Paleokarst reservoirs consist of complex cave networks, which are formed by various mechanisms and associated collapsed cave facies. Traditionally, cave structures are defined using variogram-based methods in flow models and this description does not precisely represent the reservoir geology. Algorithms based on multiple-point statistics (MPS) are widely used in modeling complex geologic structures. Statistics required for these algorithms are inferred from gridded training images. However, structures like modern cave networks are represented by point data sets. Thus, it is not practical to apply rigid and gridded templates and training images for the simulation of such features. Therefore, a quantitative algorithm to characterize and model paleokarst reservoirs based on physical and geological attributes is needed. In this study, a unique non-gridded MPS analysis and pattern simulation algorithms are developed to infer statistics from modern cave networks and simulate distribution of cave structures in paleokarst reservoirs. Non-gridded MPS technique is practical by eliminating use of grids and gridding procedure, which is challenging to apply on cave network due to its complex structure. Statistics are calculated using commonly available cave networks, which are only represented by central line coordinates sampled along the accessible cave passages. Once the statistics are calibrated, a cave network is simulated by using a pattern simulation algorithm in which the simulation is conditioned to sparse data in the form of locations with cave facies or coordinates of cave structures. To get an accurate model for the spatial extent of the cave facies, an algorithm is also developed to simulate cave zone thickness while simulating the network. The proposed techniques are first implemented to represent connectivity statistics for synthetic data sets, which are used as point-set training images and are analogous to the data typically available for a cave network. Once the applicability of the algorithms is verified, non-gridded MPS analysis and pattern simulation are conducted for the Wind Cave located in South Dakota. The developed algorithms successfully characterize and model cave networks that can only be described by point sets. Subsequently, a cave network system is simulated for the Yates Field in West Texas which is a paleokarst reservoir. Well locations with cave facies and identified cave zone thickness values are used for conditioning the pattern simulation that utilizes the MP-histograms calibrated for Wind Cave. Then, the simulated cave network is implemented into flow simulation models to understand the effects of cave structures on fluid flow. Calibration of flow model against the primary production data is attempted to demonstrate that the pattern simulation algorithm yields detailed description of spatial distribution of cave facies. Moreover, impact of accurately representing network connectivity on flow responses is explored by a water injection case. Fluid flow responses are compared for models with cave networks that are constructed by non-gridded MPS and a traditional modeling workflow using sequential indicator simulation. Applications on the Yates Field show that the cave network and corresponding cave facies are successfully modeled by using the non-gridded MPS. Detailed description of cave facies in the reservoir yields accurate flow simulation results and better future predictions. / text

One of the most challenging issues in reservoir modeling is to integrate information coming from different sources at disparate scales and precision. The primary data are borehole measurements, but in most cases, these are too sparse to construct accurate reservoir models. Therefore, in most cases, the information from borehole measurements has to be supplemented with other secondary data. The secondary data for reservoir modeling could be static data such as seismic data or dynamic data such as production history, well test data or time-lapse seismic data. Several algorithms for integrating different types of data have been developed. A novel method for data integration based on the permanence of ratio hypothesis was proposed by Journel in 2002. The premise of the permanence of ratio hypothesis is to assess the information from each data source separately and then merge the information accounting for the redundancy between the information sources. The redundancy between the information from different sources is accounted for using parameters (tau or nu parameters, Krishnan, 2004). The primary goal of this thesis is to derive a practical expression for the tau parameters and demonstrate the procedure for calibrating these parameters using the available data. This thesis presents two new algorithms for data integration in reservoir modeling. The algorithms proposed in this thesis overcome some of the limitations of the current methods for data integration. We present an extension to the direct sampling based multiple-point statistics method. We present a methodology for integrating secondary soft data in that framwork. The algorithm is based on direct pattern search through an ensemble of realizations. We show that the proposed methodology is sutiable for modeling complex channelized reservoirs and reduces the uncertainty associated with production performance due to integration of secondary data. We subsequently present the permanence of ratio hypothesis for data integration in great detail. We present analytical equations for calculating the redundancy factor for discrete or continuous variable modeling. Then, we show how this factor can be infered using available data for different scenarios. We implement the method to model a carbonate reservoir in the Gulf of Mexico. We show that the method has a better performance than when primary hard and secondary soft data are used within the traditional geostatistical framework. / text

