Indicator Kriging Case study; Geological Models of Upper Miocene Sandstone Reservoirs at the...
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Indicator Kriging Case study; Geological Models of Upper Miocene Sandstone Reservoirs at the Kloštar Oil and Gas Field Kristina Novak Zelenika Zagreb, November 2013
Indicator Kriging Case study; Geological Models of Upper Miocene Sandstone Reservoirs at the Kloštar Oil and Gas Field Kristina Novak Zelenika Zagreb,
Indicator Kriging Case study; Geological Models of Upper
Miocene Sandstone Reservoirs at the Klotar Oil and Gas Field
Kristina Novak Zelenika Zagreb, November 2013
Slide 2
Introduction Application of mathematics in geology is
relatively new approach in interpretation of underground geological
relations. Two great scientists are founders of this discipline:
Prof. Dr. Daniel Krige and Prof. Dr. George Matheron.
Geostatistical methods can be divided into deterministical and
stochastical methods.
Slide 3
Introduction determinism In deterministical methods, all the
conditions which can influence to estimation, have to be completely
known (mustn't have randomness of any kind in variables
description). Deterministical results can be unambiguously
described by the completely known finite conditions. It is clear
that geological underground is only one, but since the description
of the underground is based on well data (point data) it is not
possible to be absolutely sure that the solution obtained with
geostatistical methods is absolutely correct (all geostatistical
methods contain some uncertainty). Deterministical methods give
only one solution. It is more correct to call them deterministical
interpolation methods.
Slide 4
Introduction stochastics Stochastical realizations provide
different number of solution for the same input data set. The
solutions can be very similar, but never identical, and all
obtained solutions or results are equally probable. There are
conditional and unconditional simulations. In stochastical
processes number of realizations can be any number we want. It is
very clear that more realizations will cover more uncertainty area,
i.e. the more realizations there are, the lower uncertainty
is.
What are the principles of indicator formalism in Indicator
Kriging? Indicator formalism: Indicator transformation can be
interpreted as follows:
Slide 9
If v is continuous variable In this case we should create
cumulative probability distribution of v from the data values:
Since we generaly have finite number of data, the cumulative
probability distribution function may change with the increasing or
decreasing number of available data. That is why the cumulative
probability distribution function is called conditional probability
distribution function (ccdf) It is conditioned by number of
available data
Slide 10
Next step: Introduce the indicator formalism for this ccdf in a
way to subdivide the total range using k cut-off values
Slide 11
According to ccdf we can define the corresponding probabilities
for all these cut-offs:
Slide 12
We can choose a particular cut-off, say 2m All the locations
can be categorized in two groups: The first one is the set of
locations where the actual thickness is smaller than 2 m The next
group is locations where the actual thickness is larger than 2 m
Using this cut-off we can define an indicator variable, which takes
1 for all locations where the thickness is smaller than 2, and
takes 0 for all other locations
Slide 13
In this way we can define all other indicator variables
Actually, the larger number of cut-offs, the more precise the
continous ccdf derived are and this is the principle of Indicator
Kriging
Slide 14
With respect of 5 indicator cut-offs (2, 4, 6, 8, 10 m), we can
create 5 point maps showing the actual values (0 or 1). That means
we have 5 point maps one for each cut-off Each map contains only 0
and 1 values Unfortunately, we cannot perform any meaningful
estimation with these values
Slide 15
But, they can hold some other meaning: We suppose that at any
particular well location the probability of the thickness smaller
than a particular cut-off can be derived from the global
probability distribution of thickness We can conclude that after
making indicator transformation, the probabilities of their value
equals 1 can be estimated
Slide 16
This estimation can be performed for each individual cut-off
separately As a result we got grids showing the probabilities that
the indicator variable take 1 value
Slide 17
Output of Indicator Kriging In each row the probabilities
increase by increasing of the cut-off values All of these
probabilities belong to a particular grid point Using Indicator
Kriging the ccdf at a grid point can be estimated The final result
we can get is ccdf for each grid point
Slide 18
If v is a categorical variable Rock type The Indicator Kriging
of that variable gives the probability that this rock type appears
at a particular location
Slide 19
The Indicator Kriging is a specific geostatistical technique
for spatial phenomena with weak stationarity. In fact, this kriging
technique is weaker than any other kriging approximation. However,
this technique is designed for estimating lateral uncertainty. This
approach estimates the local probability distributions on grid
cells. Conclusion
Slide 20
Advantages and disadvantages Advantages: It does not need
normality of the input data set It can be inplemented in case of
bimodal distribution Since it estimates probabilities, it may show
the connectivity of the largest values (very important in
production plans or EOR projects) Disadvantages: Success of IK
strongly depends on the correct selection of the cut-offs values.
