Optimizing well spacing in unconventional gas reservoirs is difficult due to complex heterogeneity, large variability and uncertainty in reservoir properties, and lack of data that increase the production uncertainty. Previous methods are either suboptimal because they do not consider subsurface uncertainty (e.g., statistical moving-window methods) or they are too time-consuming and expensive for many operators (e.g., integrated reservoir characterization and simulation studies). This research has focused on developing and extending a new technology for determining optimal well spacing in tight gas reservoirs that maximize profitability. To achieve the research objectives, an integrated multi-well reservoir and decision model that fully incorporates uncertainty was developed. The reservoir model is based on reservoir simulation technology coupled with geostatistical and Monte Carlo methods to predict production performance in unconventional gas reservoirs as a function of well spacing and different development scenarios. The variability in discounted cumulative production was used for direct integration of the reservoir model with a Bayesian decision model (developed by other members of the research team) that determines the optimal well spacing and hence the optimal development strategy. The integrated model includes two development stages with a varying Stage-1 time span. The integrated tools were applied to an illustrative example in Deep Basin (Gething D) tight gas sands in Alberta, Canada, to determine optimal development strategies. The results showed that a Stage-1 length of 1 year starting at 160-acre spacing with no further downspacing is the optimal development policy. It also showed that extending the duration of Stage 1 beyond one year does not represent an economic benefit. These results are specific to the Berland River (Gething) area and should not be generalized to other unconventional gas reservoirs. However, the proposed technology provides insight into both the value of information and the ability to incorporate learning in a dynamic development strategy. The new technology is expected to help operators determine the combination of primary and secondary development policies early in the reservoir life that profitably maximize production and minimize the number of uneconomical wells. I anticipate that this methodology will be applicable to other tight and shale gas reservoirs.

One of the issues with multilateral wells is determining the contribution of each lateral to the total production that is measured at the surface. Also, if water is detected at the surface or if the multilateral well performance declines, then it is difficult to identify which lateral or laterals are causing the production decline. One way to estimate the contribution from each lateral is to run production Logging Tools (PLT). Unfortunately, PLT jobs are expensive, time-consuming, labor-intensive and involve operational risks. An alternative way to measure the production from each lateral is to use Distributed Temperature Sensing (DTS) technology. Recent advances in DTS technology enable measuring the temperature profile in horizontal wells with high precision and resolution. The changes in the temperature profile are successfully used to calculate the production profile in horizontal wells. In this research, we develop a computer program that uses a multilateral well model to calculate the pressure and temperature profile in the motherbore. The results help understand the temperature and pressure behaviors in multilateral wells that are crucial in designing and optimizing DTS installations. Also, this model can be coupled with an inversion model that can use the measured temperature and pressure profile to calculate the production from each lateral. Our model shows that changing the permeability or the water cut produced from one lateral results in a clear signature in the motherbore temperature profile that can be measured with DTS technology. However, varying the length of one of the lateral did not seem to impact the temperature profile in the motherbore. For future work, this research recommends developing a numerical reservoir model that would enable studying the effect of lateral inference and reservoir heterogeneity. Also recommended is developing an inversion model that can be used to validate our model using field data.

