INTRODUCTION
Generally, models are expressions of our ideas about the encountered
problems. Models may be classified as:
Conceptual models (qualitative models) Physical models (experimental models) for example:
• 
Flumoperated simulations of sedimentologic or stratigraphic 
• 
Phenomena at scals ranging from bedforms to basins 
Mathematical models (computer models)
• 
Deterministic models (physicallybased or processbased)
have one set of input parameters and therefore yield one unique outcome 
• 
Stochastic models have variable input parameters, commonly derived
from probabilitydensity functions (Pdf`s) and therefore have multiple
outcomes; as a consequence model runs must be repeated many times
(realizations) and subsequently averaged 
In reservoir modeling subject there are different methods for 3D reservoir
modeling. In each of these methods using geological information, mathematical
or statistical sciences and different software, properties of the reservoir
are modeled. There are some publications in different aspects of the reservoir
modeling such as dynamic reservoir simulations (Labourdette et al.,
2006; Jackson et al., 2005), fracture intensity (Wong, 2003; Masaferro
et al., 2003), 3D stratigraphy, 3D structural model (Mitra and
Leslie, 2003; Mitra et al., 2006; Hennings et al., 2000).
Geostatistical method is a powerful tool in modeling now. As a historical
review the quantification of geology has always been a fascinating topic
and of the first pioneering efforts may be noted those of Vistelius (1992)
and his many followers using Markov chain analysis (Ethier, 1975) to quantify
onedimensional lithological sequences along well. Many successes were
encountered with this approach, but it appeared difficult to generalize
to the second and third dimension. Then, in the mid sixties, the giant
Hassi Messaoud field in Algeria was the object of pioneering application
of quantitative reservoir description techniques. The distribution of
sand lenses and shale break was modeled in a vertical crosssection with
the goal of understanding their impact on effective permeability. This
model was used as a basis for reservoir simulation and it was observed
that, because heterogeneities were modeled in a realistic way, a satisfactory
historymatch could be achieved more easily (Dubrule, 1998; Clevis et
al., 2006).
Three realizations are different; such a model often consists of hundreds
of thousands of grid cells. Current reservoir simulators are not able
to handle such large data set and scalingup of heterogeneity models is
required before they can be handled by flow simulators. These models will
represent the spatial distribution of petrophysical parameters such as
porosity and water saturation (Dubrule, 1998).
Generally, geostatistics is study of phenomena that vary in space and/or
time. Geostatistics can be regarded as a collection of numerical techniques
that deal with the characterization of spatial attributes, employing primarily
random models in a manner similar to the way in which time series analysis
characterizes temporal data. In other word, geostatistics offers a way
of describing the spatial continuity of natural phenomena and provides
adaptations of classical regression techniques to take advantage of this
continuity.
Basic component of geostatistics are:
• 
Variogram analysis: Characterization of spatial
correlation. 
• 
Stochastic simulation: Generation of multiple equiprobable
image of the variable also employs semivariogram model. In geostatistics
variables are random. A random variable is a variable whose value
is a numerical outcome of a random phenomenon (Corstanje et al.,
2008). Dataset that use in stochastic are tow types. Soft data that
measured indirect such as geophysics petrophysics data and hard data
that measured direct in laboratory. 
Geostatistics is applied to geological modeling, air pollution, water
pollution, mining, biological species. Geostatistical routines are implemented
in the major reservoir modeling packages like petrel and Roxar Irap RMS;
used in the generation of grids of facies, permeability, porosity, etc.
for the reservoir.
Software for representing geology in 3D is routinely used to model subsurface
reservoir The 3D geological modeling or static reservoir modeling technology
continues to advance. Software includes some or all of the following capabilities.
• 
Seismic interpretation, Petrophysical evaluation, Data
analysis, Deterministic and geostatistical fault modeling, Deterministic
and geostatistical facies/property models, Uncertainty analysis, Flow
based upscaling. 
These capabilities allow better integration of seismic data, conceptual
geological model, static and dynamic well data into one common earth model.
In the present study the geostatistical methods is used for 3D modeling
of Asmari reservoir in Ramin oil field, in Iran. Structural and petrophysical
models for this reservoir were provided using RMS software.
MATERIALS AND METHODS
The Ramin oilfield is located at Dezful Embayment in the Zagros ranges
of Iran (Fig. 1). The oil field consisted of the Asmari
formation as a petroleum reservoir. It is limited by the Gachsaran evaporate
formation at the top and the Pabdeh Formation at the base (Fig.
2).

