3D Complex Probability Fields forStochastic Facies ModellingGerard J. Massonnat, SPE, Elf Exploration Production

2 GERARD J. MASSONNAT SPE 56652

probability is calculated using the conditioning data(original and previously simulated), the prior probabilityand variograms.When the RF is stationary, the prior probability is constant:in that case it corresponds to the average of the faciesproportions encountered in the wells.If the stationarity hypothesis is refuted, additionalinformation, generally of geological or seismic origin, mustbe input.Geological knowledge at basin scale or even at reservoirscale –if the well information is considered good–can beadded through external drift. Due to the uncertainty whichgenerally exists around the sedimentary model, thisexternal drift is usually highly smoothed, as is consequentlythe evolution of the prior probability.Other methods4,5 can be used to input non stationarity inthe stochastic simulation. However, all such methods arebased on prior knowledge usually obtained from aninterpretation, and therefore of level n+1 with respect tothe information contained in the hard data.Another, now conventional, method of building nonstationary reservoir models is to use seismic information6.Seismic information has the incomparable advantage ofbeing present over the entire 3D field. Co-simulationtechniques exist, making it possible to respect the harddata, the global statistics, and the covariance between theseismic variable and the RF being modeled.However, use of seismic attributes during co–simulation offacies can generate a certain number of problems relatedto: the resolution difference between the variable beingsimulated and the seismic information, the type of variable(a seismic attribute is a continuous RF, a geological faciesis a categorical RF) and the level of correlation betweenthe RF being simulated and the seismic attribute.In all cases, non stationary simulation of geological faciesfor a reservoir model building appears to be a delicateprocess: external drifts are over–smoothed and littledocumented, seismic variables must be used withcaution, ....The ideal solution would be to create a prior probabilityfield in which geological information would be used moreadvantageously than it is now, so that the localconditioning probability could integrate most of thepotentially available geological information.Since the development of sequence stratigraphy 7,sedimentary concepts have largely evolved and haveacquired a greater predictive nature.This paper discusses how sedimentological advances canbe used in non-stationary stochastic facies modeling whiledefining a new method constrained by sequencestratigraphy.This will finally break the paradigm saying that "Geologycannot provide quantitative trends".

• The constancy of the sedimentation rate: when a reservoiris layered in order to build a stochastic model, there are 2possible main cases: either the reservoir is considered as a"sugar box" (i.e. thickness is divided by the same numberof layers everywhere in the model), or as a stratigraphicgrid (with onlap or downlap).In both cases, and for a given location, the sedimentationrate is implicitly considered as homogenous as far as thelayers are of the same thickness all along the vertical axis.When a prior facies proportion is computed from well data,proportions are computed for each layer as if itcorresponded to a homogenous time interval. If this priorproportion exhibits vertical drift3, then non stationarity willbe considered as a very significant input parameter for thestochastic model.However, once again sequence stratigraphy has shown thatthis principle is erroneous, a time interval can in fact berepresented either by a deposit or by a surface.Through pertinent use of sequence stratigraphy during wellanalysis, this paper also proposes a method of layeringbased on time, which would make it possible to calculate amuch more realistic prior probability.

What can we learn from sequence stratigraphy?Since its advent in the late 70's, this stratigraphic theory

adapted to the seismic scale7 –seismic stratigraphy– hasevolved in major ways, and is now widely a applied concept atany scale –sequence stratigraphy–in hydrocarbon explorationand reservoir studies9.Its application at reservoir scale10 makes it possible to discernthe following items:

Accommodation and accommodation potentialAccommodation is the total available space that can

accommodate a sedimentary deposit. In marine domains, thisincludes a volume defined between sea level and thesubstratum at the beginning of the period of sedimentation(Fig. 1).

Accommodation must not be confused withpalaeobathymetry, which is the free space for sedimentationbetween sea level and the top of previously depositedsediments.

The accommodation potential is a result of regionaleustatic and local tectonic (subsidence or uplift) components.The space available for sedimentary accumulations, termedaccommodation potential, varies with time. This parameterrepresents the sum of eustatic sea level variation andsubsidence for given time

In the stratigraphic record, the accommodation potential(per time interval) is best approximated by the sum of the ∆palaeobathymetry between the bottom and top of interval, andthe thickness of the deposits.

