Bayesian model selection in hydrogeophysics and hydrogeology

Les eaux souterraines sont une ressource fondamentale. Avec la croissance démographique, le changement d’utilisation du sol, les activités économiques, l’urbanisation et le changement climatique, une gestion sûre et durable des ressources en eau souterraine devient de plus en plus cruciale. Cela doit reposer sur une caractérisation précise de l’hétérogénéité des propriétés hydrogéologiques du sous-sol, tâche qui représente toutefois un défi. Première- ment, le sous-sol est caché et la collecte locale de données renseignant sur les propriétés hydrogéologiques est difficile ou trop coûteuse. Deuxièmement, les méthodes géophysiques peuvent permettre une acquisition efficace de telles mesures, elles nécessitent néanmoins la définition des relations pétrophysiques qui sont souvent incertaines et mal connues. Troisiè- mement, la structure géologique des systèmes hébergeant les eaux souterraines est complexe et la définition d’un modèle conceptuel correspondant n’est pas unique. Cela conduit à l’une des sources d’incertitude majeure (et souvent ignorée) dans les études de modélisation, appelée incertitude conceptuelle. La sélection bayésienne de modèles, reposant sur le calcul de l’évidence et sur les facteurs de Bayes, fournit une approche quantitative permettant de comparer et de classer des modèles conceptuels alternatifs et, par conséquent, de prendre en compte l’incertitude conceptuelle. Dans cette thèse, nous étudierons l’utilisation de la sélection bayésienne de modèles en hydrogéophysique et en hydrogéologie en répondant aux questions de recherche suivantes : (1) Les données géophysiques sont-elles appropriées pour guider la sélection de modèles en hydrogéologie? (2) L’incertitude pétrophysique et sa struc- ture spatiale peuvent-elles être déduites dans des études hydrogéophysiques et quel impact ont-elles sur l’inversion bayésienne et la sélection de modèles? (3) Comment pouvons-nous réaliser la sélection de modèles lorsque nous ciblons des modèles conceptuels aux structures géologiques réalistes représentés par des images d’entraînement? Ces objectifs seront traités en utilisant une approche bayésienne complète basée sur les algorithmes de Monte Carlo par chaînes de Markov. Les objectifs de la recherche seront ensuite explorés via des études de cas synthétiques et réels, dans le but de caractériser spatialement les champs de porosité ou de conductivité hydraulique dans les aquifères. Dans notre première étude de sélection bayésienne de modèles en hydrogéophysique, nous concluons que les méthodes géophy- siques peuvent être utiles pour choisir la représentation hydrogéologique du sous-sol qui est la plus étayée par les données disponibles, parmi un ensemble de modèles conceptuels concurrents. Nous proposons une méthode pour prendre en compte et déduire l’incertitude pétrophysique et sa corrélation spatiale. Nous constatons que cette approche conduit à une diminution du biais et à une quantification plus réaliste de l’incertitude et du classement des modèles conceptuels. De plus, nous proposons et appliquons avec succès une nouvelle mé- thodologie pour effectuer la sélection bayésienne de modèles parmi des modèles conceptuels géologiquement réalistes. -- Groundwater is a fundamental source of drinking water. With population growth, land use changes, economic activities, urbanisation and climate change, a safe and sustainable man- agement of groundwater resources is becoming more and more critical. This needs to rely on an accurate characterisation of the hydrogeological heterogeneity in the subsurface, which is a challenging task. First, the subsurface is hidden from sight and collecting local hydro- geological measurements is difficult or too expensive. Second, geophysical methods can effectively support such measurements but, at the same time, they require the definition of petrophysical relationships that are often uncertain and poorly known. Third, the spatial geo- logical structure of groundwater systems is complex and the definition of the corresponding conceptual model is non-unique. This leads to one of the main (and often ignored) sources of uncertainty in modelling studies, namely conceptual uncertainty. Bayesian model selection relying on evidence computation and Bayes factors provides a quantitative approach for com- paring and ranking alternative conceptual models and, therefore, accounting for conceptual uncertainty. In this thesis, we will investigate the use of Bayesian model selection in hydrogeo- physics and hydrogeology by answering the following research questions: (1) Are geophysical data suitable for guiding model selection in hydrogeology? (2) Can petrophysical uncertainty and its spatial structure be inferred in hydrogeophysical studies and how do they impact Bayesian inversion and model selection? (3) How can we achieve model selection when targeting geologically-realistic hydrogeological conceptual models represented by training images? These objectives will be addressed using a full Bayesian approach based on Markov chain Monte Carlo algorithms. The research goals will be then explored in light of synthetic and field-based case studies with the purpose of characterising spatially-distributed porosity or hydraulic conductivity fields in aquifers. From the first comparative study of Bayesian model selection in hydrogeophysics ever, we conclude that geophysical methods can be valuable in providing guidance about which hydrogeological representation of the subsurface is the most supported by the available data among a set of competing conceptual models. We then propose a method to account for and infer the spatially-correlated uncertainty of petrophysical relationships. We find that this approach leads to less bias, more realistic uncertainty quantification and less overconfident model selection. Moreover, we propose and successfully apply a new methodology for performing Bayesian model selection among geologically-realistic conceptual models represented by training images