Fig. 1: 
Situation of Ramin oil field in SW of Iran 

Fig. 2: 
Simplified table of rock units in Zagros areas 
Gachsaran Formation is considered as the cap rock for all reservoirs
in Zagros area. The Asmari reservoir is the main pool in this field and
divided into 4 zones.
The definition of the geological model of the reservoir seems to be one
of the most important phases in the workflow of a typical reservoir study
based on core material, cuttings, outcrop evidences and logs. To generate
this model, we have passed three important phases:
• 
Structural study: Reviewing the available literature
about the regional setting, tectonic evolution of the region, 2D seismic
surveys and well information to evaluate the structure top map, its
extension and fault pattern. 
• 
Stratigraphic study: reviewing all the available geology
and core reports to infer the sedimentological settings of the Asmari
reservoir in Ramin field which will help to find out the extension
of the depositional bodies in the reservoir and building a reliable
stratigraphic framework. A 3Dmodel of structure shall be constructed
using the results of previous step. 
• 
Petrophysical properties study: Study all the available petrophysical
evaluations for the field and data analysis to build the best experimental
variogram for stochastic simulation. 
3Dgeological modeling was made using IRAPRMS software which is supported
by NISOC (National Iranian South Oil Company). All needed data to construct
3D geological model include seismic map (contours), well data, (e.g.,
location, deviation, logs etc.), well picks (entry point to each horizon)
imported to IRAPRMS data engine (Fig. 4). The workflow
for geological modeling shall be at least put through following steps
(Fig. 3).
• 
Structural modeling 
• 
Fault modeling (in this field there is no fault) 
• 
Stratigraphic modeling (Construction of layer model) 
The isochores, representing true vertical thickness information, were
calculated by combining the TST maps and the dip information from the
top surface:
The next reservoir zone surface below the seismically defined Top Asmari
(interpreted top) is calculated by adding the calculated isochore to the
smoothed Top Asmari surface (Fig. 5). Then this process
was repeated down to the top Ilam surface (next interpreted top). Between
each zonesurface generation the surface was corrected to the well points.
Well adjustment was used for each zone to fit the horizons to well point.
Total stratigraphic modeling steps:
Step 1: 
Calculate dip and azimuth from Top Asmari structural
map. 
Step 2: 
Calculate True StratigraphicThickness (TST) in all zones for the
available wells. 
Step 3: 
Calculate isochore maps; Isochore = TST/cos (dip) 
Step 4: 
Create next map; next surface = Above surface+isochore 
Step 5: 
Exact adjustment to well picks. 
Step 6: 
Repeat step 15 for all zones. 
Establish a structural model with 4 zones. Dip and azimuth data from
Top surface were used to calculate TrueStratigraphicThickness (TST)
in all 7 wells.
• 
3D fine geological grid 
• 
Block wells and data analysis 
Property modeling (stochastic petrophysical modeling) shall be performed
using stochastic method. For this purpose simulation method will be used
on the basis of actual well data. Quality control of property models will
be secured by comparing the statistical results from the model with those
of the actual well data.

