Multiscale-Network Structure Inversion of Fractured Media Based on a Hierarchical-Parameterization and Data-Driven Evolutionary-Optimization Method

SPE Journal ◽  
2020 ◽  
Vol 25 (05) ◽  
pp. 2729-2748
Author(s):  
Xiaopeng Ma ◽  
Kai Zhang ◽  
Chuanjin Yao ◽  
Liming Zhang ◽  
Jian Wang ◽  
...  
Keyword(s):  
Network Structure ◽  
Inverse Modeling ◽  
History Matching ◽  
Fractured Reservoirs ◽  
Fracture Network ◽  
Fractured Media ◽  
Naturally Fractured Reservoirs ◽  
Data Driven ◽  
Model Parameters ◽  
Parameterization Method

Summary Efficient identification and characterization of fracture networks are crucial for the exploitation of fractured media such as naturally fractured reservoirs. Using the information obtained from borehole logs, core images, and outcrops, fracture geometries can be roughly estimated. However, this estimation always has uncertainty, which can be decreased using inverse modeling. Following the Bayes framework, a common practice for inverse modeling is to sample from the posterior distribution of uncertain parameters, given the observational data. However, a challenge for fractured reservoirs is that the fractures often occur on different scales, and these fractures form an irregular network structure that is difficult to model and predict. In this work, a multiscale-parameterization method is developed to model the fracture network. Based on this parameterization method, we present a novel history-matching approach using a data-driven evolutionary algorithm to explore the Bayesian posterior space and decrease the uncertainties of the model parameters. Empirical studies on hypothetical and outcrop-based cases demonstrate that the proposed method can model and estimate the complex multiscale-fracture network on a limited computational budget.

History Matching of Naturally Fractured Reservoirs Using a Deep Sparse Autoencoder

SPE Journal ◽  
2021 ◽  
pp. 1-22
Author(s):  
Kai Zhang ◽  
Jinding Zhang ◽  
Xiaopeng Ma ◽  
Chuanjin Yao ◽  
Liming Zhang ◽  
...  
Keyword(s):  
Dimensionality Reduction ◽  
Latent Variables ◽  
History Matching ◽  
Reduction Method ◽  
Fractured Reservoirs ◽  
Fracture Network ◽  
Naturally Fractured Reservoirs ◽  
Model Parameters ◽  
Sparse Autoencoder ◽  
Dimensionality Reduction Method

Summary Although researchers have applied many methods to history matching, such as Monte Carlo methods, ensemble-based methods, and optimization algorithms, history matching fractured reservoirs is still challenging. The key challenges are effectively representing the fracture network and coping with large amounts of reservoir-model parameters. With increasing numbers of fractures, the dimension becomes larger, resulting in heavy computational work in the inversion of fractures. This paper proposes a new characterization method for the multiscale fracture network, and a powerful dimensionality-reduction method by means of an autoencoder for model parameters. The characterization method of the fracture network is dependent on the length, orientation, and position of fractures, including large-scale and small-scale fractures. To significantly reduce the dimension of parameters, the deep sparse autoencoder (DSAE) transforms the input to the low-dimensional latent variables through encoding and decoding. Integrated with the greedy layer-wise algorithm, we set up a DSAE and then take the latent variables as optimization variables. The performance of the DSAE with fewer activating nodes is excellent because it reduces the redundant information of the input and avoids overfitting. Then, we adopt the ensemble smoother (ES) with multiple data assimilation (ES-MDA) to solve this minimization problem. We test our proposed method in three synthetic reservoir history-matching problems, compared with the no-dimensionality-reduction method and the principal-component analysis (PCA). The numerical results show that the characterization method integrated with the DSAE could simplify the fracture network, preserve the distribution of fractures during the update, and improve the quality of history matching naturally fractured reservoirs.

A FRACTAL DISCRETE FRACTURE NETWORK MODEL FOR HISTORY MATCHING OF NATURALLY FRACTURED RESERVOIRS

Fractals ◽  
2019 ◽  
Vol 27 (01) ◽  
pp. 1940008 ◽  
Author(s):  
LIMING ZHANG ◽  
CHENYU CUI ◽  
XIAOPENG MA ◽  
ZHIXUE SUN ◽  
FAN LIU ◽  
...  
Keyword(s):  
History Matching ◽  
Fractured Reservoirs ◽  
Fracture Network ◽  
Naturally Fractured Reservoirs ◽  
Production Data ◽  
Multi Scale ◽  
Complex Fracture ◽  
Discrete Fracture ◽  
Dfn Model ◽  
Dimensional Optimization

