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Potpuni četverostran u pravokutnim koordinatama II
No full textThis paper is a continuation of research on a geometry of a complete quadrilateral in the Euclidean plane. We present the well-known facts on the complete quadrilateral but all proved in the same way by using rectangular coordinates, symmetrically on all four sides of the quadrilateral with four parameters a, b, c, d. The properties related to the central circle, orthopolar circle, Hervey's circle, Kantor's point and Plücker's points are observed. During this study, some new results come up.Ovaj rad je nastavak proučavanja geometrije potpunog četverostrana u euklidskoj ravnini. Iznosimo neke poznate činjenice o potpunom četverostranu, ali ih ovdje dokazujemo jedinstvenom metodom koristeći pravokutne koordinate, simetrično s obzirom na četiri stranice četverostrana, odnosno četiri parametra a,b,c,d. Promatramo svojstva vezana za centralnu kružnicu, ortopolarnu kružnicu, Herveyevu kružnicu, Kantorovu točku i Plückerove točke. Tijekom ovog istraživanja dobili smo i neke nove rezultate
Provenijencija i dijageneza gornjomiocenskih pješčenjaka jugozapadnog dijela Panonskog bazenskog sustava u Hrvatskoj : doktorski rad
No full textThis study provides a thorough examination of the Upper Miocene sandstones in the North Croatian Basin, critical sandstone reservoirs for oil and gas in Croatia and the wider Pannonian Basin System in Central Europe. Despite their longstanding role in hydrocarbon production and potential for new energy initiatives like carbon capture and geothermal projects, their sedimentary provenance and diagenesis remained largely unexplored. The research focuses on the Upper Miocene sandstones from cores of exploration wells in the Sava and Drava depressions. Various methods, including petrographic, SEM-EDS, geochemical, heavy mineral, XRD, and Raman spectroscopic analyses, alongside petrophysical measurements, were employed to characterize the sediments. Results reveal a carbonaticlastic feldspatho-litho-quartzose (fLQ) composition, with carbonate, metamorphic, and plutonic rock fragments, among quartz and feldspar, primarily sourced from the Eastern Alps (ALCAPA tectonic mega-unit), with the predominant Austroalpine nappe. Heavy mineral assemblages are dominated by almandine-rich garnet, with apatite, epidote, tourmaline, rutile, zircon, staurolite, zoisite, and clinozoisite, indicating detrital supply from low to medium-grade metamorphic source rocks. Higher Ca and Mg concentrations than in the Upper Continental Crust (UCC) standard reflect abundant limestone and dolostone rock fragments and carbonate cements. Consistent grain sizes, modal compositions, and diagenetic alterations were observed across both depressions. Mechanical and chemical compaction, with cementation by carbonate minerals (particularly calcite and Fe-dolomite/ankerite), quartz, and clay minerals (including illite, chlorite, kaolinite, and mixed-layered species), significantly affect reservoir quality and hydrocarbon productivity. Primary intergranular porosity reduction with depth, coupled with secondary porosity, resulting from dissolution processes, and microporosity, influences overall reservoir quality. This research enhances understanding of source-to-sink model of the Late Miocene Lake Pannon drainage system and the evolution of the south-western Pannonian Basin System. Strikingly similar detrital signatures observed in both depressions suggest a shared origin within the lake’s depositional setting characterized by the same sediment-dispersal system, possibly linked to Palaeo-Sava and/or Palaeo-Drava rivers. The study distinguishes the Upper Miocene reservoirs from other sedimentary units within the basin, informing about regional geological dynamics and supporting future exploration projects, with implications for hydrocarbon exploration, energy transition, and environmental sustainability efforts.Istraživanje pruža sveobuhvatnu analizu gornjomiocenskih pješčenjaka iz Sjevernohrvatskog bazena, ključnih pješčenjačkih ležišta nafte i plina u Hrvatskoj te širem Panonskog bazenskog sustava unutar Srednje Europe. Unatoč njihovoj dugogodišnjoj ulozi u proizvodnji ugljikovodika i potencijalu za nove energetske inicijative, poput zbrinjavanja ugljikovog dioksida i geotermalnih projekata, njihova provenijencija sedimenata i dijageneza nedovoljno su istraženi. Istraživanje se usredotočuje na