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Super-permeability fracture systems |
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By Joe Voelker, PhD
The Arab-D Formation of the Ghawar Field, Saudi Arabia, is the most prolific oil producing formation in the world, relative to both volume and productivity. An important hydraulic component of this carbonate formation, "super-k," provides for anomalously high, localized, fluid conductivity, and has to date eluded simple geologic characterization. Spatial prediction of super-k occurrence is desired for placement of water injection and oil production wells, and for improved production forecasting. Premature oil well abandonment has become a problem for the operator, Saudi Aramco, due to the inability to mitigate the high injection water conductivity of super-k, and associated early water breakthrough at adjacent production wells. This thesis provides a new model of Arab-D super-k, comprised primarily of interwell discrete fracture networks. The principal components of the thesis, the simulation of flow in large-scale, discrete fracture systems, preceded by the mapping of geocellular models to the flow simulation model, provide for a new general approach to modeling the flow effects these highly conductive systems. This approach is immediately applicable beyond Ghawar and super-k; in general, characterization of reservoirs which are severely affected by flow in large-scale fracture systems, most notably those oil or gas developments in which the accurate prediction of water encroachment is essential to well planning or determination of economic feasibility, may benefit from this model. The model is conducive to immediate industry application, due to two key elements. First, sources, rather than discretization, are used to incorporate discrete fracture networks into the conventional, and commercial, finite difference flow simulator, without modification of the flow simulator code. Second, a practical, stochastic discrete fracture network model serves as a tool for gradual deformation of the geocellular model in a history matching algorithm. The source model offers several advantages over fracture discretization and dual porosity models, particularly for flow simulations performed as part of an optimization algorithm, as is the case in this thesis. Without the computational and gridding burdens of fracture discretization, or the inappropriate resolution of the dual grid, the source model provides a means by which discrete fracture flow simulation may be performed with conventional flow simulators, on coarse grids, using geocellular fracture models of fine resolution. The super-k model was used successfully to predict production performance that is significantly affected by the presence of large-scale fracture systems, in the Ghawar study area.
The PDF can be downloaded from the department database |
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Upscaling and inverse modeling of flow data |
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By Inanc Tureyen, PhD
The challenge in data integration in any 3D spatial modeling lies in the fact that, each data has its own resolution and averaging process. Usually high resolution data have a small area of coverage, while on the other hand, data with a high area of coverage has low resolution. With most current approaches data are integrated independently at their respective scales. High resolution models are used for integrating small scale data while large scale data are integrated on corresponding upscaled models. The drawback of such independent process is that once the scale is changed, the model may no longer honor the data at the lost scale. In this thesis we propose a general algorithm as a solution to the scaling problem presented above. Instead of proceeding in a series fashion, we propose to construct the model jointly at multiple scales and work with all scales throughout the entire data integration process in parallel. This is accomplished by introducing upscaling in the data integration process. As a result all data are honored at their respective scales. As an example application we treat flow in porous media problems and introduce a fast optimization step when changing the model resolution. This optimization step ensures, as much as is needed, consistency between the two scales. This optimization is aided by means of streamline flow simulation. This multiple scales concept is then applied in the context of inverse modeling of flow and pressure data. In such inversion, perturbations are performed on the high resolution model while the full flow simulations are performed on the coarsened models. Fast flow simulation using streamlines are used to perform gridding optimization while ensuring that both high resolution and coarsened models match the flow data.
The PDF can be downloaded from the department database |
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Stochastic simulation with patterns |
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By Burc Arpat, PhD
In this thesis, a pattern-based geostatistical sequential simulation algorithm (SIMPAT) is proposed that redefines spatial stochastic as an image construction problem. The approach utilizes the training image concept of multiple-point geostatistics (MPS) but is not developed through probability theory. Rather, it considers the training image as a collection of multiple-scale patterns from which patterns are selected and pasted into a 3D gridded model such that they match sample data. The framework of sequential simulation is used to achieve the simulation and conditioning of patterns. During sequential simulation, at each visited grid location, the algorithm looks for a training image pattern that is most 'similar' to the data event (the neighborhood of the currently visited grid node), i.e. the traditional conditional probability models are replaced with similarity calculations of image processing. One way of conceptualizing the proposed algorithm is to envision it as a method for solving jigsaw puzzles: The technique builds images (3D models) by assembling puzzle pieces (training image patterns). The method works equally well with both continuous (such as permeability) and categorical (such as facies) variables while conditioning to a variety of data such sample data, trend data and soft data.
The PDF can be downloaded from the department database. |
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Inverse modeling with probability perturbations |
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by Todd Hoffman, PhD
Building of models in the Earth Sciences often requires the solution of an inverse problem: some unknown model parameters need to be calibrated with actual measurements. In most cases, the set of measurements cannot completely and uniquely determine the model parameters; hence multiple models can describe the same data set. Bayesian inverse theory provides a framework for solving this problem. Bayesian methods rely on the fact that the conditional probability of the model parameters given the data (the posterior) is proportional to the likelihood of observing the data and a prior belief expressed as a prior distribution of the model parameters. In case the prior distribution is not Gaussian and the relation between data and parameters (forward model) is strongly non-linear, one has to resort to iterative samplers, often Markov chain Monte Carlo methods, for generating samples that fit the data likelihood and reflect the prior model statistics. While theoretically sound, such methods can be slow to converge, and are often impractical when the forward model is CPU demanding. In this paper, we propose a new sampling method that allows to sample from a variety of priors and condition model parameters to a variety of data types. The method does not rely on the traditional Bayesian decomposition of posterior into likelihood and prior, instead it uses so-called pre-posterior distributions, i.e. the probability of the model parameters given some subset of the data. The use of pre-posterior allows to decompose the data into so-called, “easy data” (or linear data) and “difficult data” (or nonlinear data). The method relies on fast non-iterative sequential simulation to generate model realizations. The difficult data is matched by perturbing an initial realization using a perturbation mechanism termed “probability perturbation.” The probability perturbation method moves the initial guess closer to matching the difficult data, while maintaining the prior model statistics and the conditioning to the linear data. This method has been applied to complex 3D reservoirs with complex flow data
The PDF can be downloaded from the department database
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Assessment of structural uncertainty |
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By Satomi Suzuki, PhD
In many cases, particularly in subsurface modeling, one lacks the amount of data to fully determine the nature of the spatial variability. For example, many different training images could be proposed for a given study area. Such alternative training images or scenarios relate to the different possible geological concepts each exhibiting a distinctive geological architecture. Many inverse methods rely on priors that represent a single subjectively chosen geological concept (a single variogram within a multi-Gaussian model or a single training image). This thesis proposes a novel and practical parameterization of the prior model allowing several discrete choices of geological architectures within the prior. This method does not attempt to parameterize the possibly complex architectures by a set of model parameters. Instead, a large set of prior model realizations is provided in advance, by means of Monte Carlo simulation, where the training image is randomized. The parameterization is achieved by defining a metric space which accommodates this large set of model realizations. This metric space is equipped with a “similarity distance” function or a distance function that measures the similarity of geometry between any two model realizations relevant to the problem at hand. This idea is applied to various problems such as the difficult problem of structural uncertainty based on well-log, seismic and production data. In structural modeling, the prior set represents the reservoir structural uncertainty because of interpretation uncertainty on seismic sections. Several search methods such as tree search and the neighborhood algorithm are used to solve these complex inverse problems.
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PhD dissertations