nÃo hà / O presente trabalho tem por objetivo identificar equaÃÃes simplificadas que permitam determinar o comportamento de reservatÃrios a partir de um reduzido nÃmero de parÃmetros. SÃo identificados quatro parÃmetros: i) coeficiente de variaÃÃo dos volumes afluentes anuais ao reservatÃrio; ii) volume adimensional do reservatÃrio, razÃo entre a capacidade de armazenamento do reservatÃrio e o volume mÃdio afluente anual ao mesmo; iii) fator de evaporaÃÃo adimensional, funÃÃo do volume mÃdio afluente anual ao reservatÃrio, dos coeficientes de forma deste reservatÃrio e da evaporaÃÃo potencial lÃquida do espelho dâÃgua, em metros; e iv) garantia, sendo esta considerada mensal ou anual. A partir destes quatro parÃmetros, sÃo determinadas equaÃÃes que permitem prever, para um determinado reservatÃrio, os volumes adimensionais: i) evaporado; ii) vertido; e iii) regularizado. Para a determinaÃÃo destas equaÃÃes sÃo utilizados dados de reservatÃrios gerados aleatoriamente. Estes reservatÃrios foram simulados, determinando os volumes adimensionais evaporado, vertido e regularizado, variÃveis estas ditas dependentes, assim como determinados os valores dos quatro parÃmetros independentes. A partir destas variÃveis dependentes e independentes, sÃo determinadas as equaÃÃes simplificadas atravÃs da tÃcnica de regressÃo linear, determinando os limites de validade e os erros inerentes à aplicaÃÃo das mesmas. Em um segundo momento, as equaÃÃes determinadas no decorrer deste trabalho sÃo validadas atravÃs da anÃlise de setenta e cindo reservatÃrios localizados no Estado da ParaÃba. Destas equaÃÃes, à possÃvel identificar, tanto o comportamento de reservatÃrios, bem como o efeito individual de cada uma das variÃveis independentes no comportamento dos mesmos. As equaÃÃes desenvolvidas nesta Tese sÃo de fÃcil aplicaÃÃo, reduzido dispÃndio de tempo e apresentam, em certa medida, erros reduzidos. / The present research identifies simplified equations capable to determine the behavior of reservoirs. It considers four independent variables: i) coefficient of variation of annual inflow; ii) dimensionless reservoir capacity; iii) dimensionless evaporation factor, function of the average annual inflow, reservoir shape coefficients and potential net evaporation; and iv) probability of failure. The dependents variables are: i) dimensionless evaporation loss volume; ii) dimensionless spill loss volume; and iii) dimensionless release volume. Initially, were used data from reservoirs generated randomly. The reservoirs dependents and independents variables values were determined after its simulation. It was used linear regression to determine the relationship between the dependents and independents variables. Limits of validity and errors were also determined. The equations determined in this research were used in seventy-five reservoirs located in the state of ParaÃba, Brazil, in order to validate them. By using the equations determined in this research, it is possible to identify: i) the behavior of reservoirs; and ii) the individual effect of each independent variable in the reservoir dependents variables. The equations developed in this thesis are easy to apply, time saving and have acceptable errors.

The ever increasing energy demand brings about widespread interest to rapidly, profitably and efficiently develop unconventional resources, among which tight gas sands hold a significant portion. However, optimization of development strategies in tight gas fields is challenging, not only because of the wide range of depositional environments and large variability in reservoir properties, but also because the evaluation often has to deal with a multitude of wells, limited reservoir information, and time and budget constraints. Unfortunately, classical full-scale reservoir evaluation cannot be routinely employed by small- to medium-sized operators, given its timeconsuming and expensive nature. In addition, the full-scale evaluation is generally built on deterministic principles and produces a single realization of the reservoir, despite the significant uncertainty faced by operators. This work addresses the need for rapid and cost-efficient technologies to help operators determine optimal well spacing in highly uncertain and risky unconventional gas reservoirs. To achieve the research objectives, an integrated reservoir and decision modeling tool that fully incorporates uncertainty was developed. Monte Carlo simulation was used with a fast, approximate reservoir simulation model to match and predict production performance in unconventional gas reservoirs. Simulation results were then fit with decline curves to enable direct integration of the reservoir model into a Bayesian decision model. These integrated tools were applied to the tight gas assets of Unconventional Gas Resources Inc. in the Berland River area, Alberta, Canada.

Project Completion Report, OWRT Project No. A-049-ARIZ / Agreement No. 14-31-0001-4003 / Project Dates: July 1, 1973 - June 30, 1974. / Acknowledgement: The work upon which this report is based was supported by funds provided by the United States Department of the Interior, Office of Water Research and Technology, as authorized under the Water Resources Research Act of 1964. / A non-linear reservoir model is used to represent the rainfall-runoff relationships for thunderstorms on the urban watersheds of Tucson, Arizona. Two types of computer programs are developed: a calibration program to obtain a best -fit calculated hydrograph; and a verification program to generate storm hydrographs given the watershed characteristics and a hyetograph. Calibration reveals the relationship of the model parameters, namely, (f) the inflow coefficient, (a) the constant coefficient, and (TL) the time lag, to the total rainfall, drainage area, channel length, and infiltration capacity of the watershed. The average discrepancy between the predicted hydrograph and the actual hydrograph for Tucson urban watersheds is 20 -25 percent.

