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Oilfield tubulars have been traditionally designed using a deterministic working stress design (WSD) approach, which is based on multipliers called safety factors (SFs). The primary role of a safety factor is to account for uncertainties in the design variables and parameters, primarily the load effect and the strength or resistance of the structure. While based on experience, these factors give no indication of the probability of failure of a given structure, as they do not explicitly consider the randomness of the design variables and parameters. Moreover, the safety factors tend to be rather conservative, and most limits of design are established using failure criteria based on elastic theory. Reliability-based approaches are probabilistic in nature and explicitly identify all the design variables and parameters that determine the load effect and strength of the structure.
Flow around a rotating circular cylinder at a Reynolds number of 500 is investigated numerically. The aim of this study is to investigate the effect of high rotation rate on the wake flow past a circular cylinder. Simulations are performed at a constant Reynolds number of 500 and a wide range of rotation rates from 1.6 to 6. Rotation rate is the ratio of the rotational speed of the cylinder surface to the incoming fluid velocity. It is found that increasing the rotation rate beyond a critical value results in transition to a secondary instability regime where the oscillation of the lift force on the cylinder increases drastically. There is significant increase in the three-dimensionality of the flow inside the secondary instability regime. The flow pattern in the secondary instability regime is characterized by ring-type vortices wrapping around the cylinder. The oscillation of the force coefficient in the secondary instability regime is very irregular.
Vortex shedding flow in the wake of circular cylinders has been investigated extensively, mainly because of its increasing applications in (but not limited to) offshore oil and gas engineering. Many experimental and numerical studies have been conducted on the transition of the wake flow to turbulence (Roshko, 1954; Williamson, 1988; Hammache and Gharib, 1991; Karniadakis and Triantafyllou, 1992; Barkley and Henderson, 1996; Thompson et al., 1996). It was concluded that the transition of wake flow from two-dimensional to three-dimensional flow occurs when the Reynolds number is approximately Re D140–190. The Reynolds number is defined as Re = UD/v where U is the incoming velocity, D is the diameter of the cylinder, and v is the kinematic viscosity of the fluid. In the numerical study by Zhao et al. (2013), the critical Reynolds number was found to be 200. The critical Reynolds number varies in different experimental studies, mainly because of the end effects in the experimental condition.
We propose a Bayesian estimator for real-time autonomous geosteering. The Bayesian geosteering tool is capable of simultaneously estimating the stratigraphic variables and tool location. We use gamma-ray well-log measurements to perform the estimation. Given the prior information and measurements, the Bayesian estimator can rigorously compute the joint posterior probability density function of the stratigraphic and tool-location variables. Due to the inherent nonlinearity of measurements and the non-Gaussianity of the random variables involved, we propose a sequential Monte Carlo filter for performing the inference. Unlike the widely used Kalman filter and its variants, the estimation performance of sequential Monte Carlo estimator is not constrained by the nature of dynamics, measurement functions and the type of uncertainties. The computational cost of the estimation is kept manageable by making a few simplifying assumptions. The estimation performance of the proposed sequential Monte Carlo based geosteering tool is demonstrated with a simulated example involving six formation tops. The performance is evaluated in terms of the ability of the estimator to accurately track the stratigraphic boundaries and predict the correct formations. The results show that the proposed Bayesian geosteering tool can predict the stratigraphic boundaries and the type of formation in which the tool is located in a probabilistically rigorous fashion.
We propose a systematic Bayesian method for inferring the mineral composition of rock samples from transmission Fourier-transform infrared spectroscopy (FTIR) measurements. Currently available FTIR inversion methodologies depend on measuring pure minerals, using them within least-squares approaches with a hand-tuned noise model, and implementing ad hoc post-processing of the obtained solution. Within the proposed data-driven framework, we replaced these previous inversion approaches with the automatic training and estimation steps. In this approach, the linear operator, comparable with the FTIR spectral standards (FTIR spectra of end-members or pure minerals), is estimated or trained on a calibration set of rock samples for which the mineral composition has been accurately determined by other means in the laboratory. With this linear operator, we then quantify the spectral-noise covariance matrix from the calibration set, which forms the basis of our estimation of the Bayesian posterior uncertainty on a mineral-composition estimate. This quantification of uncertainty in mineral estimation is a novel feature that can be used as a reliability measure. The uncertainty also describes the correlation between estimates of mineral-weight fractions, indicating which pairs of minerals cannot be independently estimated. Our Bayesian model also addresses the uncertainty propagated from the estimated linear operator and thus captures a possible mismatch of the model parameter from the true operator (i.e., semiblindness of the model). We demonstrate the advantages of our approach by performing experiments with synthetic data.