SPE BREAKING OF A PARADIGM: GEOLOGY CAN PROVIDE 3D COMPLEX PROBABILITY FIELDS FOR STOCHASTIC FACIES MODELLING 3

Fig.1 — Accomodation as a result of eustatic, and regional / local tectonic subsidence components

Fig.2 — Genetic stratigraphy as a tool for prediction of lateral evolution of facies (from Homewood)


Stratigraphic surfaces and system tractsUsing seismic observations, an Exxon team7 has proposed

a geometric organization –type of deposits on passivecontinental margins. By integrating the sedimentation rate andthe accommodation potential, a complex evolution of thebathymetric deposits can therefore be produced for a givenpoint.Remarkable surfaces are defined with respect to thebathymetric evolution:• the sequence boundary (SB) corresponds to the most

regressive configuration in the stratigraphic architecture. Itcan be an unconformable surface in a continental orproximal position;

• the transgressive surface (TS) is an erosional surfaceproduced by wave action during transgression; it cancoincide with the sequence boundary on continentalplatforms.

• the maximum flooding surface (MFS) corresponds to themost transgressional configuration of the stratigraphicarchitecture, i.e. it corresponds to the maximum bathymetryof the deposits.

Between these different surfaces, different system tracts(stratigraphic units determined by the evolution of the sea levelwith respect to the bathymetric profile) can also be defined:• the low stand system tract (LST) between the sequence

boundary and the transgressive surface, downstream of thecontinental slope;

• the transgressive system tract (TST) between thetransgressive surface and the maximum flooding surface;

• the high stand system tract (HST) between the maximumflooding surface and sequence boundary.

All of these system tracts constitute a depositionalsequence, which is the basic stratigraphic unit at seismic scale,delimited by two sequence boundaries.Based on analyses performed in seismic stratigraphy, curveshave been produced of global sea level variations as a functionof geological time11.

Genetic unitsMoving up from reservoir scale to high resolution

sequence stratigraphy8,9,10 has required looking at things froma new angle and defining a new vocabulary.A genetic unit is therefore the smallest basic unit of thestratigraphic architecture which can be identified on anoutcrop, core or log. It is a set of genetically related faciesdelimited by two maximum flooding surfaces.A genetic unit is the response to a variation in theaccommodation rate (or sedimentary supply rate) and, throughits regional continuity, has a chronostratigraphic value.

Genetic stratigraphy and stratigraphic architectureReasoning in terms of genetic stratigraphy makes it

possible to predict lateral equivalents (Fig. 2) by producing aninterpretation in terms of accommodation variations andintegrating the effects of volumetric partitioning10.The contributions of sequence stratigraphy essentially involvepredicting the spatial distribution of deposits (by locating theavailable space => system tracts) and the volumetricpartitioning (facies distribution in time and space).Depending on whether the depositional architecture isregressive (= seaward stepping) or transgressive (landwardstepping) different facies tracts will be preserved duringsedimentation (Fig 3).

Fig.3 — Example of volumetric partitioning : facies tracts are different regarding the type of system tract (from Eischenseer)


A methodology for constraining stochastic faciesmodeling using sequence stratigraphy

Background: stratigraphic modelingThe predictive aspect of sequence stratigraphy, especially

through genetic stratigraphy, led sedimentologists, at a veryearly stage, to attempt to model a series of sedimentarydeposits using stratigraphic methods.

Stratigraphic modeling typically uses the sedimentary inputparameters to reconstruct and predict the stratigraphicarchitecture.

The accommodation potential is one of the most importantinput parameters, besides the rates of sedimentation anderosion12. The accommodation potential, i.e. the increment ofspace available for sediment accumulation, is the sum ofeustatic variations and rate of subsidence. Although mostalgorithms provide only 1D or 2D stratigraphic solutions, themost advanced stratigraphic models propose 3D solutions forsedimentary architecture13,14. These deterministic simulationsare based on the reconstruction of depositional processes in asequence of time steps from past to present. Thisreconstruction is performed using the following mainparameters: the accommodation potential (usually kridgedthroughout the domain), the sediment supply (both thesediment volume deposited in the basin and the total sedimentsupply provided by erosion are estimated by the user), and thesediment transport (the sediment transport function is adiffusive equation). The transport functions used in the modelmerely average several transport processes and therefore canonly reproduce macro-scale average geometry and faciestrends in the basin14 (typical grid size is 1 to 10 km).These large-scale modeling results can be input as an externaldrift in a stochastic simulation of geological facies at reservoirscale. This non-stationary stochastic simulation is widelyinfluenced by large scale stratigraphic modeling, a processwhich is unfortunately essentially deterministic. However, theidea of constraining in this way facies simulation using astratigraphic concepts is excellent. For this reason, the methodproposed in this paper is based on the use of accommodationpotential curves, but with a purely stochastic approach.