4. International reservoir characterization technical conference

This volume contains the Proceedings of the Fourth International Reservoir Characterization Technical Conference held March 2-4, 1997 in Houston, Texas. The theme for the conference was Advances in Reservoir Characterization for Effective Reservoir Management. On March 2, 1997, the DOE Class Workshop kicked off with tutorials by Dr. Steve Begg (BP Exploration) and Dr. Ganesh Thakur (Chevron). Tutorial presentations are not included in these Proceedings but may be available from the authors. The conference consisted of the following topics: data acquisition; reservoir modeling; scaling reservoir properties; and managing uncertainty. Selected papers have been processed separately for inclusion in the Energy Science and Technology database

Improving the convergence rate of seismic history matching with a proxy derived method to aid stochastic sampling

History matching is a very important activity during the continued development and management of petroleum reservoirs. Time-lapse (4D) seismic data provide information on the dynamics of fluids in reservoirs, relating variations of seismic signal to saturation and pressure changes. This information can be integrated with history matching to improve convergence towards a simulation model that predicts available data. The main aim of this thesis is to develop a method to speed up the convergence rate of assisted seismic history matching using proxy derived gradient method. Stochastic inversion algorithms often rely on simple assumptions for selecting new models by random processes. In this work, we improve the way that such approaches learn about the system they are searching and thus operate more efficiently. To this end, a new method has been developed called NA with Proxy derived Gradients (NAPG). To improve convergence, we use a proxy model to understand how parameters control the misfit and then use a global stochastic method with these sensitivities to optimise the search of the parameter space. This leads to an improved set of final reservoir models. These in turn can be used more effectively in reservoir management decisions. To validate the proposed approach, we applied the new approach on a number of analytical functions and synthetic cases. In addition, we demonstrate the proposed method by applying it to the UKCS Schiehallion field. The results show that the new method speeds up the rate of convergence by a factor of two to three generally. The performance of NAPG is much improved by updating the regression equation coefficients instead of keeping it fixed. In addition, we found that the initial number of models to start NAPG or NA could be reduced by using Experimental Design instead of using random initialization. Ultimately, with all of these approaches combined, the number of models required to find a good match reduced by an order of magnitude. We have investigated the criteria for stopping the SHM loop, particularly the use of a proxy model to help. More research is needed to complete this work but the approach is promising. Quantifying parameter uncertainty using NA and NAPG was studied using the NA-Bayes approach (NAB). We found that NAB is very sensitive to misfit magnitude but otherwise NA and NAPG produce similar uncertainty measures

High resolution seismic stratigraphic analysis: An integrated approach to the subsurface geology of the SE Persian Gulf

