OSNOVE MODELA ZA GRANIČNA ISPITIVANJA TROŠKOVA KOD ODLAGANJA SLOJNE VODE

Formation water is extracted throughout the life of the fields of hydrocarbons together with oil and/or gas. Oil dehydration costs, as well as those of production water reinjection represent significant component in total costs at mature oil and gas fields. The optimization of the aforesaid costs, from the point of technology and economics, can affect both profitability (cost-effectiveness) and development of the oil field in the future. Methodology of calculation of unit cost will be elaborated in this paper for treatment of produced water (dehydration) and production water reinjection. The methodology of calculation of unit cost for disposal of produced water will be applied at production of mature oil and gas field. Unit cost for disposal of produced water for the period 2009 – 2014 will be calculated in the selected example. Making of this particular model of calculation of disposal costs of produced water is crucial for economy analyses of hydrocarbons exploitation from mature fields.Slojna voda se pridobiva tijekom radnog vijeka ležišta ugljikovodika zajedno s naftom i/ili plinom. Troškovi dehidracije i utiskivanja slojne vode predstavljaju kod naftno-plinskih polja u poodmaklom razdoblju eksploatacije značajnu komponentu u ukupnim troškovima polja. S tehnološko-ekonomskog stajališta optimizacijom navedenih troškova može se značajno utjecati na rentabilnost i budući rad polja. U ovom radu obradit će se metodologija izračuna jediničnog troška (trošak po jedinici proizvoda) procesa odvajanja slojne vode (dehidracije) i utiskivanja slojne vode. Metodologija izračuna jediničnog troška zbrinjavanja slojne vode primijenit će se na naftno-plinskom polju koje je u poodmakloj fazi eksploatacije. Za razdoblje od 2009. godine do 2014. godine na odabranom primjeru izračunata je jedinična cijena zbrinjavanja slojne vode. Odabrani primjer je konkretan proizvodni pogon bez navođenja naziva ležišta. Kreiranje posebnog modela za izračun troškova odvajanja i utiskivanja slojne vode predstavlja bitnu komponentu analize ekonomičnosti eksploatacije ugljikovodika u poodmaklom razdoblju rada naftno-plinskih polja

PRIMJENA SAMONADOPUNJUJUĆE METODE NA VELIKOME SKUPU ULAZNIH PODATAKA – PRIMJENA NA ZAPADNOME DIJELU SAVSKE DEPRESIJE

The bootstrap method is a nonparametric statistical method that through the resampling of an input data set provides the ability to obtain a new data set that is normally distributed. Due to various factors, it is difficult to obtain many data sets for deep geological data, and in most cases, they are not normally distributed. Therefore, it is necessary to introduce a statistical tool that will enable obtaining a set with which statistical analyses can be done. The bootstrap method was applied to field “A”, reservoir “L” located in the western part of the Sava Depression. It was applied to the geological variable of porosity on a set of 25 data points. The minimum number of resamplings required for a large sample to obtain a normal distribution is 1000. Interval estimation of porosity for reservoir “L” obtained by the bootstrap method is 0.1875 to 0.2144 with a 95% confidence level.Samonadopunjujuća metoda neparametarska je statistička metoda koja omogućuje ponovnim uzorkovanjem ulazni skup podataka za dobivanje novoga skupa podataka koji je normalno distribuiran. Zbog različitih čimbenika teško je doći do geoloških podataka u velikome skupu, a u većini slučajeva nisu normalno distribuirani. Stoga je potrebno uvesti statistički alat koji će omogućiti dobivanje skupa s kojim se mogu raditi statističke analize. Samonadopunjujuća metoda primijenjena je na polju „A”, ležište „L” koje se nalazi u zapadnome dijelu Savske depresije. Primijenjena je na geološku varijablu šupljikavosti na skupu od 25 podataka. Minimalni broj ponovnoga uzorkovanja potreban za veliki uzorak da bi se dobila normalna raspodjela iznosi 1000. Intervalna procjena šupljikavosti za ležište „L” dobivena samonadopunjujućom metodom iznosi 0,1875 do 0,2144 s razinom pouzdanosti od 95 %

THE ANALYSIS OF WATER INJECTION SYSTEMS IN SANDSTONE HYDROCARBON RESERVOIRS, CASE STUDY FROM THE WESTERN PART OF THE SAVA DEPRESSION

