generation of regional trend from boolean log of lithofacies for … · 2017-11-23 · generation...

Generation of regional trend from Boolean log of lithofacies for building a realistic fine scalegeological model using stochastic facies modelling– A case study

BS Bisht, Ajeet Pandey*, SP Singh, Samir Walia#, Prerna Barthwal#

*Oil and Natural Gas Corporation Limited, 4th Floor GEOPIC, Dehradun-248165, Uttarakhand# Roxar, Emerson Process ManagementPresenting author*, E-mail: [email protected]: Boolean log, spatial trend, stochastic, facies, geostatistics, vertical proportion curve, variogram

Abstract:A facies is a distinctive rock unit that forms under certainconditions of sedimentation, reflecting a particularprocess or environment. To depict the geological processboth during and after deposition facies identification andits modelling in 3D space play a vital role in 3D reservoirmodel. Identification of different reservoir facies anddefining its connectivity along with variation of reservoirproperty is the basic need of geo-modelling process. Toaddress this, delineation of different facies requireddetailed core analysis, sedimentological studies and in-depth petrophysical analysis. After ascertaining theidentification of different facies at well locations theirmapping with connectivity in 3D space is required. Thefacies is defined as numerical values, therefore, dataanalysis in the geological context and its spatialrelationship become essential to reach some logicalconclusion.

The objective of the study is to build a fine scale staticmodel which can explain the heterogeneous behaviourand connectivity of the reservoir keeping in view of thegeological aspect. An integrated approach was adopted,where log, seismic data interpretation and geologicalinformation are translated into reservoir description.Present study pertains to Kalol field western onshorebasin of India with complex lithological environmentshaving multiple pay sand inter-bedded with thick coallayers. The study demonstrates methodology and workflow through a judicious combination of precisepetrophysical evaluation to build a trend maps fromBooleans log, generated from the facies logs. These trendmaps in connection with vertical proportion of faciesdistribution will guide geostatistical tools leading tofacies and reservoir property population in 3D space forrobust Geo Cellular Model building resulting better fielddevelopment and hydrocarbon exploitation from thisbrown field.

Kriging and stochastic methods are widely used in theindustry. Kriging is a deterministic interpolationtechnique giving one best local smooth estimate with thelimitation that in a large model low value trends are overestimated and high value trends are underestimated.Stochastic simulation methods are better for capturingthe extreme value variation of subsurface by assessing itsspatial variability. Schostastic Simulation reproduceshistogram and honours spatial variability throughvariogram. This technique has been applied in this fieldto build a realistic model which is validated at differentwell locations. This model is appropriate for flow

simulation and allows an assessment of uncertainty withmultiple realizations.

Introduction:Present study deals with identification of reservoir faciesand their connectivity in heterogeneous reservoirspertaining to clastic regime of a giant onland oil and gasfield of India (Fig-1) with the help of spatial trend mapand vertical proportion curve. In the study area theseismic 3D data is of average quality and picking upgeological bodies and its architecture has becomedifficult due to presence of multi layers of coal seams.Low impedance contrast between sand-shale which isinter-bedded with coal, hinders proper imaging ofreservoir geometry. Therefore uses of seismic derivedattributes are not helpful to delineate reservoir and non-reservoir facies. Spectral decomposition process has beenapplied to delineate geobodies but any significantobservations couldn’t be seen (Fig-1A).Once the facies log is created, a Booleans log has beengenerated at well locations to understand the trend of thereservoir facies in the area. As the reservoir has limitedspatial distribution across the field and use of only geostatistical methods to populate the lithofacies will notgive the correct distribution, therefore Geostatisticalmethods guided by regional trend maps is used topropagate the reservoir facies and Petrophysical propertyin proper place and direction.Sequential Indicator Simulation (SIS) with trend wasused to propagate the facies in the area. After the facieswere populated, Effective Porosity (Ф), Water saturation(Sw) & Permeability (k) are assigned to the facies in theentire 3D volume through Sequential GaussianSimulation (SGS). These methods with trend maps hasnot only given the reservoir distribution pattern but alsogives a fair indication of the quality of reservoir whichcan be expected in yet to be explored/developed areas.