gornjomiocenske pješčenjake iz jezgara istražnih bušotina u Savskoj i Dravskoj depresiji. Različite metode, uključujući petrografsku, SEMEDS, geokemijsku, analizu teških minerala, XRD i Raman spektroskopsku analizu, uz petrofizikalna mjerenja, korištene su za karakterizaciju sedimenata. Rezultati otkrivaju karbonatno-klastični feldspatno-litično-kvarcni (fLQ) sastav s karbonatnim, metamorfnim i plutonskim fragmentima stijena koji, uz kvarc i feldspate, potječu iz područja Istočnih Alpa (tektonske mega-jedinice ALCAPA), uključujući dominantnu austroalpsku navlaku. Asocijacijom teških minerala dominiraju granati obogaćeni almandinskom fazom, uz apatit, epidot, turmalin, rutil, cirkon, staurolit, zoisit i klinozoisit, koji ukazuju na detritalni izvor iz metamorfnih stijena niskog do srednjeg stupnja metamorfizma. Povišene koncentracije Ca i Mg u odnosu na standard gornje kontinentalne kore (Upper Continental Crust, UCC) odražavaju obilje fragmenata vapnenaca i dolomita te karbonatne cemente. Uočene su postojane veličine zrna, modalni sastavi i dijagenetske promjene u obje depresije. Mehanička i kemijska kompakcija, uz cementaciju karbonatnim mineralima (posebno kalcitom i Fedolomitom/ ankeritom), kvarcom i mineralima glina (uključujući ilit, klorit, kaolinit i miješano-slojne vrste), značajno utječu na kvalitetu ležišta i ugljikovodičnu produktivnost. Redukcija primarne međuzrnske poroznosti s dubinom, zajedno sa sekundarnom poroznosti, koja proizlazi iz procesa otapanja, te mikroporoznosti, utječe na ukupnu kvalitetu ležišta. Istraživanje omogućuje poboljšano razumijevanja source-to-sink modela jezera Panon iz kasnog miocena i razvoj jugozapadnog dijela Panonskog bazenskog sustava. Izrazito slični detritalni signali uočeni u obje depresije sugeriraju zajedničko podrijetlo pješčenjaka unutar taložnog okoliša jezera, koji je karakteriziran istovjetnim sustavom donosa i disperzije sedimentnog materijala, vjerojatno povezanog s paleo-Savom i/ili paleo-Dravom. Istraživanje omogućuje razlikovanje gornjomiocenskih pješčenjačkih ležišta od drugih sedimentnih jedinica unutar bazena, pružajući podatke o regionalnoj geološkoj dinamici i podržavajući buduće istraživačke projekte, s implikacijama na istraživanje nafte i plina, energetsku tranziciju i nastojanja u vezi održivosti okoliša
Hydrogeochemical characteristics of waters in the wider area of the Tounjčica spring : master's thesis
No full textU okviru rada provedena je analiza hidrogeokemijskih značajki voda u širem području izvora Tounjčice. Uzorkovanje izvorskih i površinskih voda provedeno je na 16 lokacija u srpnju 2024. godine. Za kemijsku analizu vode korištene su metode ionske kromatografije i titracije, koje su omogućile precizno određivanje koncentracija glavnih iona, uključujući kalcij (Ca²⁺) i magnezij (Mg²⁺). Omjer magnezijskih i kalcijskih iona važan je indikator hidrogeokemijskih procesa u krškim sustavima te daje uvid u podrijetlo i kretanje podzemnih voda, kao i u geokemijske procese poput otapanja karbonatnih stijena. Također, provedene su detaljne hidrološke analize izdašnosti izvora i protoka površinskih voda, što pomaže boljem razumijevanju dinamike voda u ovom krškom području.As part of the study, an analysis of the hydrogeochemical characteristics of waters in the wider Tounjčica spring area was conducted. Sampling of spring and surface waters was carried out at 16 locations in July 2024. For the chemical analysis of the water, ion chromatography and titration methods were used, which enabled precise determination of the concentrations of major ions, including calcium (Ca²⁺) and magnesium (Mg²⁺). The ratio of magnesium to calcium ions is an important indicator of hydrogeochemical processes in karst systems and provides insight into the origin and movement of groundwater, as well as geochemical processes such as the dissolution of carbonate rocks. In addition, detailed hydrological analyses of spring discharge and surface water flow were conducted, which contribute to a better understanding of water dynamics in this karst area
Analiza tržIšta bioplina i biometana u odabranim državama : završni rad
No full textBioplin i biometan su obnovljivi izvori energije koji nastaju anaerobnom fermentacijom organskog materijala. U završnom radu ukratko je opisan proces proizvodnje bioplina i biometana, njihove karakteristike i potencijal. Analizirani su njihovi izvori i uporaba u Njemačkoj, Francuskoj i Mađarskoj te stanje njihovih transpotnih plinskih mreža i uvjeti za utiskivanje plina u te plinske mreže. Zatim je na osnovi trenutnih trendova analizirana budućnost tržišta bioplina i biometana u odabranim državama