L’infiltration correspond à l’ensemble des écoulements contribuant à la recharge des réserves des systèmes karstiques ou aux variations des débits à leurs exutoires. L’objectif de cette thèse est la caractérisation de l’infiltration et son utilisation dans l’étude des transferts pour la compréhension du fonctionnement des systèmes karstiques.Deux sites sont utilisés pour analyser cette infiltration : celui de la colline de Lascaux en Dordogne et celui du Nord du Vaucluse en Provence composé de plusieurs sources karstiques. Ces sites, en milieu carbonaté, se différencient tant par leur structuration – système épikarstique et aquifère karstique perché, pour le premier, et systèmes épikarstique, fissuré ou karstiques à zone noyée, pour le second – que par les conditions climatiques rencontrées au niveau de leurs impluviums respectifs.L’étude hydrodynamique des systèmes épikarstiques par les modèles réservoirs ne convient actuellement pas : la fonction de production ne permet pas la génération d’une infiltration satisfaisante. L’utilisation d’un modèle réservoir, initialement basé sur les équations de Coutagne, a permis de souligner la nécessité d’ajouter deux modules de calcul. Le premier concerne l’estimation d’une évapotranspiration effective, issue d’une loi exponentielle, considérant la hauteur d’eau dans le réservoir sol. Le deuxième module insiste sur l’utilité d’une fonction de stockage de l’épikarst pour caractériser au mieux les transferts vers l’aval du système.L’étude hydrochimique s’appuie majoritairement sur les équilibres calco-carboniques de l’eau et donc sur les transferts de masses de carbone inorganique. Ils permettent d’accéder à différentes grandeurs telles que la pression partielle de dioxyde de carbone – équilibrante (Pco2_eq) ou à saturation (Pco2_sat) – et à l’indice de saturation vis-à-vis de la calcite (ISc). La mise en relation de ces deux paramètres au sein d’un graphique {–log(Pco2) : ISc} a permis de distinguer différents types d’eaux issus des différents compartiments du karst. Il en a résulté un schéma de transfert des différents types d’eaux passant à l’exutoire tenant compte de l’état d’ennoiement du système. L’évolution pluriannuelle de l’infiltration a aussi été mise en avant par la variation de sa composition chimique pouvant être en relation avec des facteurs climatiques.A l’issue de ce travail, il apparaît que la connaissance des processus liés à l’infiltration est fondamentale pour la compréhension des écoulements en milieux karstiques dans un objectif de quantification de la recharge et de protection de la ressource. / Infiltration corresponds to flows contributing to the system recharge and its discharge variations. This thesis aims at characterize infiltration and its utilization in transfer analyses to understand karst system behavior.Two sites are used to study this infiltration: this of the Lascaux hill in Dordogne and one in the North of the Vaucluse county composed of several karst springs. These locations are different in their structure as well as climatic conditions on their respective intake areas. The first site consists on an epikarst and a perched karst aquifer systems, since the second is composed of an epikarst, a fissured and a developed saturated zone systems.Nowadays, hydrodynamic study of an epikarst system using reservoir models is not satisfying: the production function is not able to generate a sufficient infiltration. In this study, a reservoir model initially based on Coutagne’s equations had been used. Results highlighted the necessity to add two new calculation functions. The first is related to an evapotranspiration estimation using an exponential law considering the amount of water in the soil reservoir. The second underlines the necessity of taking into account the storage function of the epikarst to characterize in a better way flows in karst systems.Hydrochemical study was carried on from calcium-bicarbonate equilibriums and then by mass transfers. They permit to describe several parameters as the carbon dioxide partial pressure at atmospheric equilibrium (Pco2_eq) or at saturation (Pco2_sat) and the saturation index with respect to calcite (SIc). These parameters can be expressed through the {–log(Pco2); SIc} graph to identify different water types. A transfer schema had been proposed, considering the saturation state of the system. Multi-year evolution of the infiltration had been underlined by variations of the chemical composition of infiltration water. This evolution can be linked to climatic conditions.Finally it appears that the knowledge of infiltration processes is essential to understand karst flows to quantify karst recharge and protect the resource.