Understanding of study area:Kalol Field falls in the Ahmedabad-Mehsana tectonicblock of Cambay Basin. It is located about 16Km northof Ahmedabad city covering an area of around 450 sq.km. There are 11 pay sands i.e. K-II to K-XII from top tobottom sequence occurring between depth of 1250 to1550m. in the present study an attempt has been made todelineate the spatial distribution in 3D space of K-XIIpay, which is limited to the NW part of the study area asshown in Fig-2. The sand quality of this reservoir ishaving good porosity and permeability.

11th Biennial International Conference & Exposition

Workflow:Understanding of geological processes during and afterdeposition play a crucial role in defining the reservoirconnectivity in 3D reservoir model. The identification ofreservoir bodies become easier if some seismic attributerespond for it within the limitation of seismic resolution.(Fig-1A). In the absence of 3D seismic data,identification of trend of strata becomes difficult. In thechannel type of environment where the orientation/trendof the object is not known all the Geostatistical methodspopulate the reservoir property in entire 3D space basedupon Variogram, VPC using SGS/SGI methods. In thisprocess the reservoir property data are taken from welllocations. If the data points are insufficient the predictionof property in unknown area mislead due to stochasticnature of algorithm.To overcome this situation, from the available log data aregional trend of the reservoir facies using Boolean logmay be derived. These trends can be used to bias thedistribution of facies within simulation/reservoir grid of aregion. Lateral variability and facies transition within thereservoir can be handled with these trends. An attempthas been made to generate a trend map based on faciesanalysis and has been applied in the area where thereservoir is limited to a certain location.

Generation of Facies spatial trend:From the interpreted Lithofacies logs, Individual andseparate facies logs were calculated thus separating eachof the facies into separate logs define in terms of 0 and 1which represents the occurrence of sand facies thus thelog created is a Boolean log (Fig-3). These Boolean logswill represent the probability trend maps for differentfacies. These trend maps restricted the spatial distributionof each log facies spread along the area where the inputwell data was present as shown in Fig-4. The figureshows that the boolean log are derived from intrepretedfacies log having code 1 & 0 for reesrvoir and non-reervoir facies espectively. Porosity and saturation of therespective facies is given in adjacent log tracks.

Vertical Proportion Curve:Vertical proportional curve depict the verticaldistribution of all the facies in all the layers in aparticular zone. This distribution helps to propagate thefacies in vertical direction along with the probabilityfunction. The trend map were used in association withVertical proportion curve in which volume fraction forfacies will be a constant value within each horizontallayer of the grid, but will vary vertically according to thespecified trend function. With this combination the

Fig-1: Location map of the study area Fig-1A: SD slice at 38 Hz in zone of interest Fig-2: Base Map showing distribution ofwell having K-XII sand

Fig-3: Generation of Boolean log from facies log having facies code 1 & 0 for reservoir and non-reservoir respectively

Reservoir withFacies code “1”

Non-Reservoirwith Facies code

“0”

SaturationPorosityFaciesLog

BooleanLog


Fig-4: Trend maps of sand and shaly sand facies

Fig-5: Vertical proportion curve showing faciesdistribution in vertical direction

volume fraction steering for each facies will steertowards a volume fraction defined by Vertical ProportionCurve as shown in Fig-5.

Up scaling of facies:Upscaling is a process of assigning a single value to thecell in a 3D grid passing though the well location. Sincea facies is discrete log the averaging method “most of”will be suitable for upscaling. In this method the majorityof same type of sample will be assigned to that particulargrid cell as shown in Fig-6.

Basic Theory:A.Principles of stochastic modeling:In general, conditional simulation requires that the basicinput parameters—the spatial model (variogram) and thedistribution of sample values (cumulative distributionfunction, or CDF)—remain constant within a givengeologic interval and/or facies, from realization torealization. Typically, the structural and stratigraphicmodel (major structural surfaces and the discretizedlayers between them) remains fixed. Because eachrealization begins with a different, random seed number,each has a unique “random walk,” or navigational paththrough the 3D volume. The random walk provides thesimulation algorithm with the order of cells to besimulated, and is different from realization to realization;therefore, the results are different at unsampled locations,producing local changes in the distribution of facies andPetrophysical properties in the interwell space. Note thatselection of the same random seed always will reproducethe same random walk. This characteristic is forcomputational convenience. In practice, multiplerealizations are performed at or close to the geologicscale, and not necessarily at the flow-simulation scale.There are two basic categories of conditional simulationmethods: Pixel-based methods operate on one pixel at a time.