Development of optimization criteria for enhanced oil recovery methods with simultaneous CO2 storage : doctoral dissertation
No full textU ovom istraživanju promatrana je proizvodnja nafte i skladištenje CO2 u više od 8000 simulacijskih slučajeva naftnih ležišta, nakon čega je izrađena ekonomska analiza za različite cijene CO2 i nafte. Simulacijski slučajevi naftnih ležišta uključuju različite kombinacije broja i rasporeda proizvodnih i utisnih bušotina, različite omjere i trajanja utiskivanja vode i plina te različite koncentracije polimera u vodi koja se utiskuje. S obzirom na to da je analizirano pet različitih naftnih polja, ujedno je predstavljena analiza utjecaja početnih ležišnih uvjeta (tlak, temperatura, dubina i debljina ležišta) i petrofizikalnih parametara. Dodatno je predstavljeno i analizirano 112 scenarija skladištenja CO2. Rezultati su pokazali kako dodavanje otopina polimera općenito negativno utječe na uskladištenje CO2, za što bi se moglo dati objašnjenje da voda zauzima prostor koji bi kod skladištenja mogao zauzeti CO2, a veća koncentracija polimera u vodi rezultira smanjenjem mobilnosti vode, tj. njenim sporijim prodorom do proizvodnih bušotina, što pak dodatno povećava zadržavanje utisnute vode u ležištu. U konceptu CCUS (engl. Carbon Capture, Utilisation and Storage), optimalni scenariji uključuju velike količine CO2 dovedene „izvan sustava“, tj. od nekog emitera. Uskladištivost, definirana kao omjer retencije i proizvedenog CO2, predstavlja dobar indikator potrošnje energije na uskladištenje, a time i dobar pokazatelj isplativosti uskladištenja uz istovremenu proizvodnju ugljikovodika. Kod „čistog skladištenja“ (BAU scenariji, engl. Business-As-Usual, nakon prestanka proizvodnje) taj parametar beskonačno je velik, dok mala uskladištivost, pored prihvatljive uskladištenosti može indicirati neisplativ projekt utiskivanja i CC(U)S skladištenja. EOR iscrpak (engl. Enhanced Oil Recovery) je dobar parametar za usporedbe u kontekstu CCUS-a. U slučaju malog iscrpka u trenutku kada se razmatralo utiskivanje, a jednakog potencijalnog dodatnog iscrpka, ne očekuje se razmatranje primjene CO2 EOR-a. Generalno se može zaključiti kako su pokazatelji visokog EOR iscrpka često upravo suprotni od pokazatelja retencije. Definiran je parametar učinkovitosti CO2 kao umnožak EOR iscrpka i uskladištivosti, a pokazuje koliko se povećavaju i iscrpak i skladištenje u odnosu na povećanje proizvodnje CO2. Vrijednost tog parametra općenito je veća na početku za manji broj proizvodnih bušotina i uočeno je da postoji moment u vremenu kad učinkovitost dosegne maksimum nakon kojeg kreće padati. Konačno, razmatrani su težinski koeficijenti za iscrpak nafte i uskladištenogCO2, koji su definirani kao udio NPV-a nafte (engl. Net Present Value) i udio NPV-a uskladištenog CO2 u ukupnom NPV-u projekta. Drugim riječima, za odabrane scenarije tržišnih cijena može se u vremenu odrediti udio prihoda koji dolazi od proizvodnje nafte, odnosno od skladištenja CO2. Analiza prikazana u ovom radu može poslužiti kao smjernica za multiparametarsku analizu i optimizaciju proizvodnje nafte CO2-EOR metodama i skladištenja CO2.Climate change is an increasingly important issue at all levels, with reducing greenhouse gas emissions being a key challenge. While renewable energy sources have the potential to reduce emissions, CO2 capture (utilisation) and storage (CCS and CCUS) technologies offer significant opportunities, particularly in the oil industry, where they can enhance oil recovery and reduce emissions. Tertiary oil recovery methods aim to extract the oil remaining after primary and secondary phases by increasing oil mobility through reducing viscosity and interfacial tension. Major methods include gas injection, chemical, and thermal methods, with thermal methods being the most relevant. Gas injection methods, especially CO2 injection, have gained popularity due to their effectiveness in enhancing oil recovery and storing CO2. The efficiency of oil displacement from reservoirs is determined by microscopic (displacement sweep efficiency, ED) and macroscopic (volumetric sweep efficiency, EV) displacement coefficients. ED measures the amount of oil displaced in contact with the displacing fluid, while EV indicates the extent