Utiskivanje slojne vode sastavni je dio proizvodnoga ciklusa ugljikovodika u sekundarnoj fazi pridobivanja. Utisni sustavi mogu se podijeliti na središnji i pojedinačni. U radu su opisani troškovi utiskivanja slojne vode na primjerima polja A (središnji utisni sustav) i B (pojedinačni utisni sustav) koji se nalaze u zapadnome dijelu Savske depresije. Ležišne su stijene naftno-plinskih polja A i B sitnozrnati do srednjezrnati pijesci i kvarcno-tinjčasti pješčenjaci donjopontske starosti. Srednja poroznost u polju A iznosi 15 – 35 %, a u polju B 10 – 31 %, ovisno o dubini i postotku cementacije. Za obrađena naftno-plinska polja u ovome radu napravljena je usporedba troškova i analiza osjetljivosti utisnoga sustava te moguća optimizacija i racionalizacija troškova utisnih sustava.Formation water injection is one of the constituent parts of the hydrocarbon production cycle in the secondary exploitation oil recovery phase. The formation water injection system can be divided the into single and central injection systems. The formation water injection costs have been described in this paper using the examples of fi eld A (central injection system) and fi eld B (single injection system). These are located in the western part of the Sava Depression. The reservoir rocks regarding the oil and gas fi elds A and B are fi ne to middle grained sands and quartz micaceous sandstones that belong to the geological age of Lower Pontian. The average porosity (intergranular) in fi eld A is 15–35% and in fi eld B it is 10-31%, depending on the depth and cementation percentage. Regarding the oil and gas fi elds described in this paper, a cost comparison has been made and an injection system sensitivity analysis as well as an analysis of possible injection systems’ costs for optimization and rationalization

THE COST ANALYSIS OF THE SEPARATION OF PRODUCED FORMATION WATER FROM THE HYDROCARBON RESERVOIR USING THE EXAMPLE OF THE UPPER MIOCENE SANDSTONE DEPOSITS OF THE SAVA DEPRESSION

Slojna voda crpi se tijekom radnoga vijeka ležišta ugljikovodika zajedno s naftom i/ili plinom, uglavnom predstavljajući dominantan fluid iscrpka. Proizvedena slojna voda odvaja se u procesu dehidracije. U ovome radu obrađeni su troškovi odvajanja slojne vode na naftno-plinskim poljima A, B i C koja se nalaze u zapadnome dijelu Savske depresije. Na polju A proces odvajanja slojne vode odvija se na trima lokacijama, dok se na poljima B i C proces obavlja na jednoj lokaciji. Prikazan je tehnološki sustav odvajanja slojne vode te geološke karakteristike ležišta na spomenutim poljima. Napravljena je statistička obrada troškova odvajanja slojne vode. Procijenjeni su troškovi te je napravljena korelacija između troškova važnih za odvijanje normalnoga procesa odvajanja slojne vode. Svrha analize troškova procesa dehidracije jest optimizacija proizvodnoga sustava te kontrola troškova procesa.Formation water is gathered during the working life of the hydrocarbon reservoir alongside the oil and/or gas and it mostly constitutes the recovery\u27s dominant fluid. The produced formation water is separated during the process of dehydration. This thesis deals with the formation water separation costs regarding the fields A, B and C which are located in the western part of the Sava Depression. The dehydration process regarding the field A is executed in three locations, and regarding the fields B and C it is executed in one location. The technological system of formation water separation and the geological characteristics of the above mentioned reservoirs is represented. A statistical analysis regarding the formation water separation costs has been made, the costs have been statistically estimated and a correlation between the costs relevant for the usual formation water separation process has also been made. The purpose of the analysis of the cost of the dehydration process is the optimization of the production system and cost control of the process

Application of the Radial Basis Function interpolation method in selected reservoirs of the Croatian part of the Pannonian Basin System