Well testing has long been used to determine the dynamic characteristics of a reservoir. However due to the increase in interest in exploring deep offshore reservoirs and the expense associated with performing well tests of sufficient duration, alternative methods for retrieving reservoir specific information from tests of limited duration are necessary. This thesis presents analysis of derivative plots from well tests in different locations along a heterogeneous channelized environment and the information that can be derived the shape of these plots. The viability of calibrating a multiple point proxy that captures the reservoir flow connectivity information contained in well test data is explored. Such a proxy can provide useful insight into the nature of reservoir heterogeneity in the vicinity of the well. The behavior of the log-log derivative plot gives invaluable information about the nature of the reservoir surrounding the penetrating wells. Based on the change in slope of the derivative plot one can tell if a flow conduit or a low permeability zone is close to the well. Proximity to these features is also indicated in the curvature of the derivative plot with the test plot showing increasing symmetry as flow boundaries are approached. This was found to be true in both systematic simulations as well as in real build up test data. The calibration of the multiple point permeability proxy also provides information about the connectivity of the reservoir. Single point statistics provide the best estimate for wells either inside a channel or very close to the channel boundary. This is because of the relative homogeneity of permeability values within the spatial template used for averaging. The further the well gets from the channel fewer high permeability blocks will be picked up by the template and thus multiple point models provide the best estimate for effective permeability, Keff. Three point models were found to be the most accurate when the template exhibited complex permeability transition from the mudstone to the channel facies. / text

A distribuição espacial e o volume dos domínios litológicos são freqüentemente as maiores fontes de incerteza na modelagem geológica. Geralmente, a interpretação destas características é baseada em critérios subjetivos de observações, sem levar em consideração a incerteza inerente a este processo. Existem métodos de simulação geoestatísticos capazes de quantificar esta incerteza tipológica das unidades geológicas. A maioria desses métodos utiliza como medida de continuidade geológica os modelos de covariância. Entretanto, estas ferramentas de estatística de dois-pontos, raramente, conseguem capturar os padrões de geometrias complexas. Uma alternativa para esta limitação é utilizar métodos de estatística de múltiplos pontos para reproduzir os padrões espaciais de heterogeneidade que são informados por uma imagem de treinamento. Nessa dissertação, será aplicada a geoestatística de múltiplos pontos (SNESIM) para simular os litotipos de um depósito de minério de ferro. A imagem de treinamento foi baseada em seções interpretadas. Os furos de sondagem são utilizados como amostras primárias. As informações geológicas são acessadas por mapas de probabilidade utilizados como informações secundárias. A metodologia é testada na simulação de um depósito de ferro brasileiro com três diferentes litotipos. Os resultados das simulações são comparados contra um modelo de referência e novos furos de sondagens. As geometrias e distribuição espacial das tipologias foram reproduzidas de forma consistente. A incerteza das distribuições e dos volumes dos domínios tipológicos foi quantificada. O algoritmo de múltiplos pontos e a metodologia proposta mostraram grande potencial de aplicação na simulação de depósitos minerais. / The spatial distribution and volumes of lithological domains are often the biggest sources of uncertainty in geological modeling. Usually, the interpretation of these characteristics is based on subjective criteria of observations, without taking into account the uncertainty inherent in this process. There geostatistical simulation methods capable of quantifying this uncertainty typological geological units. Most of these methods uses as a measure of continuity in geological models covariance. However, these two-point statistical is rarely sufficient to capture the patterns of complex geometries. An alternative to this limitation is to use statistical methods of multiple points to reproduce the spatial patterns of heterogeneity that are informed by a training image. In this dissertation, will be applied to multi-point geostatistics (SNESIM) to simulate lithotypes a deposit of iron ore. The training image was based on sections interpreted. The drillholes are used as primary samples. Geologic information is accessed by probability maps used as secondary information. The methodology is tested in the simulation of a deposit of Brazilian iron with three different rock types. The simulation results are compared against a reference model and new drillholes. The geometries and spatial typologies were reproduced consistently. The uncertainty distributions and volumes of typological domains were quantified. The algorithm of multiple points and the proposed methodology showed great potential for application in the simulation of mineral deposits.