Outline of the methodologyThe method is based on the principle that a close

relationship exists between the facies and depositionalbathymetry. This hypothesis is conventionally accepted tocalculate the accommodation potential. It consists indescribing a predetermined water depth value for givenfacies15.

The hypothesis is valid especially for platform deposits,and can be applied with good results to mixed and carbonateplatforms. Although for the latter, facies distribution is morecomplex as it involves an additional parameter, climate. Theprinciples of sequence stratigraphy usually work well16 and itsuse can thus be justified when calculating the accommodationpotential.Furthermore, this type of environment can constitute a perfectcase study for a non stationary simulation methodology. Due

to the low bathymetry of the deposits, minor variations in theaccommodation potential at a constant sedimentation rate leadto significant variations in the type of facies deposited. Thefacies proportions RF of these deposits is therefore generallynon stationary at all scales and in 3D.

The proposed methodology makes use of thecorrespondence between facies and bathymetry in order toboth calculate the accommodation potential at the well and, atthe end of the process, to generate an inversion and provide aprior facies probability which is a function ofpalaeobathymetry and system tract to the stochastic model.

The key step in the method resides in building a 3D grid ofthe palaeobathymetry which is used in the inversion.Three main steps are therefore distinguished in the proposedmethodology:• Constructing curves of accommodation potential at wells;• Processing of these curves in order to obtain a 3D

palaeobathymetry grid;• Stochastic modeling based on a prior probability deduced

from the inversion.

Constructing curves of accommodation potential at wells

Constructing palaeobathymetry curves at wellsA series of sedimentary facies is described at the well using

logs and cores, and is then interpreted and divided into geneticunits.

The facies are grouped into associations bysedimentologists who propose palaeobathymetry ranges forthese associations (= environments), potentially supported byfaunal indications.Assigning a palaeobathymetry value to each depth takes intoaccount the sedimentary environment encountered at thatdepth and the direction of evolution of the curve with respectto successive environments pre-established for that sequence-palaeogeography (Fig. 4).A palaeobathymetry curve is thus automatically produced foreach well. Depending on the position of the well in thepalaeobathymetry profile, the palaeobathymetry curve willmore or less exhibit high-frequency variations.

Probability of facies = f (palaeobathymetry, system tract)Using the bathymetry ranges provided by sedimentologists

for each environment (= facies association), the probability ofthe occurrence of an environment for a givenpalaeobathymetry can be calculated (Fig. 4).Furthermore, palaeobathymetry curves were calculated at thewells either directly from the faunal data, or using thebathymetry ranges of the environments. Statistics cantherefore be calculated to test the relation between facies andpalaeobathymetry. These statistics must be producedindependently for each type of environment and system tract.• Probability (Environment) = f(palaeobathymetry)• Probability (facies) = f (palaeobathymetry, environment,

system tract)⇒ can then be used to calculate Probability (facies) =

f (palaeobathymetry, system tract).


Fig.4a — Bathymetry range per environment(for given system tract)

ENVIRONMENT FACIES

1 A

2 B, C

3 D, E, F

4 G, H

5 I

Fig.4b —Facies partitionning within environments (for given system tract)

Fig.4c — Environment probability versus Bathymetry Fig.4d — Evolution of facies probability within an(for given system tract) environment, from experimental statistics

Example of Env. 3. (for given system tract)

Fig.4e — Facies probability versus Bathymetry (for given system tract)

Fig.4 From sedimentology to prior proportions of facies for stochastic modelling

PriorProportionsof Facies

+

GeologicalKnowledge


The cumulation of these probabilities for each facies (Fig. 4)makes it possible to obtain the prior probability field when a3D palaeobathymetry grid is available for the inversion.

From Bathymetry to Accommodation PotentialThe interval being modeled is then discretized into a given

number of layers such that the discretization interval allows agood representation of heterogeneity in the stochastic model.For each genetic unit, layering is applied with a constantnumber of layers in the field, each layer representing the samereservoir thickness proportion along a given vertical cross-section (Fig. 5). Such “sugar box” layering, implicitlyacknowledges that the sedimentation rate preserved in eachlayer was constant over the entire structure. This amounts tosaying that layering represents a constant time scale over theentire domain. This hypothesis is erroneous, of course, andcorrections will be discussed further down.