Fig. 3: 
Schematic flow chart of the modeling steps of the Asmari
reservoir in Ramin oil field 

Fig. 4: 
Primary data imported to the software for modeling.
Well trajectories, Well picks and contours line (A), well logs (B) 

Fig. 5: 
Schematic image, use of isochors in create layer model 
RESULTS AND DISCUSSION
Generating a high quality structural framework is an essential first
step in the 3Dmodeling workflow. The approach used include seismic data,
well data and construction of a series of structural cross sections to
understand the evolution of the structure (Mitra and Leslie, 2003; Mitra
et al., 2006) and provide a structural framework for property (petrophysical
) modeling.
Primary data needed to modeling of the Ramin oil field was taken from all information
available for this field and import to the RMS (Reservoir Modeling System) software.
These data consisting contour lines that provide from digitizing of the tops
of the Asmari and Ilam formations in underground maps (UGC), well trajectories,
well markers (well picks) and well logs. Underground maps were provided from
2Dseismic interpretations provide interpreted horizons in structural model.
Calculated horizons as intermediate horizons, derived by combining interpreted
horizons and thickness data (Isochors maps), dip map and azimuth map of top
Asmari formation were plotted (Fig. 68).
we have used geostatistics method to interpolate and extrapolate the values
of reservoir variables at unsampled locations. Then the contour maps were built
by the estimated value (Kelkar and Perez, 2002). Stratigraphic modeling between
two interpreted surfaces was done by interpolation method (Fig.
9A) which is computed intermediate values or estimated between measured
values, usually using a mathematical function (local Bspline). Local BSpline
is the algorithm that calculates the amplitude to a family of bell shaped functions
(Bsplines) using a local heuristic approach. The sum of these functions defines
a function in (x, y) which approaches the input data. Spatial interpolation
as a method of constructing new data points from a discrete set of known data
points was applied to estimate values on maps.

Fig. 6: 
Dip map of top Asmari (A) and Isochore map for zone
1 (B) 

Fig. 7: 
Isochore map for zone 2 (A) and zone 3 (B) 
A series of cross sections was
made for model to check the horizons they have to be (1) sorted in depth order,
(2) not intersect each other and (3) should not have holes or spikes (Fig.
9B).
After these stages, to attain the model, the next phase was to build
a 3D grid which is the cellular framework to take place all other geological
modeling within Irap RMS.

Fig. 8: 
Isochore map for zone 4 

Fig. 9: 
Stratigraphic model of Asmari reservoir in Ramin oil
field (A), cross sections that use for check the structural framework
(B) 
Table 1: 
The average thickness of 4 zones and grid cells dimensions
in 7 wells of the Ramin oil field 

In each cell of a 3D grid all parameters (continuous or discrete), can
be defined (e.g., porosity or water saturation). Such parameters are a
key control on hydrocarbon production, including sweep efficiency (Pringle
et al., 2004; Larue and Friedman, 2005). In this study 4 zones
of the Asmari reservoir are gridded. In x and y directions the increment
of cells is 100 m. In Z direction, the increment of cells in zone 1 and
2 is 6 m and in zone 3 and 4 is 12 m. The cells in zone 1 and 2 are finer
because these two zones are important than zone 3 and 4 in view of hydrocarbon
production. In other words in zone 1 and 2 the dimensions of cells are
100x100x6 m and in zone 3 and 4 are 100x100x12 m (Table
1, Fig. 10A).
In the last stage in entering the model, the well data were scaled up
to the vertical resolution of the 3D grid. The cells intersected by the
well tracks identified and each cell was given an average value for the
various log properties. Each cell in this new blocked well was then assigned
values based on the log data that had been selected to get the average.
The geometry of block well will depend on that of the 3D grid (Fig.
10B).
Data analysis and petrophysical modeling geostatistical models have
this advantage than other methods to compare data from different sedimentary
basins, formations and horizons. They also enable geologist for example,
to put their valuable information in a format in that can be used by reservoir
engineers (Journel and Stanford, 1990). Fortunately, however, a full range
of deterministic and stochastic modeling techniques is available, but
the techniques used will depend on the data available and the project
aims it is also kept in our mind that geostatistical methods are optimal
when our used data are:
• 
Normally distributed 
• 
Stationary (mean and variance not vary significantly in space) 
It is therefore a requirement that the input well data must be transformed
to remove any trends (Fig. 12A, B) and to create a
normal distribution (Fig. 11A, B).