A distribuição espacial e o volume dos domínios litológicos são freqüentemente as maiores fontes de incerteza na modelagem geológica. Geralmente, a interpretação destas características é baseada em critérios subjetivos de observações, sem levar em consideração a incerteza inerente a este processo. Existem métodos de simulação geoestatísticos capazes de quantificar esta incerteza tipológica das unidades geológicas. A maioria desses métodos utiliza como medida de continuidade geológica os modelos de covariância. Entretanto, estas ferramentas de estatística de dois-pontos, raramente, conseguem capturar os padrões de geometrias complexas. Uma alternativa para esta limitação é utilizar métodos de estatística de múltiplos pontos para reproduzir os padrões espaciais de heterogeneidade que são informados por uma imagem de treinamento. Nessa dissertação, será aplicada a geoestatística de múltiplos pontos (SNESIM) para simular os litotipos de um depósito de minério de ferro. A imagem de treinamento foi baseada em seções interpretadas. Os furos de sondagem são utilizados como amostras primárias. As informações geológicas são acessadas por mapas de probabilidade utilizados como informações secundárias. A metodologia é testada na simulação de um depósito de ferro brasileiro com três diferentes litotipos. Os resultados das simulações são comparados contra um modelo de referência e novos furos de sondagens. As geometrias e distribuição espacial das tipologias foram reproduzidas de forma consistente. A incerteza das distribuições e dos volumes dos domínios tipológicos foi quantificada. O algoritmo de múltiplos pontos e a metodologia proposta mostraram grande potencial de aplicação na simulação de depósitos minerais. / The spatial distribution and volumes of lithological domains are often the biggest sources of uncertainty in geological modeling. Usually, the interpretation of these characteristics is based on subjective criteria of observations, without taking into account the uncertainty inherent in this process. There geostatistical simulation methods capable of quantifying this uncertainty typological geological units. Most of these methods uses as a measure of continuity in geological models covariance. However, these two-point statistical is rarely sufficient to capture the patterns of complex geometries. An alternative to this limitation is to use statistical methods of multiple points to reproduce the spatial patterns of heterogeneity that are informed by a training image. In this dissertation, will be applied to multi-point geostatistics (SNESIM) to simulate lithotypes a deposit of iron ore. The training image was based on sections interpreted. The drillholes are used as primary samples. Geologic information is accessed by probability maps used as secondary information. The methodology is tested in the simulation of a deposit of Brazilian iron with three different rock types. The simulation results are compared against a reference model and new drillholes. The geometries and spatial typologies were reproduced consistently. The uncertainty distributions and volumes of typological domains were quantified. The algorithm of multiple points and the proposed methodology showed great potential for application in the simulation of mineral deposits.

A distribuição espacial e o volume dos domínios litológicos são freqüentemente as maiores fontes de incerteza na modelagem geológica. Geralmente, a interpretação destas características é baseada em critérios subjetivos de observações, sem levar em consideração a incerteza inerente a este processo. Existem métodos de simulação geoestatísticos capazes de quantificar esta incerteza tipológica das unidades geológicas. A maioria desses métodos utiliza como medida de continuidade geológica os modelos de covariância. Entretanto, estas ferramentas de estatística de dois-pontos, raramente, conseguem capturar os padrões de geometrias complexas. Uma alternativa para esta limitação é utilizar métodos de estatística de múltiplos pontos para reproduzir os padrões espaciais de heterogeneidade que são informados por uma imagem de treinamento. Nessa dissertação, será aplicada a geoestatística de múltiplos pontos (SNESIM) para simular os litotipos de um depósito de minério de ferro. A imagem de treinamento foi baseada em seções interpretadas. Os furos de sondagem são utilizados como amostras primárias. As informações geológicas são acessadas por mapas de probabilidade utilizados como informações secundárias. A metodologia é testada na simulação de um depósito de ferro brasileiro com três diferentes litotipos. Os resultados das simulações são comparados contra um modelo de referência e novos furos de sondagens. As geometrias e distribuição espacial das tipologias foram reproduzidas de forma consistente. A incerteza das distribuições e dos volumes dos domínios tipológicos foi quantificada. O algoritmo de múltiplos pontos e a metodologia proposta mostraram grande potencial de aplicação na simulação de depósitos minerais. / The spatial distribution and volumes of lithological domains are often the biggest sources of uncertainty in geological modeling. Usually, the interpretation of these characteristics is based on subjective criteria of observations, without taking into account the uncertainty inherent in this process. There geostatistical simulation methods capable of quantifying this uncertainty typological geological units. Most of these methods uses as a measure of continuity in geological models covariance. However, these two-point statistical is rarely sufficient to capture the patterns of complex geometries. An alternative to this limitation is to use statistical methods of multiple points to reproduce the spatial patterns of heterogeneity that are informed by a training image. In this dissertation, will be applied to multi-point geostatistics (SNESIM) to simulate lithotypes a deposit of iron ore. The training image was based on sections interpreted. The drillholes are used as primary samples. Geologic information is accessed by probability maps used as secondary information. The methodology is tested in the simulation of a deposit of Brazilian iron with three different rock types. The simulation results are compared against a reference model and new drillholes. The geometries and spatial typologies were reproduced consistently. The uncertainty distributions and volumes of typological domains were quantified. The algorithm of multiple points and the proposed methodology showed great potential for application in the simulation of mineral deposits.

