SREDNJE MIOCENSKI TALOŽNI MODEL U DRAVSKOJ DEPRESIJI OPISAN GEOSTATISTIČKIM MAPAMA POROZNOSTI I DEBLJINE (POLJE: STARI GRADAC-BARCS NYUGAT)

Neogene depositional environments in the Drava depression can be classified in two groups. One group is of local alluvial fans, which were active during the period of Middle Miocene (Badenian) extension through the entire Pannonian Basin. The second group is represented by continuous Pannonian and Pontian sedimentation starting with lacustrine environment of partly deep water and partly prodelta (turbidity) fans and terminating at the delta plain sedimentation. The coarse-grained sediments of alluvial fans have the great hydrocarbon potential, because they often comprise reservoir rocks. Reservoir deposits are mostly overlain (as result of fan migration) by pelitic seal deposits and sometimes including organic rich source facies. That Badenian sequences are often characterised by complete petroleum systems, what is confirmed by large number of oil and gas discoveries in such sediments in the Drava and other Croatian depressions. Alluvial environments are characterised by frequent changes of petrophysical properties, due to local character of depositional mechanism and material sources. In the presented paper, Stari Gradac-Barcs Nyugat field is selected as a case study for demonstrating the above mentioned heterogenic features of the Badenian sequences. Structural solutions are compared by maps of parameters related to depositional environment, i.e. porosity and thickness maps. Geostatistics were used for spatial extension of input dataset. The spatial variability of porosity values, i.e. reservoir quality, is interpreted by transition among different sub-environments (facies) in the alluvial fan system.Neogenski taložni okoliši u Dravskoj depresiji mogu se podijeliti u dvije skupine. Prva skupina obuhvaća lokalne okoliše aluvijalnih lepezi, koje su bile aktivne u razdoblju srednjomiocenske (badenske) ekstenzije u cijelom Panonskome bazenu. Druga skupina predstavljena je kontinuiranom panonskom i pontskom sedimentacijom u lakustričkom okolišu, koja je započela djelomično s dubokovodnom, a dijelom taloženjem u prodeltnim lepezama (turbiditni facijesi). Taj ciklus završio je sedimentima karakterističnim za deltne ravnice. Krupnozrnati sedimenti aluvijalnih lepezi karakterizirani su velikim naftnoplinskim potencijalom, jer vrlo često obuhvaćaju ležišne stijene. Ti sedimenti uglavnom su prekriveni (a kao rezultat migracije aluvijalnog okoliša u vremenu i prostoru) pelitskim izolatorskim stijenama koje ponegdje sadrže i matične facijese bogate organskom tvari. Zato takve badenske sekvence često obuhvaćaju cjelovite naftnoplinske sustave, što je potvrđeno otkrićem velikog broja naftnih i plinskih ležišta u tim sedimentima, kako unutar Dravske tako i u drugim depresijama u hrvatskom dijelu Panonskog bazena. Aluvijalni okoliši su karakterizirani čestim promjenama petrofizikalnih svojstava, a zahvaljujući lokalnom karakteru takvoga taložnog okoliša i izvora materijala. U prikazanom radu odabrano je polje Stari Gradac-Barcs Nyugat kao ogledni primjer, na kojemu je prikazana ranije spomenuta heterogenost badenskih sekvenci. Strukturna rješenja su uspoređena s karatama onih parametara čije vrijednost ovisi o taložnom okolišu, tj. s kartama poroznosti i debljina. Geostatistika je upotrijebljena za prostornu analizu ulaznog skupa mjerenja. Prostorna varijabilnost vrijednosti poroznosti, tj. kvaliteta ležišta, je objašnjenja prijelazom između različitih podokoliša (facijesa) unutar sustava aluvijalne lepeze

Kriging, cokriging or stochastical simulations, and the choice between deterministic or sequential approaches