Sub-seismic meter-scale interwell depositional facies heterogeneity and microporosity are critical components behind properties and fluid flow heterogeneities of many Middle eastern giants and supergiants carbonate reservoirs. The Hanifa reservoir is one of the most petroliferous Arabian carbonate strata that hosts the notoriously heterogenous stromatoporoid/coral facies. Paradoxically, the 3D geometry, architecture, and subsurface implication of these facies are poorly understood or completely ignored in most studies. The lower part of the Arab-D reservoir is dominated by microporosity. However, studies that investigate the influence of microcrystals that host microporosity to petrophysical properties and upscale it to reservoir simulation grid-block scale are modicum. This dissertation aims to bridge this paucity by performing an advanced three-dimensional outcrop analog investigation and multiscale microporosity studies of these formations. We document the 3D morphology and spatial distribution of the stromatoporoid/coral facies part of the Hanifa reservoir outcrop analog in Wadi Birk, Saudi Arabia, using 3D drone-based digital outcrop model, cores, near-surface geophysical measurements, and deep-learning methodology. We construct a high-fidelity outcrop analog reservoir model from these observations and utilize it for dynamic simulation during waterflood. Further, based on the Upper Jubaila Formation outcrop analog in Wadi Laban, Saudi Arabia, we investigate the influence of microcrystals that host microporosity on petrophysical properties. We upscale the relationships and utilize seismic-derived acoustic-impedance data to arrive at reservoir grid block-scale microporosity distribution. Our results provide a novel and valuable insight into the growth morphology of the stromatoporoid/coral buildups and their relationship with subsurface fluid flow previously unknown for the Hanifa reservoir. The results demonstrate that sweep efficiency is greatly influenced by the interaction between the buildup clusters with the background strata. Our results also provide a practical method to integrate key sub-grid scale micro and macro heterogeneities into reservoir grid block-scale property models.

Master of Science / Department of Geology / Matthew Totten / The Petersilie oil field in Ness County, Kansas produces out of the Mississippian System, a reservoir composed mainly of shallow water carbonates, at depths of around 4375 ft (1334 m). The lithology of the field ranges from limestone to dolomite, to interlaminated limestone-dolomite beds. Chert is commonly found throughout. Petersilie field lies to the west of the Central Kansas Uplift, and to the east of the Hugoton Embayment. The field saw much drilling activity in the 1960’s, when it reached a production peak of nearly 378,000 barrels of oil per year. Production declined swiftly after that until the late 1990’s, when waterflooding was successfully employed. In this study, a reservoir model was produced for the Mississippian as it occurs in Petersilie field using the Department of Energy’s EdBOAST reservoir modeling software, with the intent of providing a reference for future drilling activity in the Mississippian and determining reservoir characteristics that may have contributed to the effectiveness of waterflooding in this area. The reservoir model was checked by simulation with a companion reservoir simulator program, BOAST 98. Subsequent comparison of simulated and actual oil production curves demonstrates the reliability of well log and drill stem test data for the field and proves the reservoir model to be a good fit for the Mississippian in Petersilie. Production curve analysis of Petersilie indicates the field was an ideal candidate for waterflooding because it has a solution-gas drive mechanism. As the field approached depletion from primary recovery, oil saturations remained high. Petersilie also exhibits high porosity and good permeability. The BOAST software was found to be an effective and inexpensive means for understanding the Mississippian reservoir in central to south-central Kansas. It was determined that BOAST has potential for practical use by smaller independent oil companies targeting the Mississippian in Kansas.