La vallée de la Komadougou Yobé constitue un site privilégié de recharge de l'aquifère quaternaire du bassin du lac Tchad. Depuis les années 1980, le développement des cultures de rente (p. ex. poivron) a conduit à un doublement des surfaces irriguées (1995-2005) dans sa partie aval. Afin de quantifier la recharge supplémentaire induite, une modélisation des flux hydriques verticaux dans la zone non-saturée (0-8 m) a été engagée. La première étape, objet de ce travail de thèse, consiste à décrire l'organisation spatiale et les propriétés hydrodynamiques des corps sédimentaires constitutifs de l'alluvium.Des forages à travers les formations superficielles mettent en évidence des alternances sable-sable argileux dans la totalité de la zone non-saturée, conséquence des migrations du lit mineur de la Komadougou Yobé. Le calcul de la corrélation entre les forages indique une forte analogie avec les hétérogénéités identifiées en surface à partir de données de télédétection (Landsat 7 binarisée). Ces données sont donc utilisées pour l'apprentissage de statistiques multipoints représentatives des hétérogénéités et un modèle géologique 3D de l'alluvium est généré via l'algorithme snesim.Des suivis neutroniques de l'humidité le long de plusieurs profils caractéristiques des différentes unités sédimentaires associées à ce modèle sont réalisés pour des conditions de flux contrôlées en surface. A partir de simulations numériques 1D, des jeux de paramètres hydrodynamiques permettant de reproduire les humidités mesurées sont déterminés par une approche de type Monte-Carlo. Des densités de probabilité intégrant l'incertitude sur les mesures sont obtenues pour les paramètres de Mualem - van Genuchten décrivant les courbes de rétention et de conductivité hydraulique des sédiments.Une procédure 1D-distribuée est utilisée pour simuler les écoulements non-saturés verticaux au sein de plusieurs réalisations du modèle géologique et pour différents jeux de paramètres hydrodynamiques probables. La recharge diffuse calculée se montre particulièrement sensible au paramètre de pression d'entrée d'air attribué aux dépôts superficiels, siège des principales interactions sol-plante-atmosphère, ainsi qu'aux contrastes verticaux de conductivité hydraulique. / The downstream part of the Komadugu Yobe River is an important recharge area for the Lake Chad Quaternary aquifer. Since the 1980s, cash crop development (e.g. sweet pepper) has led to the doubling (1995-2005) of irrigated surfaces in the vicinity of the river. A modeling approach of vertical water fluxes through the vadose zone (0-8 m) was designed to quantify the related increase in groundwater recharge. The first step, which is the main topic of this PhD thesis, consisted in describing both spatial arrangement and hydrodynamic properties of the sedimentary bodies that make up the alluvium.Boreholes in surficial deposits highlighted sandy to clayey alternations within the whole unsaturated zone; this was interpreted as the result of frequent migrations of the River channel. Spatial correlation between bore logs showed strong similarities with heterogeneities depicted on ground by means of remote sensing data (binarized Landsat 7 image). This data were therefore used to train multiple-point statistics representative of heterogeneities, and a 3D geological model was generated through the snesim algorithm.For each representative sedimentary unit, soil moisture under controlled hydraulic surface conditions was monitored by vertical neutron probe soundings. Using 1D numerical simulations, different data sets of hydrodynamic properties that reproduced moisture measurements were determined by a Monte-Carlo approach. Probability density functions including measurement uncertainties were deduced for the Mualem - van Genuchten parameters which describe both retention and hydraulic conductivity curves.A 1D-distributed procedure was applied for modeling vertical flows in the unsaturated zone within several geological model realizations with different probable sets of hydrodynamics parameters. The simulated diffuse recharge was shown to be particularly sensitive to two main parameters: air-entry pressure linked to superficial deposits, where soil-plant-atmosphere interactions do occur, and vertical hydraulic conductivity contrasts within the alluvium.