Papers included in this dissertation: Paper 1: Farzadi, P. 2006a. The development of Middle Cretaceous carbonate platforms, Persian Gulf, Iran: Constraints from seismic stratigraphy, well and biostratigraphy. Petroleum Geoscience, 12, 59-68. Paper 2: Farzadi, P. 2006b. Seismic facies analysis based on 3D multi-attribute volume classification, Dariyan Formation, SE Persian Gulf. Journal of Petroleum Geology,29/2, 159-174. Paper 3: Farzadi, P. & Hesthammer, J. (Submitted 2006). Diagnosis of the Upper Cretaceous paleokarst and turbidite systems from the Iranian Persian Gulf using volume-based multiple seismic attribute analysis and pattern recognition. N.B.: Originally accepted for publication in the AAPG Bulletin, later rejected because the US government prohibits the publication of papers using Iranian government datasets. The manuscript has been re-submitted to Petroleum Geoscience. Paper 4: Farzadi, P. & Alaei, B. (Submitted 2006). Stratigraphic architecture of the Zagros Basin: towards an objective comparison of the Fold-Thrust Belt and Foreland provinces. Submitted to the Journal of Petroleum Geology; under consideration for a thematic issue. Presentation (at international meeting and on web): Farzadi, P. 2005. Stratal geometries of the Cretaceous carbonate systems: application of multiple volumes attributes analysis to 3-D seismic data from the Persian Gulf. At: Middle to Far East Carbonate Reservoirs: Exploration, Development and Exploitation. PESGB Carbonate conference, 15th & 16th Nov. 2005 London

Advanced Reservoir Modeling and Fluid Flow Studies of Natural Gas Production from the Hydrate Reservoirs of the Alaska North Slope

The emerging possibility of the production of gas hydrates as an unconventional source of energy have spurred many objectives for research studies going on in this area. One of these is the U.S national hydrate research program with a primary goal of determining the tools and technologies for environmentally safe gas production from hydrate reservoirs. The work presented in this thesis is motivated by the need to provide reliable reservoir model-based predictions to support proposed long-term hydrate field production tests on the Alaska North Slope permafrost. While first order predictions have been made from reservoir models based on assumptions of homogeneity of properties, it has been shown that the degree of reservoir heterogeneity can significantly affect the quantitative and qualitative results.;This study is an advanced and robust evaluation of the gas production potential of hydrate reservoirs. The hydrate deposits within the region of Prudhoe Bay Unit (PBU) L-Pad and Mt. Elbert Well vicinity of the Milne Point Unit of the Alaska North Slope are primary subjects of investigation. It is an effort to build data-driven heterogeneous hydrate reservoir models by applying both conventional and novel methods of reservoir characterization to maximize the utilization of the available field data. Using well log data obtained from 78 L-Pad wells, geostatistical techniques were employed to obtain stochastic simulations of the 3D distribution of reservoir properties in the target hydrate units of the L-Pad region. Models for the Mt. Elbert deposit were developed by combining data obtained from well logs obtained during the 2007 Mt. Elbert stratigraphic test and a 3D seismic survey of the region. Additionally, wellbore flow assurance studies were coupled with reservoir models in order to predict potential production issues arising from the formation of secondary hydrates or ice within the wellbore fluids being produced under high pressure and low temperature conditions.;CMG STARS, a finite difference reservoir modeling software package, was used to solve the material and energy balance equations in which an equilibrium model of hydrate dissociation was used. The simulator also provides a means to couple artificial lift design of the wellbore with the reservoir model using established pressure drop-heat loss correlations. Gas and water production rates and the evolution of reservoir properties were extensively studied in varying production scenarios with depressurization as the primary recovery technique.;Predictions from 10 geostatistical realizations of the L-Pad model were within narrow ranges, which is an indication of the robustness and reliability of the model. Uncertainty assessment and sensitivity studies on the Mt. Elbert model showed that higher gas production rates were achieved in deeper (hence warmer) reservoirs and confirmed earlier studies that production from the Mt. Elbert prospect may too cold to be economically feasible. Furthermore, contrary to predictions from homogeneous models, the effect of secondary hydrate formation in the reservoir on gas flow was found to be very minimal. However, flow assurance and artificial lift design studies show that wellbore pressure and temperature conditions must be effectively managed to prevent formation of secondary hydrates or ice

FACIES ARCHITECTURE AND CONTROLS ON RESERVOIR BEHAVIOR IN THE TURONIAN WALL CREEK MEMBER OF THE FRONTIER FORMATION, POWDER RIVER BASIN, WYOMING