Purpose. The use of interpolation methods of mapping Radial Basis Function (RBF) on reservoir data from one field in Croatian part of Pannonian Basin System (CPBS). Methods. The RBF method (with five single basic mathematical functions) was applied to small datasets. Application of the Radial Basis Function (RBF) method and comparison with previous application of the Inverse Distance Weighting (IDW) method applied in the CPBS area. The IDW and RBF methods were compared by cross-validation value and visual inspection of interpolated maps. Findings. The RBF method was tested on a small data sample. The RBF method can be used independently when using the Inverse Multiquadric Function (RBF-IM) mathematical function, while the remaining analyzed mathematical multilog function (RBF-M) and “multiquadric function” (RBF-M2) can be used as additional sources of information when mapping. Originality. For the first time RBF is applied as a method in the CPBS area for small input data sets. Practical implications. For small sample the RBF method cannot be applied independently. According to the cross-validation value and visual inspection of interpolated maps, the method that can be used with the IDW method when mapping a small sample is RBF-IM. It could be primary or additional method for a small sample, while for a large sample it offers additional information.Мета. Використання методу інтерполяції при картуванні радіальної базисної функції (РБФ) стосовно даних одного родовища в хорватській частині Паннонського басейну. Методика. Метод РБФ (з п’ятьма основними математичними функціями) застосовувався у порівнянні з використовуваним раніше методом ОВР (зворотних зважених відстаней) для хорватської частини Паннонського басейну. Методи РБФ і ОВР порівнювалися за значенням перехресної перевіркою і візуальним оглядом інтерпольованих карт. Метод РБФ застосовувався до невеликих масивів даних. Результати. Встановлено, що при візуальному огляді карт метод RBF-IM може застосовуватися до невеликого набору даних (менше 20 точок), в той час як методи RBF-M і RB-M2 не можуть застосовуватися незалежно, але в якості додаткової інформації про просторовий розподіл відображається змінна, тобто про зону сильного локалізованого ефекту. Даний метод може застосовуватися автономно при використанні зворотної мультиквадратичної математичної функції (ОММФ), при цьому залишилися математичні багатофункціональна функція (МФФ) і мультиквадратична функція (МКФ) можуть бути використані як додаткові джерела інформації при картуванні. Порівнюючи карту, отриману IDW і двома іншими методами RBF-M і RBF-M2, можна спостерігати відмінності через різних використовуваних математичних функцій. Обидва допоміжних методи більш кращі для великих закритих областей в частинах з низькою вибіркою, наприклад, область, закриту лінією ізопористості 0.22. Наукова новизна. Вперше використаний метод РБФ для аналізу невеликих масивів даних, що стосуються хорватської частини Паннонського басейну. Практична значимість. Для невеликої вибірки недостатньо використовувати тільки метод РБФ. У відповідності зі значенням перехресної перевірки і візуальної перевірки інтерпольованих карт, метод, який може використовуватися з методом IDW при відображенні невеликої вибірки, є ОММФ. Він може застосовуватися як основний або додатковий метод у разі невеликої вибірки, і як метод отримання додаткової інформації в разі великої вибірки.Цель. Использование метода интерполяции при картировании радиальной базисной функции (РБФ) применительно к данным одного месторождения в хорватской части Паннонского бассейна. Методика. Метод РБФ (с пятью основными математическими функциями) применялся в сравнении с использовавшимся ранее методом ОВР (обратных взвешенных расстояний) для хорватской части Паннонского бассейна. Методы РБФ и ОВР сравнивались по значению перекрестной проверкой и визуальному осмотру интерполированных карт. Метод РБФ применялся к небольшим массивам данных. Результаты. Установлено, что при визуальном осмотре карт метод RBF-IM может применяться к небольшому набору данных (менее 20 точек), в то время как методы RBF-M и RB-M2 не могут применяться независимо, но в качестве дополнительной информации о пространственном распределении отображаемая переменная, т.е. о зоне сильного локализованного эффекта. Данный метод может применяться автономно при использовании обратной мультиквадратичной математической функции (ОММФ), при этом оставшиеся математические многофункциональная функция (МФФ) и мультиквадратичная функция (МКФ) могут быть использованы как дополнительные источники информации при картировании. Сравнивая карту, полученную IDW и двумя другими методами RBF-M и RBF-M2, можно наблюдать различия из-за различных используемых математических функций. Оба вспомогательных метода более предпочтительны для больших закрытых областей в частях с низкой выборкой, например, область, закрытую линией изопористости 0.22. Научная новизна. Впервые использован метод РБФ для анализа небольших массивов данных, касающихся хорватской части Паннонского бассейна. Практическая значимость. Для небольшой выборки недостаточно использовать только метод РБФ. В соответствии со значением перекрестной проверки и визуальной проверки интерполированных карт, метод, который может использоваться с методом IDW при отображении небольшой выборки, является ОММФ. Он может применяться как основной или дополнительный метод в случае небольшой выборки, и как метод получения дополнительной информации в случае большой выборки.Some data from the technical documentation of INA Plc. was used and presented in some maps and tables. This was collected during doctoral research by J. Ivšinović. This research (analyses) was partially supported with the project “Mathematical methods in geology IV” (led by T. Malvić). Funds were given from the University of Zagreb, Faculty of Mining, Geology and Petroleum Engineering, for the 2019 year