In each well grid block, the accommodation potential isbuilt using the following equation:

AP = (T + ∆B)t0 → t1 where:

AP t0 → t1 = Accommodation Potential between t0 and t1

T = Thickness of the layer

∆ t0 → t1 = ∆ Bathymetry between the underlying layer and thelayer being considered

Finally, along each vertical line studied, a cumulativeaccommodation curve was produced by summing the values ofthe accommodation potential. A long-term accommodationincrease is usually observed, due to thermal subsidence.

Short-term fluctuations are induced by eustatic variationsand local tectonics.

Readjusting accommodation potential curvesFor any 2 sections or wells of varying thickness,

discretized with the same number of layers, the graphicrepresentation makes it possible to compare the 2accommodation potential curves. This representation consistsin stretching the curve which corresponds to the thinnest layer(Fig. 5). Each layer represents a constant thickness vertically,but a variable thickness laterally.

Working this way favors discretization of thickness. Afterstretching, gridding would have a chronostratigraphicsignification if the sedimentation rate is constant in both timeand space. But this hypothesis is false, proving that there is acertain discrepancy between the different accommodationpotential curves since events were not necessarily recorded atthe same relative level in the series.

It is therefore necessary to readjust the accommodationpotential curves in order to find the proper time lines.Examination of similar structures representing variations inisochron accommodations was therefore undertaken.Potential accommodation curves are readjusted by translatingcumulative accommodation curves and accumulated thickness,all of which will be readjusted simultaneously and in the sameway.

The distribution of the accommodation potential istherefore modified but the cumulative accommodation ispreserved. From this cumulative curve, it is thus possible torecalculate an accommodation potential which will ultimatelybe used (Fig. 6), since the readjustment induces a modificationin the amplitudes of the curves due to the modification in thetime scale.

Similarly, cumulated thickness curves make it possible torecalculate the thickness of each layer. At the end of thisoperation, all wells are discretized with the same number oflayers, but each grid corresponds to a sedimentary thicknesswhich can vary along a vertical axis. This time, layeringfavors time as each layer is actually a time line (Fig. 5).

This steps constitutes a significant advancement withrespect to all other existing methods. It could help managemore complex sedimentary configurations in the future such aserosions, onlaps, ....

Constructing a 3D grid of palaeobathymetry

Analysis of accommodation potential curvesThe objective of this phase is to extract components which

could easily be extrapolated in 3D, from the signal obtainedfrom recalculated accommodation potential curves.The recalculated accommodation potential curves are theresult of the sum of the common factor (corresponding toeustatic variations and reservoir scale subsidence) and ofspecific factors (representing local subsidence variations aswell as of the sum of local uncertainties: assigning facies,palaeobathymetry range, readjustment, ...).In order to break down the signal and identify the commonfactor, a Principal Components Analysis (PCA) wasperformed18 using SAS software19.

The principle of PCA is to reduce the number ofdimensions in space, while integrating available data using anew variables, factors or main components. In the presentcase, the space is reduced to one dimension, since only a singlecommon factor is sought.

The mean, m, and standard deviation, σ, are calculated foreach accommodation potential curve. The mean can varyconsiderably from one well to another, which would be anindication of differential subsidence at reservoir scale. Theseaccommodation potential curves are then standardized in orderto eliminate local characteristics ; when the curves arestandardized, m = 0 and sigma = 1.

This renders the curves equivalent to each other in terms ofdispersion and hence prevents a given curve from beingawarded too much importance if it contains information ofgreat amplitude.The standardized curves are processed by CPA. The result ofthis analysis is a standardized common factor.


Fig.5 — Comparison between usual layering for stochastic models and proposed layering preserving time lines

Without readjustment :13 usual isopachous layers→ proportional thickness is

preserved

Raw data:Original Accomodation

Potential Curves. 13 layers.