Inter-well heterogeneities influencing fluid migration in deltaic reservoirs are controlled by lateral lithofacies changes and vertical complexities such as low permeability thin-beds. Subsurface tools often cannot predict the spatial and stratigraphic organization of these architectural elements, nor their influence on effective reservoir properties and connectivity. This study integrates sedimentological, stratigraphic, and fluid simulation data to 1) document the facies architecture and depositional evolution of the Turonian Wall Creek Member (WCM) of the Frontier Formation, and 2) quantify the role of multi-scale stratigraphic heterogeneity on reservoir behavior. Upscaled permeability properties derived from fluid simulation of nested, small-scale facies models condition the observed architecture within a 500m x 715m geocellular model. Key surfaces recognized across the study area separate the WCM into three depositional sequences, each of which contain multiple parasequences that form the geomodel framework. Sequence 1 consists of a top-truncated package of river-dominated delta lobes, interpreted as highstand deposits (HST1); sequence 2 is made of wave-dominated delta sandstones deposited during subsequent highstand (HST2); sequence 3 consists of heterolithic tidal bar deposits of a tidally-influenced delta (LST). Detailed mapping of the HST1/HST2 show the spatial distribution of intra-parasequence lithofacies is largely controlled by their proximity to high energy conditions above wave-base and near distributary channels. Modelling results show that permeability of the fine-grained component within heterolithic deposits is the most critical parameter in reservoir behavior. In wave-dominated environments, relatively simple bed geometries of thin-beds induce low vertical permeability. Conversely, more architecturally complex tidal deposits maintain better vertical connectivity but limited horizontal permeability. Flow compartmentalization on any scale happens only when thin-beds are assumed to be impermeable barriers; mud drapes with lower clay content act only as flow baffles. Fine-scale heterogeneities carry through as controlling factors in geomodel (500m x715m) reservoir simulations. In the wave-dominated setting, continuous horizons of low vertical permeability facies delineate parasequence-scale flow units. Within individual parasequences, the lithofacies distribution plays an important role on effective permeability pathways and total volume in place. Results from this outcrop-to-geomodel study can be applied to WCM reservoirs in the subsurface and used as guidance to build more accurate geomodels in other basins

Adequate model complexity and data resolution for effective constraint of simulation models by 4D seismic data

4D seismic data bears valuable spatial information about production-related changes in the reservoir. It is a challenging task though to make simulation models honour it. Strict spatial tie of seismic data requires adequate model complexity in order to assimilate details of seismic signature. On the other hand, not all the details in the seismic signal are critical or even relevant to the flow characteristics of the simulation model so that fitting them may compromise the predictive capability of models. So, how complex should be a model to take advantage of information from seismic data and what details should be matched? This work aims to show how choices of parameterisation affect the efficiency of assimilating spatial information from the seismic data. Also, the level of details at which the seismic signal carries useful information for the simulation model is demonstrated in light of the limited detectability of events on the seismic map and modelling errors. The problem of the optimal model complexity is investigated in the context of choosing model parameterisation which allows effective assimilation of spatial information in the seismic map. In this study, a model parameterisation scheme based on deterministic objects derived from seismic interpretation creates bias for model predictions which results in poor fit of historic data. The key to rectifying the bias was found to be increasing the flexibility of parameterisation by either increasing the number of parameters or using a scheme that does not impose prior information incompatible with data such as pilot points in this case. Using the history matching experiments with a combined dataset of production and seismic data, a level of match of the seismic maps is identified which results in an optimal constraint of the simulation models. Better constrained models were identified by quality of their forecasts and closeness of the pressure and saturation state to the truth case. The results indicate that a significant amount of details in the seismic maps is not contributing to the constructive constraint by the seismic data which is caused by two factors. First is that smaller details are a specific response of the system-source of observed data, and as such are not relevant to flow characteristics of the model, and second is that the resolution of the seismic map itself is limited by the seismic bandwidth and noise. The results suggest that the notion of a good match for 4D seismic maps commonly equated to the visually close match is not universally applicable