Uloga projektnog tima u faznom odobrenju projekta

Fazno odobrenje projekta je postalo dugotrajna praksa u naftnoj industriji. Omogućuje kontrolu i kvalitetu pripreme i izvođenja kompleksnijih razradnih remontnih projekata. U svakoj pojedinoj fazi projekta uključenost tima je maksimalna i vrlo važna. Njihov doprinos i inicijativa usmjeravaju projekt u smjeru odobrenja ili ne odobrenja. U ovom članku se obrađuje uloga projektnog tima unutar faznog odobrenja i implementacije razradnih remontnih projekata. Opisuju se funkcije, obaveze i doprinosi u savladavanju prepreka unutar projekta od ideje, odobrenja, implementacije sve do naučenih lekcija

Recent advances in geomathematics in Croatia: examples from subsurface geological mapping and biostatistics

http://sherpa.ac.uk/romeo/issn/2076-3263/Geomathematics is extremely important in geosciences, particularly in the geology. The key for any geomathematical analysis is the definition of a typical model to be applied for further prognosis, either through deterministic or stochastic approaches. The selection of the appropriate procedure is presented in this paper. Two different geomathematical subfield datasets were used in subsurface geological mapping and palaeontology and different biostatistics applications, representing important geomathematical subfields in the Croatian geology. The different subsurface interpolation methods tested, validated and recommended for application were used to obtain the best possible outcome in reservoir modelling, in the cases with small datasets. Cross- validation may be chosen as the main selection criteria, applied to the Croatian part of the Pannonian Basin System (CPBS). Recent advances in biostatistics applied in palaeontology and case studies from Croatia are also presented, where biometric studies are of significant importance in fossil biota. Data, methods and problems in geosciences are vast subjects, and address a wide spectrum of fundamental science. Because geology includes subsurface and surface geology, and very different datasets regarding variable and number of data, we have chosen here two representative case study groups with original samples from Northern Croatia. Subsurface mapping has been presented on limited petrophysical datasets from the Northern Croatian, Miocene, hydrocarbon reservoirs. Biostatistics have been presented on very different samples, allowing us to achieve paleoenvironmental reconstructions of the size of relevant fossils, such as dinosaurs or other species and their paleoenvironments. All examples highlight examples of the valuable application of geomathematical tools in geology. The results, cautiously validated and correlated with other, non-numerical (indicator, categorical) geological knowledge, are of enormous assistance in creating better geological models.info:eu-repo/semantics/publishedVersio

Geological risk calculation through probability of success (PoS), applied to radioactive waste disposal in deep wells: a conceptual study in the pre-neogene basement in the Northern Croatia

https://v2.sherpa.ac.uk/id/publication/24819The basic principles of geological risk calculation through probability of success (PoS) are mostly applied to numerical estimation of additional hydrocarbon existence in proven reservoirs or potential hydrocarbon discoveries in selected geological regional subsurface volumes. It can be adapted and validated for a comprehensive input dataset collected in the selected petroleum province, by dividing up geological events into several probability categories and classes. Such methodology has been widely developed in the last decades in the Croatian subsurface—mostly in the Croatian Pannonian Basin System (CPBS). Through the adaptation of geological categories, it was also applied in hybrid, i.e., stochastic, models developed in the CPBS (Drava Depression), mostly for inclusion of porosity values. As the robustness of this methodology is very high, it was also modified to estimate the influence of water-flooding in increasing oil recovery in some proven Neogene sandstone reservoirs in the CPBS (Sava Depression). This new modification is presented to be applied to geological risk calculation, intending to assess the safety of geological environment storage in deep wells, where spent nuclear fuel (SPN) would be disposed, a subject of great importance. The conceptual study encompassed the magmatic and metamorphic rocks in the pre-Neogene basement of the CPBS, intended to be used for such purpose. Regionally distributed lithologies are considered for nuclear waste disposal purpose, in order to detect the safest ones, considering petrophysical values, water saturation, recent weathering and tectonic activity.info:eu-repo/semantics/publishedVersio