Fig. 10: 
The 3D geomodel grid in Ramin oilfield (A) and block
wells (B) 

Fig. 11: 
Histogram of porosity data (A) and water saturation
data (B) in 4 zone 

Fig. 12: 
Scatterplot of distribution porosity (A) and water
saturation (B) in 4 zone 

Fig. 13: 
The variogram models of parameters for Asmari reservoir
in Ramin oil field, (A) the variogram model for porosity in 3 directions,
(B) the variogram model for Sw in 3 directions 

Fig. 14: 
Distribution of porosity (A) and water saturation (B)
in 3 dimension in Ramin oil field and distribution of porosity and
Sw in 4 zones 
These transformations
can be carried out in the data analysis and then applied to the stochastic
petrophysical modeling. Data analysis is crucial to understanding the
property distribution within the reservoir. Much of the petrophysical
modeling work is carried out during the data analysis stage. In this stage,
the data is investigated for trends and transformed to a normal (Gaussian)
distribution. The variogram analysis also takes place as a part of data
analysis. The trend is modeled and removed and residual variograms are
computed (Li and White, 2003). The variogram shows the increase in dissimilarity
between sample values versus increasing separation distance (Journel and
Stanford, 1990). A variogram illustrates the spatial statistics of a variable.
It measures the variability between sample points (well locations) as
the distance between the points increase.
The values defining the experimental variogram are calculated by computing
the squared difference between all pairs of sample values. The resulting
points are plotted against the separation distance between the points
(lag). The dissimilarity between the points is a function of the heterogeneity
of the reservoir. Normally, the average dissimilarity between points increases
as the distance between samples increases.
The variogram model was provided in three directions: (1) Main, (2) Perpendicular
in the horizontal and (3) Vertical. The vertical variogram will normally
be well defined due to the quantity of data available from the well logs.
The variogram model was created based on knowledge of the geology (Fig.
13). In the next stage of stochastic petrophysical modeling, 3D distribution
of porosity and water saturation in reservoir was generated (Fig.
14).

Fig. 15: 
Distribution of porosity (A) and water saturation (B)
for all 4 zones in a cross section of upper culmination 

Fig. 16: 
Distribution of porosity (A) and water saturation (B)
for all 4 zones in a cross section of lower culmination 
Plotting the main reservoir parameters (porosity and water saturation)
in Ramin oil field present that zone 1 and 2 (the upper parts of reservoir)
have higher porosity and lower water saturation from zone 3 and 4. It
means that zone 1 and 2 have higher oil saturation and are most important
parts in hydrocarbon production of the field.
Also petrophysical model (Fig. 1416)
indicate that water saturation in the upper culmination is higher than
lower culmination; therefore zone 1 and 2 of the lower culmination are
the best situations of reservoir for future drillings.
CONCLUSION
Stochastic modeling method allows more control on the spatial statistics
of the model. This method has great potential for identification best
locations for drilling with reduced risks.
The structural model of the Ramin oil field indicated that the Ramin
anticline has the same trend as the Zagros Mountains (NWSE) and exhibits
a smooth structure. This anticline showing two culminations that the east
one is dipper than the west one.
Plotting the main reservoir parameters (porosity and water saturation)
in the Ramin oil field presented that the two first zones, 1 and 2, (the
upper parts of reservoir) have the higher porosity and lower water saturation
the two last zones 3 and 4. It means that zone 1 and 2 have higher oil
saturation and are most important parts in hydrocarbon production of the
field.
Also petrophysical model indicated that the water saturation in the upper
culmination is higher than the lower culmination; therefore, zone 1 and
2 of lower culmination are the best situation of the reservoir for future
drillings project.
ACKNOWLEDGMENTS
The author thanks Susan Maleki for her guidance and cooperation, thanks
anonymous referees of journal of applied sciences and dear editor and
also NISOC (National Iranian South Oil Company) for their attentions.