With readjustment :13 layers with different

thicknesses → time-lines arepreserved


-5 0 5 10 15

0 5 10 15

0 2 41 3 5

-4 -2 0 2 4 6

-4 -2 0 2 4 6 -5 0 5 10 15

0 5 10 15

-10 -5 0

Fig.6 — Example of the transformation of Accomodation and Thickness curves at well, after readjustment (genetic units based)

Cumulativeaccomodation

Cumulative thickness

Accomodationpotential

BathymetryCurve

EnvironnementDescription

ReadjustedCumulative accomodation

ReadjustedCumulative thickness

ReadjustedAccomodation potential


-0,8 -0,3 0,2 0,7 1,2-0,8 -0,3 0,2 0,7 1,2

-2 0 2 4 6

5

9

13

17

21

25

29

33

37

41

45

49

53

57

61

-0,8 -0,3 0,2 0,7 1,2

Fig.7 - Example of extraction of common factor and residualsfor Accomodation potential

Accomodation potentialat wells afterreadjustment

Accomodationpotentialat wells

Residuals: Localaccomodation

potential

Standardizedcommon factor :

Regional accomodationpotential


The part of the whole variance represented by the commonfactor can be evaluated. Higher is this proportion, more thecommon factor does represent a general behavior, and morethe platform can be considered as having a quiet evolution. Inall the field cases on which this approach was run, the commonfactor represents more than 50% of the variance.

The common factor must be resized if it is to berepresentative of the true evolution of accommodationpotential.

At the well, the common factor is resized using known mand σ variables. The residual values at the wells are thencalculated by subtracting the resized common factor from theraw data (Fig. 7).

Constructing a 3D grid of accommodation potentialThis grid must be able to represent the sum of the two

signal components, the common factor and the residuals.• 3D grid of the common factor: in the same way as the

common factor was resized at the well, it must be resized atall points in order to reflect its true value.However, its mean and standard deviation are not knownfor all (x, y) coordinates and must therefore be extrapolatedfrom the well data.This information is extrapolated from the isopach map ofthe reservoir obtained from the seismic data and tied to thewell data.The concept is obviously based on the assumption that arelationship exists between the thickness of the sedimentsand accommodation. If the mean correlates to thethickness, then it is possible that sedimentation wascontrolled by subsidence or that there was a bypass ofsediments to more areas of greater subsidence.If the mean and thickness are anti-correlated, the maximalthickness corresponds to a minimum subsidence, and it canbe considered that sediments were deposited in aretrograding phase.In both cases, the mean values are generated by co-krigingthe mean with the reservoir thickness.Regarding the standard deviation, its extension is moredelicate as it is more difficult to link it to physical data inthe depositional system.However, there can be good correlat0ion with the sedimentthickness, as is the case in the example presented (Fig. 8).Co-kriging could therefore be applied in this case. In thecontrary case, ordinary kriging would have to be used.Once the mean and standard deviation of the commonfactor are modeled in 3D, resizing the common factor ineach of the grids can be used to create a 3D grid of thecommon factor.It is important to note that the common factor is notreproduced identically over the entire reservoir. The gridobtained therefore represents the general trend in theevaluation of accommodation potential, but the amplitudeof this trend is locally controlled (Fig. 9a).

m

0

0,02

0,04

0,06

0,08

0,1

0,12

3 4 5 6 7

thickness

σ

0

0,04

0,08

0,12

0,16

0,2

3 4 5 6 7

thickness

Fig.8 — Mean Value and Standard Deviation of Common Factor ofAccomodation Potential (from PCA)

versus Reservoir Thickness

• 3D grid of residuals: residuals represent local variations inthe accommodation potential and are therefore equal to thesum of the local uncertainties.The local parameters are important in sequencestratigraphy. They affect not only the stratigraphicexpression of system tracts and sequences, but also thetiming and lithological expression of the sequences17.Residuals are difficult to interpret since they are the resultof several phenomena which are difficult to distinguish.In some cases, the spatial organization of the residualslinked to the tectonic scheme deduced from the seismicdata can be can be discerned. This makes it possible toenvisage kriging the residuals by area.In other cases, small-scale tectonic phenomena orsedimentary avulsion phenomena tend to induce a randomdimension, which is significant of local noise. Gaussiansimulations must then be considered, and the variogramrange is chosen according to the geological significance.The best solution often consists in combining the two typesof residuals modeling -by sorting the average of residualsby layer. This makes it possible to take into considerationboth the organized and noisy aspects of residuals.In all cases, a 3D grid of residual is obtained, which can besummed with the 3D common factor grid to create a 3Dgrid of accommodation potential (Fig.9b).