The data presented here for the first time in the Croatian geomathematical community, aims to establish several criteria which will aid in the selection of deterministic or stochastic geostatistical methods of estimation. This review associates the theoretical background of kriging, cokriging or stochastic simulations with some results obtained by mapping Badenian clastic reservoirs in the Drava Depression. The selected reservoirs are located in the Stari Gradac-Barcs Nyugat field, in the Western part of the Drava Depression, and at the Beničanci field in the Eastern part of this depression. Both datasets (each with 14 points) include mean porosity values taken from well log analysis in the reservoir interval at the well sites. This resulted in significant uncertainties in the variogram models, especially with the determination of range (at the secondary variogram axis). The critical advantage was the availability of a seismic attribute that could be used as a secondary and co-regionalized variable (porosity is the primary variable). In the first example (the Beničanci field) the seismic attribute was correlated with the average logged porosities. This made it possible to apply the cokriging method as the best interpolation option. The cross-validation result was 2.19 for 14 wells. In contrast, the existence of only a primary variable at the Stari Gradac-Barcs Nyugat field, forced the application of stochastic simulations as the better estimation tool, which can better describe the porosity changes in inter-well areas

Stochastical approach in deterministic calculation of geological risk - theory and example

Za izračun geološkoga rizika (ili vjerojatnosti, engl. skr. POS) otkrića ugljikovodika u postojećem ili novome stratigrafskom intervalu ili izglednom području unutar Dravske depresije upotrijebljen je dobro poznati deterministički postupak. Isti se može primijeniti, uz male dorade, za gotovo sve litologije ležišta u bilo kojem naftno-plinskom bazenu ili depresiji. Takav izračun, iako već pomalo zastario, predstavlja pouzdani alat te, zahvaljujući tomu, još uvijek ga primjenjuju brojne nafto-plinske tvrtke i konzultantske kuće. Analiza je načinjena u najmlađem dijelu ležišta (obuhvaća četiri litofacijesa) u polju Stari Gradac-Barcs Nyugat koji je predstavljen krupnoklastičnim sedimentima badenske starosti. To polje je odabrano s obzirom da su tamo već načinjene određene procjene postojanja dodatnih količina ugljikovodika u \u27skrivenim\u27 zamkama, ali i brojne geostatističke analize na podatcima poroznosti iz svih ležišnih litofacijesa. Naravno, najmlađi i najplići litofacijes obuhvatio je najveći broj takvih mjerenja, a ujedno je to (uz sljedeći dublji litofacijes) ujedno dio ležišta s najvećim rezervama ugljikovodika. Deterministički pristup izračuna POS-a nadograđen je u determinističko-stohastički, upotrebom geostatističkih karata poroznosti gdje je ona izražena kroz tri moguće realizacije (minimalnom, medijanskom i maksimalnom) za analizirani badenski litofacijes. Ukupni POS ostao je isti kao i onaj dobiven isključivo deterministički (POS=0,375). Razlog tomu je što srednja poroznost u analiziranim badenskim klastitima varira u uskome intervalu te ne utječe na procjenu vjerojatnosti postojanja novih količina ugljikovodika. No, u dubljim litofacijesima, gdje je litologija heterogenija i/ili znatnije raspucana varijacije poroznosti su znatno veće te bi uvođenje determinističko-stohastičkog pristupa dovelo do promjena u vrijednostima POS-a, ovisno o tomu koja je stohastička realizacija odabrana kao reprezentativna.Calculation of geological risk (or Probability Of Success; abbr. POS) of hydrocarbon discovery in existing or new play or prospect in the Drava depression has been done using well-known deterministical procedure. Such approach, with slightly modifications, can be used in almost all reservoir lithologies in any hydrocarbon basin or depression. This calculation, although already an old-fashion tool, represent reliable tool and it is why it is still applicable in many oil and gas companies or consulting firms. Analysis is performed in the youngest part of reservoir (which encompasses four lithofacies) in the Stari Gradac-Barcs Nyugat field. It is represented by coarse-grained sediments of Badenian age. This field is selected regarding there are already done some estimations of existence of additional hydrocarbon reserves in the ‘subtle’ traps, but also numerous geostatistical analysis with porosity data taken from all reservoir’s lithofacies. Of course, the youngest and the shallowest lithofacies included the most such measurements, and also it is (together with the next, deeper lithofacies) reservoir’s part with the largest hydrocarbon reserves. Deterministical approach in POS calculation had been improved in deterministical-stochastical, by using geostatistical porosity maps, where this variable is expressed through three possible realizations (minimal, median and maximal) for analysed Badenian lithofacies. Total POS remained the equal as such value calculated only deterministically (POS=0.375). It is because average porosity in analysed Badenian clastics varying in narrow interval, and its selection from stochastical results did not have influence on estimation of probability of new hydrocarbon reserves existence. But, in deeper lithofacies, where lithology is more heterogeneous and/or more cataclised, variations in porosity are significantly higher. In such case, introducing of deterministical-stochastical approach could result in changes in POS values, depending on which stochastical realization had been selected as representative