They can be used with either continuous orcategorical data.

Object-based methods operate on groups of pixelsthat are connected and arranged to represent geneticshapes of geologic features. They are used onlywith categorical data.

B.Stochastic simulation methods:There are several theoretically sound and practicallytested conditional-simulation approaches and choosingone can be bewildering and daunting for a novice tostochastic methods. Parametric-simulation techniquesassume that the data have a Gaussian distribution, so thata transform of the data typically is prerequisite. Note thatindicator data do not undergo such a transform.Furthermore, data transformations are not required in theobject-based method, where only indicator data arerequired. The steps of parametric simulation are: Normal-score data transformation Computation of variogram biased to facies along

vertical, major and minor direction. Run the modelling using Sequential Gaussian

Simulation with multi-realizations for each faciescode.

Selection of most suitable equal probablerealization through testing at blind wells, which arenot considered during modelling process.

C.Sequential simulation: Sequential indicator simulation (SIS) simulates

discrete variables, to create equal probablerealization of facies (having various facies codes)

Sequential Gaussian simulation (SGS), simulatescontinuous variables, such as petrophysicalproperties e.g. Porosity, water saturationconditioned to facies propagation.

The general sequential simulation workflow can beformulated as:1. A normal-score transformation of upscaled logs of

the facies and petrophysical properties.Fig-6: Upscaling of facies log


Fig-7A: Variogram showing field deposition trend

Fig-7B: Directional variogram showing the range ofvertical and spatial distribution

Major

Minor

Vertical

2. Randomly selection of a node that is not yetsimulated in the grid.

3. Estimation of the local conditional probabilitydistribution function (LCDF) for the residuals at theselected node. The residuals can be calculated bysubtracting the grid of an unconditional simulationfrom a kriged grid of the unconditional valuessampled at the geographic coordinates of the wells.

4. Creation of a newly simulated value by addingtogether the randomly drawn residual value and themean of the transformed data.

5. Inclusion of the newly simulated value in the set ofconditioning data, within a specified radius of thenew target location. This ensures that closely spacedvalues have the correct short-scale correlation.

6. Multi-level iterative processes until all grid nodeshave a simulated value.

Stochastic facies modeling:Sequential Indicator Simulation method was used and theupscaled facies were populated using lateral trend mapsand vertical proportion curve. The sequential simulationworks by visiting each point on the grid to be simulated,calculating the conditional distribution at that point andsampling from that distribution. The conditionaldistribution is the probability distribution for the facies atthe point, given knowledge of the facies at nearby welllocations and of previously simulated points nearby. By‘nearby’ which mean within the search neighborhood ofthe point to be simulated. The conditional distribution isfound approximately using a krigging approach, with theexact methodology depending on the type of simulationthat is being applied. With these trend setting as input tothe model, indicator variogram model for each facieswere also specified. The idea of sequential simulation isto use previously krigged/simulated values as datareproduces the covariance between all of the simulatedvalues.A variogram is a mathematical tool used to quantify thespatial continuity of a variable. Variogram estimationand definition involves looking at the well observations,and investigating their similarity as a function of thedistance between the data points. In general, thesimilarity between two observations depends on thedistance between them. That is, the variability increaseswith increasing separation distance between twoobservations. This variability is quantified by calculatingthe Variance of the increment. For each separationdistance, the variance is the sum of the squareddifference between all the pairs of observations with thatseparation distance, divided by the number ofobservations. Semivariance is generally defined by theequation:

2)(

1

))()(()(

1

2

1)( ii

hn

i

xZhxZhn

h

Where z is a datum at a particular location, h is thedistance between ordered data, and n (h) is the number ofpaired data at a distance of h. The semi variance is halfthe variance of the increments,

Z ( )() ii xZhx , but the whole variance of z-

values at given separation distance h (Bachmaier andBackus, 2008).