The fewer the numbers of cut-offs are, the fewer details of the
distribution can be got.
Slide 21
Case study; Klotar Field
Slide 22
Introduction research location There are many reservoirs in
Croatian part of Pannonian Basin interpreted with deterministical
and stochastical methods (like reservoirs of the fields Ivani,
Molve, Kalinovac, Stari Gradac- Barcs Nyugat, Benianci, Ladislavci,
Galovac-Pavljani, Velika Ciglena). Klotar Field was very detail
analyzed in the joint study of INA and RGNF, led by Prof. Dr. J.
Veli and Prof. Dr. T. Malvi. Klotar Field was chosen as research
location i.e. its sandstone reservoirs as objects with high and
accurate base of the measured data and many geostatistical results
and interpretations.
Slide 23
Introduction used methods and analyzed variables Stochastic
Used methods Deterministic OKIKSGSSIS Analyzed variables
PorosityDepthThickness
Slide 24
Introduction - goals Goals: (1) Construction of geostatistical
model of the Klotar field (reservoirs T and Beta); using of
geostatistics as tool for improving of mapping accuracy (2)
Geostatistical models will represent upgrade for previously
available deterministic models from field study.
Slide 25
Location of the Klotar Field Klotar Field location (CVETKOVI et
al., 2008)
Slide 26
About the Klotar Field wells Total no. of wells: 197 Measured
wells: 57 Technically abandoned: 73 Water injection wells: 5
Production wells: 62
Slide 27
Location of the Beta and T reservoirs Location of the Beta
reservoirLocation of the T reservoir
Slide 28
Lithology and log curves of Klo-62 well Lithology and log
curves of Klo-145 well
Slide 29
Core data
Slide 30
Core data cores from INA laboratory Klo 57 (788.9 793.3 m, III
m) Rocks top section of T+U+V reservoir Determination: Lithoarenite
(VELI & MALVI, 2008) Klo 82 (1404.6 1411.7 m, II m) Beta
Reservoir Determination: Lithoarenite (VELI & MALVI, 2008)
Slide 31
Structural modeling of the Klotar Field Klotar Field is
anticline with direction northwest-southeast Normal fault (Klotar
fault) divides structure into two parts, northeastern and
southwestern Conceptual models were constructed based on structural
maps of the Upper Pannonian and Lower Pontian reservoirs, well data
and structural maps and palaeotectonic profiles from the paper VELI
et al. (2011)
Slide 32
Structural modeling of the Klotar Field During Badenian to Late
Pannonian new accommodation space opened Sandstone reservoirs were
deposited Evolution of the Klotar Field during Late Pannonian
Slide 33
Structural modeling of the Klotar Field At the transition from
Late Pannonian to Early Pontian normal fault appeared, which caused
down lifting of the NE part NE of the fault and SW of the Moslavaka
gora Mt. new deeper area for sedimentation was created It is very
possible that two source of material were active: (1) Eastern Alps
and (2) Moslavaka gora Mt. Evolution of the Klotar Field during
Early Pontian
Slide 34
Structural modeling of the Klotar Field During Late Pontian
transpression began, which is active still today Main normal faults
changed to reverse. Smaller faults in the field are normal because
of the local extension at the top of the Klotar structure Evolution
of the Klotar Field during Late Pontian Evolution of the Klotar
Field during Pliocene and Quaternary
Indicator Kriging mapping of the Beta reservoir porosity data
transformation Indicator transformation of the porosity input
data
Slide 37
Indicator Kriging mapping of the Beta reservoir porosity
variograms Experimental variograms (left) and their approximation
with theoretical curves (right) of the Beta reservoir porosity for
cutoffs: a-15%, b-16%, c-18% and d-19%
Slide 38
Indicator Kriging mapping of the Beta reservoir porosity
Probability map for porosity less than cutoff 15% Probability map
for porosity less than cutoff 18% Probability map for porosity less
than cutoff 16% Probability map for porosity less than cutoff
19%
Slide 39
Indicator Kriging mapping of the Beta reservoir thickness data
transformation Indicator transformation of the thickness input
data
Slide 40
Indicator Kriging mapping of the Beta reservoir thickness
variograms Experimental variograms (left) and their approximation
with theoretical curves (right) of the Beta reservoir thickness for
cutoffs: a-7m, b-9m, c-15m and d- 21m
Slide 41
Indicator Kriging mapping of the Beta reservoir thickness
Probability map for thickness less than cutoff 7m Probability map
for thickness less than cutoff 9m Probability map for thickness
less than cutoff 15m Probability map for thickness less than cutoff
21m
Slide 42
Indicator Kriging mapping of the T reservoir porosity data
transformation Indicator transformation of the porosity input
data
Slide 43
Indicator Kriging mapping of the T reservoir porosity
variograms Experimental variograms (left) and their approximation
with theoretical curves (right) of the T reservoir porosity for
cutoffs: a- 14%, b-18%, c-19%, 20% and d- 22%
Slide 44