Linearity and Lagrange Linear Multiplicator in the Equations of Ordinary Kriging

Analizirane su jednadžbe jednostavnoga i običnoga kriginga kako bi se uočila razlika u izračunu procjene u točki, te zorno prikazalo na koji način se Lagrangeov multiplikator iskazuje kao veličina u tehnici običnoga kriginga koja minimizira varijancu procjene. Detaljnom analizom matrica i linearnih jednadžbi, koje se inače automatski izračunavaju u pozadini računalnih programa za kartiranje, prikazana je važnost geomatematike u jednoj od temeljnih geoloških djelatnosti – kartiranju. Nadalje, izvođenjem niza jednadžbi kroz članak pruža se na inženjerski način razumijevanje algoritama jednostavnoga i običnoga kriginga, koje su danas dvije najčešće korištene geostatističke tehnike (uz indikatorski kriging kao treće). U zaključku su predloženi postupci kojima se može odrediti najprimjerenija vrijednost Lagrangeovog multiplikatora za bilo koju jednadžbu običnoga kriginga.The equations of Simple and Ordinary Kriging are compared to outline their differences in the estimation procedure. Emphasis is given to the Lagrange multiplicator as a variable that allows the minimization of variance in Ordinary Kriging. The matrices and linear systems of kriging, which are most often performed in the background of the computer mapping algorithm, are analyzed and presented in detail. The intention is to show the importance of geomathematics in one of the basic geological tasks, mapping. Furthermore, a detailed presentation of equation sets provides a better understanding of the Simple and Ordinary Kriging algorithms for geological engineers, as the two most-used geostatistical techniques (included Indicator Kriging as the third). The conclusion includes proposals, presented in four steps, for the determination of the Lagrange multiplicator value in any Ordinary Kriging equation

Stochastic simulations of dependent geological variables in sandstone reservoirs of Neogene age: A case study of Kloštar Field, Sava Depression

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

Miljenko Lapaine i Dušan Marjanović (Ed.): Elementa Geometriae Practicae, Zemlyomirje, Introduction to Practical Geometry / Surveying

It has been my pleasant task to write a review of a very interesting book with its attractively archaic appearance of the cover and a layout which, it needs to be said, completely matches its contents. Furthermore, it is interestingly conceptualized; a working result of scientific teams from Croatia and Hungary within a framework of bilateral project Najstariji hrvatski udžbenik geodezije (The oldest Croatian textbook of Geodesy) in a way that its preface and abstract have been written trilingually – in Croatian, Hungarian and English. The results of the project work have been conjoined, in a fitted final whole, by the book’s editors Miljenko Lapaine and Dušan Marjanović

Production of a Porosity Map by Kriging in Sandstone Reservoirs, Case Study from the Sava Depression