The indicator variogram parameters indicate to whatdegree the facies values in one position are related to the

facies values in a position nearby, as a function of theirseparation distance. This means that they provideinformation on the confidence with which the value of acell can be estimated, based on its distance from a cell ofknown or calculated value.

Variograms were generated for each of thefacies.Prediction of facies was checked against the blindwells and found satisfacory (Fig-7A & 7B).

Based on these variograms, VPC and trend maps facieshas been populated in the entire zone of particular sandwhich is limited to a particular area of the field. Thedistribution matches with the wells which were not takenin facies modelling process. Fig-8A and B shows acomparison of the distribution of a facies without andwith trend maps. In Fig-8a the sand facies is available inthe entire zone of the field because of stochastic nature ofthe algorithm while fig-8b depict the correct picture asobserved in the well drilled in the area shown in greencolor.


Fig-8A& 8B: Stochastic facies modeling without and with trend maps

Fig-10A & 10B: Porosity modeling without and with trendmaps using Sequential Gaussian Simulation.

Fig-11A & 11B: Water saturation modeling without andwith trend maps using Sequential Gaussian Simulation.

Fig-9A& 9B: Normal and Gaussian distribution ofpetrophysical property (porosity) for SGS.

Property modeling:Based on this facies model the property modelling hasbeen done for porosity and saturation model biased to thefacies in this field.

Porosity Modeling: The upscaled porosity logs wereused in the Porosity Modeling. Using SGS techniqueporosity derived from upscaled logs were propagatedbiased to facies. The samples from petrophysicalparameters were transformed to a Gaussian (normal)distribution (Fig-9A & B) by the application of certaingeological and statistical transformations.

Variograms for porosity were generated for each faciescode in the zone and prediction of the property waschecked against the blind wells.

Saturation Modelling: Saturation modeling was carriedout stochastically using SGS technique. The propertywas populated using upscaled Saturation logs biased withfacies as shown in Fig-11A & 11B


Fig-12A: Cross sectional view across the facies model showing facies distribution, which is well corroborated withporosity and water saturation in zone of interest.

Facies

Porosity

WaterSaturation

Fig: 7A.VPC for K-II

Results and Conclusion:This study has clearly brought out a regional facies trendbased on available log data and well performance withgeological understanding.in the absence of seismicattribute these trend maps are the only tool which canguide the Geostatistical methods to propagate thereservoir facies and property in proper direction and theirvalues. The study has also given a comparison of usingSGS methods based on variogram and VPC with respectto SGS methods with trend maps. The method used withtrend maps has given satisfactory answer with the wellperformance of the sand. This process has given foroptimum exploitation strategy of this brown field andright estimation of in-place reserves.

AcknowledgementThe authors are indebted to Shri Anil Sood, ED-HOI-GEOPIC, Dehradun, India for providing the technicalinput and guidance for writing this paper. Thanks are dueto Dr. Harilal Head-INTEG, GEOPIC, Dehradun, Indiafor providing all kind of support for this work. Theauthors are grateful to Shri Anil Kumar, GM (SSM) andMr. Surender Kumar, DGM (G), Ahmedabad Asset, forproviding necessary input during the project work andwriting this paper. We thank ONGC management forallowing us to submit this paper in 11th BiennialInternational Conference & Exposition at Jaipur 2015.

NB: The views expressed in this paper are solely of theauthors and do not necessarily reflect the view ofONGC.

References:1. Pandey, Singh, N.P. Krishna, B. R., Sharma, D. D.,

Paraiki, A.K, Nath, S.S. “Lithostratigraphy of IndianPetroliferous Basin Document-III”, ONGC, 1993.

2. Richarrd L. Chambers, Jeffrey M. Yarus, Kirk B.Hird“Petroleum geostatistics for non geostatisticians”,The leading Edge, May2000

3. Mallet, J.-L., Geomodeling, Applied GeostatisticsSeries. Oxford University Press. ISBN 978-0-19-514460-4

4. Bachmaier, M. and Backes, M. 2008 “Variogram orsemivariogram? Understanding the variance in avariogram”, article DOI 10.1007/511119-008-9056-2,Precision, Agriculture, Springer-Verlag, Berlin, andHeidelberg, New York.


generation of regional trend from boolean log of lithofacies for … · 2017-11-23 · generation...

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