Selection and geomathematical calculation of variables for sets with less than 50 data regarding the creation of an improved subsurface model, case study from the western part of the Sava Depression : doctoral dissertation

Objekti doktorskoga istraživanja su dva gornjomiocenska pješčenjačka ležišta ugljikovodika zapadnoga dijela Savske depresije. Trenutačno se iz njih pridobivaju ugljikovodici sekundarnom metodom, tj. utiskivanjem slojne vode. Istraženost toga prostora na razini je koja dopušta značajna poboljšanja i nadogradnju geoloških modela s ciljem povećanja iscrpka ležišta. To se posebno odnosi na metode statističke i geomatematičke analize niza ležišnih varijabli poput šupljikavosti, propusnosti (primarne varijable) te utisnutih volumena vode (sekundarna varijabla). Većinu postojećih karata ležišta (strukturnih, šupljikavosti i sl.) treba načiniti znatno detaljnije, poglavito s većim brojem ulaznih vrijednosti. Matematički algoritmi poput variograma i krigiranja bili su glavni alati u izučavanju prostorne zavisnosti i moguće anizotropije spomenutih varijabli. Statističke metode ponovnoga uzorkovanja bile su alat kojim se proširio broj vrijednosti statističkih parametara te time unaprijedile analize prostora u kojima je broj podataka oskudan, tj. približno manji od 50 mjerenja po odabranoj regionaliziranoj varijabli. Za mali ulazni skup podataka (<20) primijenjene su sljedeće interpolacijske metode: inverzne udaljenosti, najbližeg i prirodnoga susjedstva. Metodologija izračuna geološke vjerojatnosti (POS) je primijenjena prilikom izračuna postojanosti preostalih ekonomskih količina ugljikovodika. Modifikacija metodologije izračuna POS-a je primijenjena za ležišta koja su sekundarnoj fazi pridobivanja (zavodnjavanje ležišta). Izračun neutralne vrijednosti novčanih jedinica je primijenjen za istraživanje dodatnih količina ugljikovodika u postojećim strukturama te pridobivanje ugljikovodika prilikom zavodnjavanja ležišta.The objects of the doctoral research are two hydrocarbon fields with Upper Miocene sandstone reservoirs, located in the western part of the Sava Depression. Namely, those are the "A" field with "L" reservoir and the "B" field with "K" reservoir. Both currently produce hydrocarbons using a secondary method (water injection). This is very mature explored and developed area, what allows significant improvements and upgrades of geological models in order to increase hydrocarbon recovery. This applies especially for methods of statistical and geomathematical analysis of numerous reservoir variables such as porosity and permeability (primary variables) and injected water volumes (secondary variable). Furthermore, the most existing reservoirs maps (structural, porosity, etc.) should be made in much more detail, using advancing mapping algorithms. Mathematical algorithms such as variograms and Kriging had been the main tools in analysing spatial dependence and possible anisotropy of the selected variables. The Kriging method has a long history of application in the field of Croatian part of the Pannonian Basin System (CPBS). The statistical method Jack-knifing was a tool who extend the number of values of statistical parameters and thus to improve the analysis in which the number of data deficient, i.e. approximately less than 50 measurements per selected regionalized variable (porosity: reservoir “L” 25 data, reservoir “K” 19 data). For a small input data set (<20), for variables injected volume of water (reservoir “L” 10 data; reservoir “K” 3 data) and permeability (reservoir “L” 10 data; reservoir “K” 18 data) following interpolation methods are applied: Inverse Distance, Nearest and Natural Neighbourhood. The size of the small input set for different types of variables, i.e., measured points, was defined by 20 or more „solid“ data, and about 15 has been sufficient to apply the Inverse Distance and Nearest Neighbourhood methods. For a small input data set, the recommended mapping method is the Inverse Distance method. When interpreting mapping results after applying Ordinary Kriging (before or after Jack-knifing method) or interpolation method for a small sample of the final evaluation of the resulting maps is necessary to fulfill the following: visually (maps with no expressed local value („bull-eyes“ or „butterflies“), are appropriate) and numerically (using the cross-validation value). According to the results of the cross-validation values, the Inverse Distance method in the cases of mapping permeability and injected volume of water for reservoirs “K” and “L” is most acceptable. The methodology for calculating geological probability was applied in calculating the persistence of the remaining economic quantities of hydrocarbons in the western part of the Sava Depression. A modification of the methodology for the calculation of geologic probability was applied to the reservoirs that are in the secondary hydrocarbon production phase. The variables that are included in the geological probability calculation are: trap, reservoir, source rocks, migration and hydrocarbons preservation. The calculated value of exploratory geological probability for the western part of the Sava Depression is 0.4218, while the value of the modified geological probability for reservoirs in the secondary hydrocarbons production phase is 0.5625. The calculation of the risk neutral value of monetary units has been applied to: exploration of additional hydrocarbons in existing structures and production hydrocarbons from water flooding reservoirs. The calculated value of 2.32·106 risk-neutral USD (500 000 m3 of geological reserves of hydrocarbons) for the exploration geological probability value is the investment maximum in the western Sava Depression exploration area for the company's 50 million USD hydrocarbon exploration budget. For the value of the modified geological probability, the amount of the risk-neutral USD for the “L” reservoir is 1.21·106, and for the “K” reservoir 1.17·106, which is also the investment maximum for the company’s 35 million USD hydrocarbon production budget

