Indicator based geostatistical methods (Indicator Kriging and Sequential Indicator Simulations) are the mostly used methods for facies mapping or modelling. Although it is assumed that in facies ...variables should be discrete, it is possible to apply these methods on continuous variables as well. If a variable is continuous, a cumulative probability distribution function has to be created. Methodology includes a series of cut-offs. On the cumulative probability distribution function, probabilities for all cut-offs can be defined. Based on cut-offs, all the data can be divided into two groups: (1) the data which has values lower than the cut-off and (2) the data which has values higher or equal than the cut-off. In this way, the indicator variable takes a value of 1 at all locations where the value is higher or equal than the cut-off and o otherwise. The larger number of cut-offs, the more precise the cumulative distribution function is. Indicator Kriging maps show the probability of certain lithofacies appearing in some location. On the other hand, stochastical realizations provide a different number of solutions for the same input data set. Those solutions can be very similar, but never identical. It is important to emphasize that all obtained solutions are equally probable. Results of Sequential Indicator Simulations are also probability maps. There are several advantages for Indicator based methods. They do not ask for a normal distributed input dataset (e.g., can be implemented for bimodal distribution), and show connectivity of the largest or smallest values. Indicator Kriging and Sequential Indicator Simulations are applied for porosity mapping of the Upper Miocene sandstone reservoir in the Sava Depression. During the Upper Miocene, sands were deposited through turbiditic currents in the deepest part of the sedimentation area, forming turbiditic channels. Such channels can be recognized on the probability map for the cut-off 19 % in Indicator Kriging as well as in Sequential Indicator Simulation maps.
The sweetness seismic attribute is a very useful tool for proper description of the depositional environment, reservoir quality and lithofacies discrimination. This paper shows that depositional ...channels and turbidity sandstones deposited during the Upper Pannonian and Lower Pontian in the Sava Depression can be described using porosity–thickness and sweetness seismic attribute maps. Two studied reservoirs are of Neogene stage (“UP” reservoir of Upper Pannonian age and “LP” reservoir of Lower Pontian age) and located in the Sava Depression, Croatia. Both reservoirs contain medium to fine grained sandstones that are intercalated with basinal marls. A comparison of the sweetness seismic attribute and porosity–thickness maps show a good visual match with correlation coefficient of approximately 0.85. A mismatch was observed in areas with small reservoir thickness. This work demonstrates the importance of using porosity–thickness maps for reservoir characterization. The workflow presented in this work has wider applications in frontier areas with poor seismic data or coverage.
Deterministic methods are still widely used for reservoir characterization and modelling. The result of such methods is only one solution. It is clear that our knowledge about the subsurface is ...uncertain. Since stochastic methods include uncertainty in their calculations and offer more than one solution sometimes they are the best method to use. This paper shows testing of the deterministic (Ordinary Kriging) and stochastic (Sequential Gaussian Simulations) methods of reservoir properties distribution in the Lower Pontian hydrocarbon reservoirs of the Sava Depression. Reservoirs are gas- and oil-prone sandstones. Ten realizations were obtained by Sequential Gaussian Simulation, which are sufficient for defining locations with the highest uncertainties of distributed geological variables. The results obtained were acceptable and areas with the highest uncertainties were clearly observed on the maps. However, high differences of reservoir property values in neighbouring cells caused the numerical simulation duration to be too long. For this reason, Ordinary Kriging as a deterministic method was used for modelling the same reservoirs. Smooth transitions between neighbouring cells eliminated the simulation duration problems and Ordinary Kriging maps showed channel sandstone with transitional lithofacies in some reservoirs.
The research presented herein is the first attempt to perform geostatistical simulations on three geologic variables, porosity, thickness, and depth to reservoir, in the Croatian Pannonian basin. The ...data were collected from a reservoir of Lower Pontian age in Kloštar Field, located in the western part of the Sava Depression.
