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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

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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.

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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.

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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.

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Introduction – determinism and stochastics

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Indicator Kriging theory

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Indicator Kriging Where: I(x)- indicator variable; z(x)- measured value; cutoff - cutoff value. Location map of 38 data: 1 represents sandstone, 0 represents other lithofacies Recommended no. of cutoffs: 5-11 Results: probabilities

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What are the principles of indicator formalism in Indicator Kriging? Indicator formalism: Indicator transformation can be interpreted as follows:

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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

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Next step: Introduce the indicator formalism for this ccdf in a way to subdivide the total range using k cut-off values

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According to ccdf we can define the corresponding probabilities for all these cut-offs:

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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

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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

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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

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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

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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

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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

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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

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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

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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.

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Case study; Kloštar Field

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Introduction – research location There are many reservoirs in Croatian part of Pannonian Basin interpreted with deterministical and stochastical methods (like reservoirs of the fields Ivanić, Molve, Kalinovac, Stari Gradac- Barcs Nyugat, Beničanci, Ladislavci, Galovac-Pavljani, Velika Ciglena). Kloštar Field was very detail analyzed in the joint study of INA and RGNF, led by Prof. Dr. J. Velić and Prof. Dr. T. Malvić. Kloštar 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.

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Introduction – used methods and analyzed variables Stochastic Used methods Deterministic OKIKSGSSIS Analyzed variables PorosityDepthThickness

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Introduction - goals Goals: (1) Construction of geostatistical model of the Kloštar 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.

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Location of the Kloštar Field Kloštar Field location (CVETKOVIĆ et al., 2008)

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About the Kloštar Field wells Total no. of wells: 197 Measured wells: 57 Technically abandoned: 73 Water injection wells: 5 Production wells: 62

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Location of the Beta and T reservoirs Location of the Beta reservoirLocation of the T reservoir

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Lithology and log curves of Klo-62 well Lithology and log curves of Klo-145 well

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Core data

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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 (VELIĆ & MALVIĆ, 2008) Klo – 82 (1404.6 – 1411.7 m, II m) Beta Reservoir Determination: Lithoarenite (VELIĆ & MALVIĆ, 2008)

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Structural modeling of the Kloštar Field Kloštar Field is anticline with direction northwest-southeast Normal fault (Kloštar 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 VELIĆ et al. (2011)

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Structural modeling of the Kloštar Field During Badenian to Late Pannonian new accommodation space opened Sandstone reservoirs were deposited Evolution of the Kloštar Field during Late Pannonian

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Structural modeling of the Kloštar 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 Moslavačka 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) Moslavačka gora Mt. Evolution of the Kloštar Field during Early Pontian

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Structural modeling of the Kloštar 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 Kloštar structure Evolution of the Kloštar Field during Late Pontian Evolution of the Kloštar Field during Pliocene and Quaternary

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Deterministical geostatistical mapping of the reservoir variables Well Porosity (%) Depth (m) Thickness (m) Klo-5 18,01365,03,0 Klo-19 1502,515,5 Klo-60 17,91447,023,0 Klo-62 15,31400,022,5 Klo-63 16,61437,09,0 Klo-64 15,01397,010,0 Klo-70 12,21387,53,5 Klo-73 13,31373,04,0 Klo-74 1358,020,5 Klo-75 17,51375,020,0 Klo-76 18,51362,514,5 Klo-77 1386,022,0 Klo-78 16,21376,513,5 Klo-79 18,51393,014,0 Klo-81 19,11362,011,5 Klo-82 18,31396,518,5 Klo-83 16,01368,58,5 Klo-84 1406,09,0 Klo-86 1338,08,5 Klo-87 17,31409,010,0 Klo-88 15,51405,08,0 Klo-89 17,91395,07,0 Klo-163 1394,018,0 Well Porosity (%) Depth (m) Thickness (m) Klo-1 19,9940,013,0 Klo-12 19,5991,012,0 Klo-16 19,6916,012,0 Klo-20 21,11026,013,0 Klo-22 23,3966,011,5 Klo-23 20,51014,012,0 Klo-24 20,11020,511,0 Klo-26 21,21016,09,5 Klo-27 17,9880,020,0 Klo-28 19,2994,017,0 Klo-35 13,8790,03,0 Klo-43 5,5765,54,5 Klo-48 19,71019,013,5 Klo-57 18,2795,025,0 Klo-58 21,8803,06,0 Klo-59 18,1890,09,0 Klo-71 18,5838,010,0 Klo-72 19,6785,011,0 Klo-95 22,0957,08,0 Klo-104 18,4912,56,0 Analyzed variables of the T reservoirAnalyzed variables of the Beta reservoir

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Indicator Kriging mapping of the Beta reservoir porosity – data transformation Indicator transformation of the porosity input data

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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%

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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%

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Indicator Kriging mapping of the Beta reservoir thickness – data transformation Indicator transformation of the thickness input data

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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

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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

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Indicator Kriging mapping of the T reservoir porosity – data transformation Indicator transformation of the porosity input data

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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%

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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%

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Indicator Kriging mapping of the T reservoir thickness – data transformation Indicator transformation of the thickness input data

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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

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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

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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.

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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 Moslavačka 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)

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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)

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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 Moslavačka 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%

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Discussion and conclusion Geostatistical methods were used for detail modeling of the two most important and significantly different reservoirs of the Kloštar 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.

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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 Kloštar 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.

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Thank you for your attention!

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