of contact between the displacing fluid and the oil-bearing parts of the reservoir. Macroscopic displacement efficiency depends on reservoir heterogeneity, fluid mobility, and well placement, while microscopic displacement efficiency is influenced by capillary number and fluid mobility, represented by the mobility ratio (M) between displacing and displaced fluids. The selection criteria for CO2 injection include historical production analysis, response to secondary recovery, oil and reservoir rock properties, encompassing parameters such as oil density and viscosity, oil saturation, and reservoir depth and permeability. Suitable reservoirs for CO2-EOR (Enhanced Oil Recovery) projects include both carbonate and sandstone reservoirs, where the ability to achieve pressures above the minimum miscibility pressure (MMP) and the absence of geological barriers that would prevent CO2-oil contact are critical factors. Correlations can be useful for preliminary determination of MMP, but their accuracy varies depending on oil composition. Several correlations have been developed for estimation MMP, including works by Holm and Josendal, Yellig and Metcalfe, Cronquist, Lee, Alston, and others. However, due to the variability in oil composition and specific reservoirconditions, none of them is universally applicable. In chemical EOR methods polymers or surfactants are injected to improve the mobility ratio between oil and water and thus increase the efficiency of water-alternating-gas (WAG) injection. Althoug they are effective, their application is limited by high costs, environmental impact, sensitivity to reservoir water salinity, and chemical adsorption on reservoir rock. In recent years, the use of chemical methods in global EOR projects has increased, emphasising the importance of understanding their mechanisms of action. Pilot projects dominate field applications, with only a few examples of systematic polymer and surfactant injection. Conceptual models of oil reservoirs were developed using general reservoir data, petrophysical analyses, PVT (Pressure-Volume-Temperature) data, a database of simulation inputs and results, and processing and correlating resultant data. The data were obtained from official documentation and published studies of INA Plc. (a Croatian national oil company). The PVT data were entered into an input parameter database, and equations of state were adjusted for simulation using the PETEX PVTp program. The first step was to prepare the PVT input data, followed by the creation of numerical reservoir models to be matched with historical production data. Static input data included average values of reservoir parameters such as permeability, porosity, thickness, temperature, and pressure. Following model validation, predictive models were created using Python code to generate text input files for tNavigator. WAG process optimization, including parameters such as WAG ratio, slug duration, injection pattern, and well spacing, was conducted to determine the optimal oil recovery. Various WAG ratios and cycle durations were considered, resulting in 1152 simulation cases per reservoir, totalling 5752 predictive cases for five reservoirs with additional hypothetical 1152 cases per field for two fields where EOR is already implemented. Matching simulation data with historical results is crucial for the validation and calibration of oil reservoir models. The focus was placed on oil production volumes, as it is difficult to achieve complete alignment of produced and injected fluids with homogeneous conceptual models. The results were presented in relevant tables and figures. The matching focused on aligning oil production volumes at the end of the primary production phase (end of 2004) andat the end of 2019. Production was extended until 2024 under the same conditions, with predictive models developed accordingly. EOR has been conducted on the Ivanić Field since 2001, and on the Žutica field since 2015. Additional hypothetical historical cases without EOR implementation before 2025 were created, resulting in 1152 additional predictive cases per field. The results showed that the polymer concentration generally has a negative effect on the storage of CO2, which can be explained by the fact that water occupies the space that could have been occupied by CO2 during storage, and that a higher concentration of polymers in water reduces the mobility of water, which means that water