Primerjava učinkovitosti kartiranja za majhne podatkovne nize z uporabo metode inverzne utežene razdalje in metode drsečega povprečja v miocenskem rezervoarju ogljikovodikov, Severna Hrvaška

Mapping of geological variables in the Croatian part of the Pannonian Basin System (CPBS) is mostly based on small input datasets. In the case of the analyzed hydrocarbon field "B", reservoir "K", due to the complex geological structure and pronounced tectonics, the interpretations are restricted on several blocks, where each has very limited dataset. The porosity (19 data) and permeability (18 data) variables were analyzed. The applied interpolation methods are the Inverse Distance Weighting (IDW) and the Moving Average (MA). They were compared and analyzed by visual inspection of the obtained maps, comparison of mathematical background and by calculation of cross-validation (CV). The cross-validation value for the porosity of the "K" reservoir in the case of IDW application is 0.0011, and in the case of MA 0.0010while in the case of permeability the IDW is 480.84, and in the case of MA 1346.41. According to the visual review of maps, the values of descriptive statistics of estimated values and the results of cross-validation, the IDW method is recommended for mapping the porosity and permeability of reservoirs blocks in the Sava Depression.Kartiranje geoloških spremenljivk v hrvaškem delu Panonskega bazena temelji večinoma na majhnih vhodnih podatkovnih nizih. V primeru preučevanega polja ogljikovodikov »B«, rezervoarja »K« je zaradi kompleksne geološke zgradbe in močno izražene tektonike, interpretacija omejena na nekaj blokov, od katerih ima vsak zelo omejen nabor podatkov. Analizirane spremenljivke so bile poroznost (19 podatkov) in prepustnost (18 podatkov). Kot interpolacijski metodi sta bili uporabljeni metoda inverzne utežene razdalje (IUR) in metoda drsečega povprečja (DP). Metodi smo primerjali in analizirali s pomočjo vizualnega pregleda dobljenih kart, primerjavo matematičnega ozadja in z izračunom navzkrižne validacije. Vrednost navzkrižne validacije za poroznost rezervoarja »K« pri uporabi IDW je 0,0011, v primeru uporabe DP pa 0,0010. Vrednost navzkrižne validacije v primeru prepustnosti pa je bila pri uporabi IDW 480,84 in pri uporabi DP 1346,41. Glede na vizualni pregled kart, vrednosti opisne statistike ocenjenih vrednosti in rezultate navzkrižne validacije, se je metoda IDW izkazala za priporočljivo metodo pri kartiranju poroznosti in prepustnosti rezervoarskih blokov v Savski depresiji