Gao, Guohua (Shell Global Solutions US) | Jiang, Hao (Shell Global Solutions US) | Chen, Chaohui (Shell Exploration and Production Company) | Vink, Jeroen C. (Shell Global Solution International) | El Khamra, Yaakoub (Shell Global Solutions US) | Ita, Joel (Shell Global Solutions US) | Saaf, Fredrik (Shell Global Solutions US)
It has been demonstrated that the Gaussian-mixture-model (GMM) fitting method can construct a GMM that more accurately approximates the posterior probability density function (PDF) by conditioning reservoir models to production data. However, the number of degrees of freedom (DOFs) for all unknown GMM parameters might become huge for large-scale history-matching problems. A new formulation of GMM fitting with a reduced number of DOFs is proposed in this paper to save memory use and reduce computational cost. The performance of the new method is benchmarked against other methods using test problems with different numbers of uncertain parameters. The new method performs more efficiently than the full-rank GMM fitting formulation, reducing the memory use and computational cost by a factor of 5 to 10. Although it is less efficient than the simple GMM approximation dependent on local linearization (L-GMM), it achieves much higher accuracy, reducing the error by a factor of 20 to 600. Finally, the new method together with the parallelized acceptance/rejection (A/R) algorithm is applied to a synthetic history-matching problem for demonstration.
Generating an estimate of uncertainty in production forecasts has become nearly standard in the oil industry, but is often performed with procedures that yield at best a highly approximate uncertainty quantification. Formally, the uncertainty quantification of a production forecast can be achieved by generating a correct characterization of the posterior probability-density function (PDF) of reservoir-model parameters conditional to dynamic data and then sampling this PDF correctly. Although Markov-chain Monte Carlo (MCMC) provides a theoretically rigorous method for sampling any target PDF that is known up to a normalizing constant, in reservoir-engineering applications, researchers have found that it might require extraordinarily long chains containing millions to hundreds of millions of states to obtain a correct characterization of the target PDF. When the target PDF has a single mode or has multiple modes concentrated in a small region, it might be possible to implement a proposal distribution dependent on a random walk so that the resulting MCMC algorithm derived from the Metropolis-Hastings acceptance probability can yield a good characterization of the posterior PDF with a computationally feasible chain length. However, for a high-dimensional multimodal PDF with modes separated by large regions of low or zero probability, characterizing the PDF with MCMC using a random walk is not computationally feasible. Although methods such as population MCMC exist for characterizing a multimodal PDF, their computational cost generally makes the application of these algorithms far too costly for field application. In this paper, we design a new proposal distribution using a Gaussian mixture PDF for use in MCMC where the posterior PDF can be multimodal with the modes spread far apart. Simply put, the method generates modes using a gradient-based optimization method and constructs a Gaussian mixture model (GMM) to use as the basic proposal distribution. Tests on three simple problems are presented to establish the validity of the method. The performance of the new MCMC algorithm is compared with that of random-walk MCMC and is also compared with that of population MCMC for a target PDF that is multimodal.
Baltazar, João (Instituto Superior Técnico (IST), Universidade de Lisboa) | de Campos, José A. C. Falcão (Instituto Superior Técnico (IST), Universidade de Lisboa) | Bosschers, Johan (Maritime Research Institute Netherlands (MARIN)) | Rijpkema, Douwe (Maritime Research Institute Netherlands (MARIN))
This article presents an overview of the recent developments at Instituto Superior Técnico and Maritime Research Institute Netherlands in applying computational methods for the hydrodynamic analysis of ducted propellers. The developments focus on the propeller performance prediction in open water conditions using boundary element methods and Reynolds-averaged Navier-Stokes solvers. The article starts with an estimation of the numerical errors involved in both methods. Then, the different viscous mechanisms involved in the ducted propeller flow are discussed and numerical procedures for the potential flow solution proposed. Finally, the numerical predictions are compared with experimental measurements.