breakthrough is slower, which in turn further increases the retention of the injected water in the reservoir. In the CCUS context, the optimal scenarios include large amounts of CO2 supplied "outside the system", i.e. from an emitter. The storability is defined as the ratio of CO2 retained to CO2 produced, and it is a good indicator of the energy required for storage, which in turn can be a good indicator of the profitability of storage with simultaneous production of hydrocarbons. In pure storage (BAU scenarios, Business-As-Usual after production) this parameter is infinitely large, while low storability may indicate an unprofitable project of CO2 injection and CCUS storage. EOR recovery is a good parameter for comparisons in the context of CCUS. If the recovery is low at the time injection is being considered and the potential additional recovery is equally high, it can be assumed that consideration of CO2-EOR is less likely. In general, it can be observed that indicators followed by high EOR recovery are often the exact opposite of retention indicators. The CO2 efficiency parameter is defined as the product of EOR recovery and storability, and shows how much both recovery and storage increase in relation to the increase in CO2 production. The value of this parameter is generally higher at the beginning for a lower number of production wells, and it was observed that there is a moment when the efficiency reaches a peak value, after which it starts to fall. Finally, the weight coefficients for oil recovery and stored CO2 were considered, and are defined as the share of the net present value (NPV) of oil produced and the share of NPV of stored CO2 in the overall NPV of the project. In other words, for selected price scenarios, the percentage of income from oil production and the percentage share of income from CO2 storage can be determined
Surface waves dispersion analysis for determination of soil properties : master's thesis
No full textThe goal of the MASW method is to estimate soil stiffness, where one of the parameters is the speed of S-waves (Vs). S-wave velocity is used as a parameter because it is closely related to the modulus of elasticity. In the field, surface waves (most often Rayleigh waves) are recorded, and seismograms are loaded for selected ignition points, on which the interval in which Rayleigh waves appear is selected, after which a dispersion image is obtained. By picking the maximum on the dispersion image, the dispersion curve is defined. The property of dispersion, as a characteristic property of Rayleigh waves, enables waves of lower frequency and longer wavelength to spread deeper into the medium than waves of higher frequency and shorter wavelength. By interpreting the dispersion curve, a onedimensional model of the change in S-wave velocities at depth is obtained by the inversion process. Using S-wave velocity and density it is possible to calculate the shear modulus (μ) by depth for the selected ignition points
Lithofacies characteristics of Miocene deposits in the vicinity of Voćin : master's thesis
No full textTerenskim istraživanjem detaljno je istraženo područje neposredne okolice Voćina, prilikom kojeg su snimljeni sedimentološki sljedovi i prikupljeni uzorci stijena u sklopu istraživanja na znanstvenom projektu financiranom od strane Hrvatske zaklade za znanost – GEODEP (UIP2019-04-3846). Snimljena su četiri sedimentološka slijeda miocenskih naslaga (VOC-A, VOC-C, VOC-D i VOC-E). Mikropetrografski je analizirano 47 preparata i pritom je određeno četiri litofacijesa – biokalkruditi, biokalkareniti, lapori i vapnenci. Unutar litofacijesa lapora prepoznato je pet različitih litotipova – homogeni lapor, laminirani lapor, siltozni lapor, pjeskoviti lapor i silicificirani lapor. Opisane su genetske karakteristike litofacijesa te se može zaključiti kako biokalkruditi i biokalkareniti nastaju trošenjem i erozijom postojećih, uglavnom vapnenačkih stijena, s manjim udjelom siliciklastične komponente. Novonastali klasti povremeno su doneseni gravitacijskim tokovima u dubljevodni okoliš. Tome svjedoče teksture kose i horizontalne laminacije u biokalkarenitu, kao i karakteristike detritnog toka u biokalkruditu. U dubljevodnom okolišu se u vrijeme izostanka gravitacijskih tokova iz suspenzije talože lapori u čijem sastavu se nalaze planktonski organizmi i maleni udio siltozne/pjeskovite komponente. Litofacijes vapnenaca obilježen je pojavama tankih mikritnih slojeva