Ziel der Dissertation ist die hydrogeologische Charakterisierung von Karstgrundwasserleitern in der semi-ariden Klimazone, welche oftmals durch Übernutzung und anthropogene Verschmutz-ung bedroht sind. Trotz oft eingeschränkter Datenlage und einem unzureichenden Systemver-ständnis müssen quantitative und qualitative Faktoren, wie z.B. Grundwasserneubildungsrate, Aquiferparameter, Strömungs- und Stofftransportdynamik, Verschmutzungsempfindlichkeit und anthropogene Einflüsse quantifiziert werden. Jedoch können diese Gebiete auch günstige Eigenschaften für eine Charakterisierung, wie eine zeitlich eng begrenzte Impulsfunktion der Grundwasserneubildung durch intensive, kurze Niederschlagsereignisse sowie lange ungestörte Rezessionsperioden, aufweisen. Dies gilt für das in der Levante gelegene Untersuchungsgebiet. Die zeitliche und räumliche hydrologische Variabilität wurde durch ein ausgedehntes Messnetz hochaufgelöst erfasst. Zur Auswertung dieser Daten wurden konzeptionell korrekte, jedoch möglichst einfach anwendbare quantitative Verfahren und Modelle entwickelt und angewandt, was die Übertragbarkeit der Methoden auf weitere Trockengebiete ermöglicht. Durch eine Zusammenstellung und Auswertung hydrochemischer Langzeitdaten konnte die natürliche Hintergrundkonzentration von Chlorid im Grundwasser für 33 Quelleinzugsgebiete ermittelt werden. Darauf aufbauend war es möglich, durch eine Chloridmassenbilanz sowohl den langjährige mittlere Anteil der Grundwasserneubildung am Niederschlag (25–50%) zu bestimmen, als auch den Abwasseranteil im Quellwasser anhand rezenter Proben zu quantifizieren (0–20%). Anhand eines Speicher-Durchflussmodelles konnten sowohl Aquiferparameter im Einzugs-gebietsmaßstab als auch eine Tageszeitreihe der Grundwasserneubildung exemplarisch für die Auja-Quelle, die größte Süßwasserquelle im Unteren Jordantal, erfasst werden. Diese sowie weitere Quellen der Region sind durch ein „röhrengedrosseltes“ Abflussverhalten, d.h. eine Begrenzung der Quellschüttung, gekennzeichnet. Der hydrogeologisch komplexe Aquifer und das nichtlineare Systemverhalten bei Erreichen der maximalen Schüttung erfordern ein besonders angepasstes Modell, welches auch einen ausgeprägten hydraulischen Austausch zwischen den Karströhren und der geklüfteten Gesteinsmatrix berücksichtigen muss. Eine Reihe von Parametern konnte aus einer Rezessions- und Ereignis-Analyse der Abflussganglinie ermittelt werden. Das Speicher-Durchflussmodell benötigt lediglich sechs Kalibrierparameter und erlaubt eine sehr gute Simulation der Abflussganglinie. Die effektive Aquifer-Porosität wurde durch Kalibration ermittelt (ca. 2.4%). Über den simulierten 45-Jahres-Zeitraum führten die fünf niederschlagsreichsten Jahre zu einem Drittel der gesamten Grundwasserneubildung. Die zeitlich hoch aufgelösten Quellmessungen ermöglichten eine Quantifizierung der hydraulischen Reaktionszeiten sowie der mittleren Verweilzeiten, der Durchbruchsdauer und der relativen Anteile der schnellen Fließkomponente nach Niederschlagsereignissen. Diese Daten dienen sowohl einer Abschätzung der schnellen Neubildungsprozesse (vor allem Fokussierung im Epikarst und schnelles präferentielles Fließen durch die Vadose Zone) als auch einer Beurteilung der Verschmutzungsempfindlichkeit der Karstquellen. Weiterhin konnte eine Zugehörigkeit der beiden, 3500 m voneinander entfernten, artesischen Jericho-Quellen Sultan und Duyuk zu einem gemeinsamen Röhren- und damit Karstsystem nachgewiesen werden.

[pt] A extração e visualização de isosuperfícies de campos escalares são importantes para inspeções e análises de modelos em diversas áreas. Uma isosuperfície é representada por uma malha de triângulos que aproxima um conjunto de nível do volume de dados. O foco deste trabalho é a extração e visualização de isosuperfícies de modelos de reservatório de petróleo, representados por malhas de hexaedros levemente côncavos. Para uma melhor representação das isosuperfícies, optou-se pela substituição de triângulos planares por superfícies curvas. Para assegurar a extração de superfícies contínuas e suaves, este trabalho propõe o uso de envelopes para determinação das normais. A técnica proposta é implementada em GPU com uso de subdivisão adaptativa das superfícies. / [en] The extraction and visualization of isosurfaces of scalar fields are important for inspections and analysis of models in several areas. An isosurface is represented by a mesh of triangles that approximates a level set of a data volume. The main focus of this work is the extraction and visualization of isosurfaces of black oil reservoir models, represented by hexahedral meshes with slightly concave cells. For a better representation of the isosurfaces, we have opted to replace planar triangles for curved patches. To ensure the extraction of continuous and smooth surfaces, this work proposes the use of envelopes to determine normals. The proposed technique is implemented in GPU with the usage of adaptive subdivision of patches.