All three variables were analyzed using sequential Gaussian simulations (SGS). Information regarding present-day depth, thickness, and locations of areas with higher porosity values were used to reconstruct paleo-depositional environments and the distribution of different lithotypes, ranging from medium-grained, to mostly clean sandstones and to pure, basin marls. Estimates of present-day thickness and depth can help to define areas of gross tectonic displacement and the role of major faults that have been mapped in the field. However, since mapping of the raw data (including porosities) does not allow the reconstruction of paleo-depositional environments, sequential indicator simulations (SIS) were applied as a secondary analytical tool. For this purpose, several cutoff values for thickness were defined in an effort to distinguish the orientation of depositional channels (main and transitional). This was accomplished by transforming porosities to indicator values (0 and 1) and by applying a non-linear “indicator kriging” technique as the “zero” map for obtaining numerous indicator realizations by SIS.
In the SGS and the SIS approaches, the simulations encompassed 100 realizations. A representative realization was then selected using purely statistical criteria, i.e., two realizations were almost always chosen in accordance with the order of calculation. The 1st and 100th realizations were selected for each variable in the SGS and SIS and five “indicator kriging” maps were chosen for the thicknesses cutoffs.
Deterministic methods are still widely used for reservoir characterization and modelling. The result of such methods is only one solution. It is clear that our knowledge about the subsurface is ...uncertain. Since stochastic methods include uncertainty in their calculations and offer more than one solution sometimes they are the best method to use. This paper shows testing of the deterministic (Ordinary Kriging) and stochastic (Sequential Gaussian Simulations) methods of reservoir properties distribution in the Lower Pontian hydrocarbon reservoirs of the Sava Depression. Reservoirs are gas- and oil-prone sandstones. Ten realizations were obtained by Sequential Gaussian Simulation, which are sufficient for defining locations with the highest uncertainties of distributed geological variables. The results obtained were acceptable and areas with the highest uncertainties were clearly observed on the maps. However, high differences of reservoir property values in neighbouring cells caused the numerical simulation duration to be too long. For this reason, Ordinary Kriging as a deterministic method was used for modelling the same reservoirs. Smooth transitions between neighbouring cells eliminated the simulation duration problems and Ordinary Kriging maps showed channel sandstone with transitional lithofacies in some reservoirs.
Geostatistical methods are very successfully used in Upper Miocene (Lower Pontian) Kloštar structure modelling. Mapping of the two variables (porosity and thickness) and their common observation in ...certain cut-off values gave the insight in depositional channel location, transitional lithofacies, material transport direction and variables distribution within representative Lower Pontian reservoir. It was possible to observe direction of the turbidites and role of the normal fault in detritus flow direction in the analyzed structure. Intercalation between turbiditic sandstones and basinal pelitic marls were the locations with the highest thicknesses. Sequential Indicator Simulations highlighted porosity maps as primary and thickness maps as secondary (additional) data source (the paper is published in Croatian).
The volume of geological structures is often calculated by using the definite integral. Though in some cases the integral can be solved analytically, in practice we usually approximate its value by ...numerical integration techniques. The application of definite integral in volume calculation is illustrated by two examples. The volume of Mount Fuji, the world-known “conic” geomorphological structure, is calculated by analytical integration. Two basic numerical integration methods, that is, the trapezoidal and Simpson’s rule are applied to subsurface hydrocarbon reservoir volume calculation, where irregular anticline is approximated by a frustum of a right circular cone.
Geostatistical methods are very successfully used in Upper Miocene (Lower Pontian) Klostar structure modelling. Mapping of the two variables (porosity and thickness) and their common observation in ...certain cut-off values gave the insight in depositional channel location, transitional lithofacies, material transport direction and variables distribution within representative Lower Pontian reservoir. It was possible to observe direction of the turbidites and role of the normal fault in detritus flow direction in the analyzed structure. Intercalation between turbiditic sandstones and basinal pelitic marls were the locations with the highest thicknesses. Sequential Indicator Simulations highlighted porosity maps as primary and thickness maps as secondary (additional) data source.
Geostatistical methods are very successfully used in Upper Miocene (Lower Pontian) Klostar structure modelling. Mapping of the two variables (porosity and thickness) and their common observation in ...certain cut-off values gave the insight in depositional channel location, transitional lithofacies, material transport direction and variables distribution within representative Lower Pontian reservoir. It was possible to observe direction of the turbidites and role of the normal fault in detritus flow direction in the analyzed structure. Intercalation between turbiditic sandstones and basinal pelitic marls were the locations with the highest thicknesses. Sequential Indicator Simulations highlighted porosity maps as primary and thickness maps as secondary (additional) data source.
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