Indicator Kriging mapping of the T reservoir porosity
Probability map for porosity less than 14% Probability map for
porosity less than 18% Probability map for porosity less than 19%
Probability map for porosity less than 20% Probability map for
porosity less than 22%
Slide 45
Indicator Kriging mapping of the T reservoir thickness data
transformation Indicator transformation of the thickness input
data
Slide 46
Indicator Kriging mapping of the T reservoir thickness
variograms Experimental variograms (left) and their approximation
with theoretical curves (right) of the T reservoir thickness for
cutoffs: a- 5m, b-9m, c-13m, 17m and d-21m
Slide 47
Indicator Kriging mapping of the T reservoir thickness
Probability map for thickness less than 5m Probability map for
thickness less than 9m Probability map for thickness less than 17m
Probability map for thickness less than 13m
Slide 48
Discussion and conclusion 1 st assumption - higher porosity
represents sandy lithofacies and lower marly lithofacies. In this
way it was possible to distinguish sandstones, marly sandstones,
sandy marls and pure marls. 2 nd assumption - higher thicknesses
should point to central part of depositional channel, where the
coarsest material was deposited. In Upper Pannonian reservoir Beta
higher porosity locations matched higher thickness locations. In
Lower Pontian reservoir highest thicknesses were only partly
matched higher porosities. In the deepest parts of the depositional
channel sandstones were deposited and toward the channel margins
more and more marly component could be expected.
Slide 49
Main material transport direction in Upper Pannonian was NW-SE.
Lateral thickness changes points to transition into marls and sandy
marls. The coarsest material was deposited in local synclines and
today they can be recognized with the highest thicknesses of the
sandy layers. Thin marls and clayey marls were deposited in the N
and NE direction, i.e. in the direction of the Moslavaka gora Mt.
Material transport direction during Late Pannonian interpreted on
the probability map for the porosity higher than 18% (left) and
thickness higher than 15 m (right)
Slide 50
The coarsest material in this part of the Sava Depression
mostly came from north. Part of material was transported parallel
with the fault toward SE. Locations of the highest probabilities
for the highest thicknesses does not match location of the highest
probabilities for the highest porosity. The highest thicknesses
match sandstone and marl intercalations, so it could not represent
depositional channel. Probability map for porosity more accurate
shows depositional channel than the probability map for thickness.
Material transport direction during Early Pontian interpreted on
the probability map for the porosity higher than 19% (left)
thickness higher than 13 m (right)
Slide 51
13 Upper Pannonian and Lower Pontian cores were examined. Upper
Pannonian reservoirs have more mica. Local material source could
not be directly interpreted based on 13 core data. Local material
source should be noticed on the probability maps as direction
NNE-SSW. NE part of the reservoir has high probability that
porosity is higher than 18%. It was concluded that it was possible
that Moslavaka gora Mt. was a local source for one part of sandy
and silty material Material transport direction interpreted on the
probability map for the porosity lower (left) and higher (right)
than 18%
Slide 52
Discussion and conclusion Geostatistical methods were used for
detail modeling of the two most important and significantly
different reservoirs of the Klotar Field. Every geological model is
always stochastical because it contains uncertainty. It is possible
to perform additional geostatistical analysis by increasing number
of input data and number of mapped reservoir variables. Reliability
of the model also depends on used software. Mapped variables were
porosity and thickness of the Beta and T reservoirs. All previous
solutions as well as E-logs were taken into the consideration. Two
mentioned reservoirs were chosen as the most widespread, the
thickest and typical Upper Miocene reservoirs.
Slide 53
Discussion and conclusion The Indicator Kriging method have
been used in the probability mapping of the certain variable value.
Probability maps for certain cutoff value showed material transport
direction and distribution channel location. The Indicator Kriging
maps proved heterogeneity of the reservoirs by existence of
different lithofacies starting with sandstones in the central part
of the channel to marly sandstones, sandy marls and marls. In this
way it is easier to create precise boundary around the reservoirs
and to get accurate estimation of the original hydrocarbon in
place. The methodology applied in the Klotar Field can be used in
all Upper Pannonian and Lower Pontian sandstone reservoirs in the
Sava Depression, primarily because all depositional conditions,
migrations and traps forming were almost the same.