Construction of a 3D palaeobathymetry gridOnce this 3D accommodation potential grid is available,

like the 3D thickness grid, only a 2D bathymetry map of eachlayer is required to build a 3D palaeobathymetry grid (Fig. 9c).

This palaeobathymetry map is built for the layer for whichit is the easiest to make such a map. Available well data andthe chosen sedimentary scheme are used to produce the map.This map is an extremely simple means of introducing the realuncertainty which exists around the geological model becausedifferent hypotheses of this 2D map can be used to construct3D palaeobathymetry models that are extremely different.


Fig.9a — Accomodation Potential Common Factor

Fig.9b — Accomodation Potential (Common Factor + Residuals)

Fig.9c — Paleobathymetry

Fig.9d — Geological Facies

Fig.9 — Longitudinal (YZ) cross-section in 3D grid.Vertical Axis : Time layering (not thickness) not to scale.


Stochastic facies modeling

Creating a prior probability fieldUsing the 3D palaeobathymetry grid and the probability of

facies occurrence = f (palaeobathymetry, system tract) it ispossible to build the prior probability field required for thestochastic model.

Creating a "Well constraints" fileWhen modeling facies, the simulation must be constrained

to well data.However, due to the particular layering constructed to fit

the time events, with varying vertical thicknesses, it isnecessary to resample the facies as well as possible. In thecontrary case, there is a risk that a contradiction will arisewithin the grid blocks at the well, between the facies and thedeposit bathymetry.

Conditional facies simulationAt the end of the process yields constraining values and a

prior probability field which represents the non stationaryaspect of the Facies Proportion RF, as well as the volumetricpartitioning within genetic units and sedimentary sequences.A stochastic simulation can be undertaken20, 21, using either anobject-based technique or the SIS method (Fig. 9d).

Converting the data back into true thicknesses will providehighly realistic images of the reservoir heterogeneity due to thetime layering.

Conclusions− The method proposed in this paper has made it possible to

obtain significant advances in the realistic and predictiveaspects of stochastic models.• For the first time ever, soft geological data has been

quantified making it possible to obtain a priorprobability field for stochastic modeling, which is littledependent on the quantity of available well data andtheir spatial distribution.This prior probability field is complex and can accountfor volumetric partitioning that corresponds to a faciesdistribution which differs, depending on whether thedepositional architecture is seaward or landwardstepping.

• The realistic aspect of stochastic models is augmentedby the fact that this type of modeling is applied tolayering based on time lines. Taking into accountdifferent sedimentation rates in space and in time isparticularly important in carbonate environments, inwhich deposition is affected by various ecologicalparameters resulting in extremely variable sedimentaryproduction.

• For these two reasons -realistic facies distribution andtime layering- this method should yield significantlyimproved reservoir models, thereby making it possibleto reproduce flow behavior more easily. Theassessment of connectivity and vertical exchangesshould ultimately be enhanced.

− Finally, this method will make it possible to obtain a

realistic quantification of geological uncertainties:• the uncertainty on the sedimentary model - platform

inclination, position of the slope - can be easilyrendered by uncertainties on the original bathymetrymap,

• the uncertainty on the palaeobathymetry ranges perenvironment is easily quantifiable through the faciesprobability matrix.

• other sources of uncertainty -subseismic scale tectonics,facies determination, errors, ...- can be rendered by theselected method of residual values modeling.

This quantification of geological uncertainty and its impacton reservoir characteristics and their dynamic behaviorthrough truly geological parameters constitutes a majornew challenge which will be increasingly investigated inthe near future.The modeling method discussed in this paper offers apotentially rich tool which will enable reservoir engineersand geologists to reach that objective.

AcknowledgementsThe author wishes to give special thanks to the students

who tested the concepts exposed in this paper on real casesand through such testing furthered the advancement of thismethodology (Vincent TROCMÉ, Michael VANHALST,Nicolas ROUSSEAU, Lionel AIRAUD, Enrico PERNACIC).Great thanks equally goes to Annie and to Hubert ARNAUDfor their dataset and highly constructive remarks, as well asJean-Paul VALOIS for his contribution to the statistical studyof the signal.The author also wishes to thank Elf Exploration Production forauthorizing the publication of the present paper.

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2 Massonnat, G.J., 1997. "Sampling Space of UncertaintyThrough Stochastic Modelling of Geological Facies", PaperSPE 38746 presented at the 72nd SPE Annual TechnicalConference and Exhibition, San Antonio, Texas, 5-8 October1997.

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