Variogramske analize te upotreba geostatističke interpolacije predstavljaju u zadnjih pet godina standardni alat u hrvatskoj geologiji. Takve analize posebno su primjenjivane prilikom kartiranja naftnogeoloških podataka. U ovome članku opisani su prostorno modeliranje podataka poroznosti te kartiranje s pomoću krigiranja naćinjeno za relativno veliki ulazni skup vrijednosti prikupljenim na naftnom polju smještenom u hrvatskom dijelu Panonskoga bazena, tj. u području Savske depresije. Analizirani skup podataka obuhvatio je vrijednosti poroznosti u pješčenjačkom ležištu panonske starosti. Izvorni podaci, svojom brojnošću, rijetko su obiman skup vrijednosti poroznosti dostupnih u ležištima ugljikovodika u Hrvatskoj. To je omogućilo vrlo pouzdano semivariogramsko modeliranje te interpolaciju tih podataka krigiranjem. Krigeova metoda (krigiranje) istaknuta je kao najprimjerenija interpolacijska tehnika za poroznost, ali i druge geološke podatke u pješčenjačkim ležištima miocenske starosti.Variogram analyses and usages of geostatistical interpolations have been standard analytical tools in Croatian geology in the last five years. Such analyses have especially been applied in the mapping of petroleum geological data. In this paper, spatial modelling of porosity data and, consequently, kriging mapping are described for a relatively large dataset obtained at an oil field located in the Croatian part of Pannonian basin (Sava depression). Analyzed datasets included porosity values measured in a sandstone reservoir of Pannonian age. The original dataset can be considered as a rare extensive porosity set available for Croatian hydrocarbon reservoirs. It made possible very reliable semivariogram modelling and kriging interpolation of porosity. The obtained results point out kriging as the most appropriate interpolation approach for porosity, but also for other geological data in sandstone reservoirs of Miocene age

The Bjelovar Subdepression as an Area with Conventional and Unconventional Hydrocarbon and Geothermal Reserves

Bjelovarska subdepresij a, kao geološki određen prostor, sadrži – uz dokazane rezerve ugljikovodika – i njihove potencij alne rezerve te rezerve geotermalne energij e. Dan je pregled pridobivanja i uporabe takvih energenata, a zatim sastav, dubina i rasprostranjenost takvih ležišta u dij elovima gdje su istraživana i pretpostavljena. Geotermalno ležište izučavano je u prostoru mezozojskih karbonata te donjomiocenskih i srednjomiocenskih krupnih klastita u sinklinali Velika Ciglena, najvećoj pojedinačnoj strukturi u subdepresij i. Dokazano je postojanje termalne vode na dubinama od oko 2.500 m, no do danas nij e privedena pridobivanju na površinu i uporabi bilo za proizvodnju struje bilo za grij anje. Nekonvencionalna ležišta također su pretpostavljena u tom istom prostoru, unutar gornjobadenskih, sarmatskih i donjopanonskih matičnih stij ena, koje su dostigle termalnu zrelost. No, takvih ležišta, posebice plina, moglo bi se naći i na rubu subdepresij e, u Bilogorskoj zoni, unutar struktura gdje nisu dokazana konvencionalna ležišta ugljikovodika (Cremušina, Gakovo), no opažene su pojave plina i naft e u slabopropusnim pješčenjacima gornjega miocena.The Bjelovar Subdepression is geologically very well defi ned area where are discovered proven hydrocarbon reserves. However, there are assumed as well potential hydrocarbon and geothermal reserves. Here is fi rstly given review of forming and application of fossil fuels and geothermal energy. It is followed by review of lithologies, depths and distributions of unconventional and geothermal reservoirs in subdepression parts where they are explored and assumed. Geothermal reservoir is studied in Mesozoic carbonates and Karpatian to Badenian coarse grained clastics in Velika Ciglena Syncline. It is the largest single structure in Velika Ciglena Syncline, where is proven geothermal water at depth more than 2500 m. However, it still is not proven and used for electricity of thermal applications. Unconventional hydrocarbon reservoirs are also assumed in the same area, i.e. in Upper Badenian, Sarmatian and Lower Pannonian sediments in the thermal mature phase. Also, such unconventional reservoirs, especially of gas, could be proven at subdepression margin, in the Bilogora Zone, in structures where conventional reservoirs are not proven (Cremušina, Gakovo), but are registered oil and gas shows in weakly permeable Upper Miocene sandstones