Ducted propellers have been widely used for marine applications. Nowadays, they may be found in tugs, trawlers, tankers, bulk ships, warships, and in dynamic positioning systems of offshore platforms or vessels. The duct may be classified as an accelerating or decelerating type. Accelerating ducts are often used to increase the efficiency and thrust of heavily loaded propellers. In the case of a decelerating duct, they are used to reduce the risk of cavitation and resulting noise.
The complex interaction which occurs between the propeller and duct makes the hydrodynamic design of such systems a complicated task. For the selection of the numerical simulation tool, the designer has to choose between a simplified method that predicts the main features of the flow field around the ducted propeller, and a more complex tool that provides detailed information in problematic areas such as the gap region between propeller and duct inner surface. On the other hand, model tests in a towing tank or cavitation tunnel may be seen as an alternative, but they are usually expensive. Presently, the development of an accurate and cost-effective numerical method for the design and analysis of ducted propellers is still not complete.
Reservoir simulation models that represent Saudi Arabia’s unique large reservoirs require significant use of High-Performance Computing resources. Several solutions aim to reduce the load of an individual simulation such as up-scaling to consequently reduce the number of grid cells of the model, cropping the model which loses the flux boundary conditions and running the studies independently, or dividing the model to sectors which preserves the flux boundary condition and running these models independently. Sector modeling could potentially result in the least erroneous solution, especially if the sectors are defined on the regions of least connectivity.
This paper aims to propose an automated, intelligent method to divide the reservoir model into an arbitrary number of least-connected smaller sectors. Streamline simulation output is used as a representation of reservoir connectivity. A graph is built using cells as graph vertices, and the edge weight is calculated based on the time of flight of oil and water between cell pairs.
By presenting the problem in this manner, a graph is built where the non-water cells have equal weight and the stronger the connection between two cells, represented by the lower time of flight, the larger the edge weight. A graph partitioning tool is used with the purpose of minimizing the total weight of edges cut while keeping the number of vertices in each sub-graph balanced up to a specified tolerance. Partitioning of a graph specified this way is equivalent to splitting the reservoir model into sub-models while avoiding cutting of strongly connected parts, hence minimizing the boundary flux. Applying this method to sector modeling allows splitting a model into a number of smaller sub-models that can be used independently as the interactions between them are minimized, as demonstrated by minimizing flux between them.
The proposed novel method has been tested on several real-field as well as synthetic reservoir models. The method has shown to result in sub-models of loosely connected reservoirs. The advantage of our proposed method is especially seen for strongly connected models where it is difficult to identify the least erroneous partitioning for sector generation manually. However, with the use of our method, it is guaranteed to automatically find the least connection, while minimizing the error that sector division produces as evident by the low flux between the sector models.
Providing an overview of an ensemble of oil reservoir models could help users compare and analyze their characteristics. Approaches that show a single model at a time may hamper analysts’ understanding of the whole model set. In this paper, we propose two visualization approaches that show multiple reservoir models, simultaneously and on a single screen, with the goal of helping users to compare models and improve their understanding of ensemble characteristics. First, we calculate 2D models from the ensemble's 3D models. We then create two visualizations that represent ensembles of these 2D models. The
All subsurface models derived from seismic and offset well data have uncertainties inherent in the data even after all possible steps have been taken to process the data to maximize the accuracy. There is, however, one more step that could be taken – to quantify the remaining uncertainty. This is a relatively new technology that has value in exploration and drilling. For drilling applications this means a statistical 3D earth model at the well location instead of a fixed, deterministic one. The drilling marker positions (depths) are represented as the best estimate plus an uncertainty distribution, for example 10% - 90% probability window, around it.