koji su nastali precipitacijom karbonatnih čestica u mirnom i dubljem marinskom okolišu uz izostanak kopnenog donosa materijala.Field research was carried out in the vicinity of Voćin. Sedimentological sections were recorded and rock samples were collected while conducting research for a project financed by Croatian Scientific Foundation GEODEP (UIP2019-04-3846). Four sedimentological sections (VOC-A, VOC-C, VOC-D and VOC-E) in miocene deposits were sampled. A total of 47 thin sections were obtained and micorpetrographically analyzed. Four lithofacies were determined - biocalcrudites, biocalcarenites, marls and limestones. Marl lithofacies is differentiated into five lithotypes – homogenous marl, laminated marl, silty marl, sandy marl and silicified marl. Genetical chararactersistics were disscussed and described, leading to the conclusion that biocalcrudites and biocalcarenites are formed due to weathering and erosion of dominantly carbonate rocks, with minor siliciclastic components. Newly formed clasts are episodically transported via gravity currents to deeper marine areas. Cross and horizontal lamination in biocalcarenites support this interpretation, as well as the debris flow characteristics of the biocalcrudite. During the periods of erosional standstill, marls were deposited in the deeper marine areas with minor content of silty/sandy grains and abundant plankton organisms. Limestone lithofacies is characterized by thin micrite beds formed by precipitation of carbonate particles in a calm and deeper environment with the absence of continental input
Water wells design at the Bregana well field : master's thesis
No full textPredmet istraživanja ovog diplomskog rada je projektiranje zamjenskih zdenaca vodocrpilišta Bregana koje zahvaća podzemnu vodu samoborsko-zaprešićkog vodonosnika. Vodonosnik je otvorenog tipa i međuzrnske poroznosti, izgrađen od kvartarnih aluvijalnih naslaga. Niske razine podzemne vode najznačajnije su za projektiranje vodocrpilišta jer ukazuju na količinu vode dostupnu tijekom cijele godine. Numeričkim modeliranjem tečenja podzemne vode simulirano je sniženje razina podzemne vode uzrokovano crpnom količinom triju zdenaca ukupnog iznosa 120 l/s. Prognozne razine podzemne vode nakon 365 dana simuliranog crpljenja nalaze se oko 1 m iznad kota gornjeg ruba filtra u zdencima.The subject of this thesis is the design of new water wells at the Bregana well field where groundwater is pumped from the Samobor-Zaprešić aquifer. The aquifer is unconfined with intergranular porosity and is composed of Quaternary alluvial deposits. Low groundwater levels are most significant for the well field design because they indicate the amount of water available throughout the year. Numerical groundwater flow modeling simulated the drawdown of groundwater levels caused by the pumping rate of three water wells with a total rate of 120 l/s. After 365 days of simulated pumping, the predicted groundwater levels are approximately 1 m above the elevations of the top of the well screen
Influence of shear strain on the deflection of girders
No full textNumerical calculations are a standard part of modern structural design. Engineers remain particularly interested in real problems where analytical and numerical solutions can be compared with experimental results. Such cases are typical examples of benchmarks because they are used to verify the assumptions introduced. This study shows in detail how shear stresses affect the deflection of a relatively short and high cantilever when the span-to-height ratio of the cross-section is less than five. Such models are frequently used in the design of cantilevers that support heavily loaded beams, for example in the cement industry (e.g., often as structural elements for a heat exchanger system) or for the assessment of short cantilever limit states that appear during excavation in rock sediments. The models are also suitable for designing the various details and joints in the industry of prefabricated elements. This work analyzes in depth the analytical solutions for the displacement field of the linear elastic plane stress theory with two displacement boundary conditions. Also, the solutions were compared with the beam, two-, and three-dimensional numerical models using SAP2000. The results highlight the fundamental principles and solutions behind plane stress and beam theories, with an insight into the advantages and limitations of such models