The distribution of fractures is highly uncertain in naturally fractured reservoirs (NFRs) and may be predicted by using the assisted-history-matching (AHM) that calibrates the reservoir model according to some high-quality static data combined with dynamic production data. A general AHM approach for NFRs is to construct a discrete fracture network (DFN) model and estimate model parameters given the observations. However, the large number of fractures prediction required in the AHM process could pose a high-dimensional optimization problem. This difficulty is particularly challenging when the fractures form a complex multi-scale fracture network. We present in this paper an integrated AHM approach of NFRs to tackle these challenges. Two essential ingredients of the method are (1) a 2D fractal-DFN model constructed as the geological simulation model to describe the complex fracture network, and (2) a mixture of multi-scale parameters, built according to the fractal-DNF model, as an inversion parameter model to alleviate the high-dimensional optimization burden caused by complex fracture networks. A reservoir with a multi-scale fracture network is set up to test the performance of the proposed method. Numerical results demonstrate that by use of the proposed method, the fractures well recognized by assimilating production data.

scholarly journals A new methodology to reduce uncertainty of global attributes in naturally fractured reservoirs

2018 ◽  
Vol 73 ◽  
pp. 41 ◽  
Author(s):  
Luís Augusto Nagasaki Costa ◽  
Célio Maschio ◽  
Denis José Schiozer
Keyword(s):  
Sensitivity Analysis ◽  
History Matching ◽  
Fractured Reservoirs ◽  
Probabilistic Approach ◽  
Fracture Network ◽  
Naturally Fractured Reservoirs ◽  
Fracture Aperture ◽  
Practical Case ◽  
Fractured Reservoir ◽  
Naturally Fractured

Accurately characterizing fractures is complex. Several studies have proposed reducing uncertainty by incorporating fracture characterization into simulations, using a probabilistic approach, to maintain the geological consistency, of a range of models instead of a single matched model. We propose a new methodology, based on one of the steps of a general history-matching workflow, to reduce uncertainty of reservoir attributes in naturally fractured reservoirs. This methodology maintains geological consistency and can treat many reservoir attributes. To guarantee geological consistency, the geostatistical attributes (e.g., fracture aperture, length, and orientation) are used as parameters in the history matching. This allows us to control Discrete Fracture Network attributes, and systematically modify fractures. The iterative sensitivity analysis allows the inclusion of many (30 or more) uncertain attributes that might occur in a practical case. At each uncertainty reduction step, we use a sensitivity analysis to identify the most influential attributes to treat in each step. Working from the general history-matching workflow of Avansi et al. (2016), we adapted steps for use with our methodology, integrating the history matching with geostatistical modeling of fractures and other properties in a big loop approach. We applied our methodology to a synthetic case study of a naturally fractured reservoir, based on a real semi-synthetic carbonate field, offshore Brazil, to demonstrate the applicability in practical and complex cases. From the initial 18 uncertain attributes, we worked with only 5 and reduced the overall variability of the Objective Functions. Although the focus is on naturally fractured reservoirs, the proposed methodology can be applied to any type of reservoir.

Effect of DFN Upscaling on History Matching and Prediction of Naturally Fractured Reservoirs

2013 ◽  
Author(s):  
Mohamed Ahmed Elfeel ◽  
Sarim Jamal ◽  
Chukwuemeka Enemanna ◽  
Dan Arnold ◽  
Sebastian Geiger
Keyword(s):  
History Matching ◽  
Fractured Reservoirs ◽  
Naturally Fractured Reservoirs ◽  
Naturally Fractured

Pressure-Transient Tests and Flow Regimes in Fractured Reservoirs

2015 ◽  
Vol 18 (02) ◽  
pp. 187-204 ◽  
Author(s):  
Fikri Kuchuk ◽  
Denis Biryukov
Keyword(s):  
History Matching ◽  
Fractured Reservoirs ◽  
Flow Regimes ◽  
Naturally Fractured Reservoirs ◽  
Dual Porosity ◽  
Hydraulic Fractures ◽  
Fractured Reservoir ◽  
Pressure Transient ◽  
Matrix Block ◽  
Naturally Fractured

Summary Fractures are common features in many well-known reservoirs. Naturally fractured reservoirs include fractured igneous, metamorphic, and sedimentary rocks (matrix). Faults in many naturally fractured carbonate reservoirs often have high-permeability zones, and are connected to numerous fractures that have varying conductivities. Furthermore, in many naturally fractured reservoirs, faults and fractures can be discrete (rather than connected-network dual-porosity systems). In this paper, we investigate the pressure-transient behavior of continuously and discretely naturally fractured reservoirs with semianalytical solutions. These fractured reservoirs can contain periodically or arbitrarily distributed finite- and/or infinite-conductivity fractures with different lengths and orientations. Unlike the single-derivative shape of the Warren and Root (1963) model, fractured reservoirs exhibit diverse pressure behaviors as well as more than 10 flow regimes. There are seven important factors that dominate the pressure-transient test as well as flow-regime behaviors of fractured reservoirs: (1) fractures intersect the wellbore parallel to its axis, with a dipping angle of 90° (vertical fractures), including hydraulic fractures; (2) fractures intersect the wellbore with dipping angles from 0° to less than 90°; (3) fractures are in the vicinity of the wellbore; (4) fractures have extremely high or low fracture and fault conductivities; (5) fractures have various sizes and distributions; (6) fractures have high and low matrix block permeabilities; and (7) fractures are damaged (skin zone) as a result of drilling and completion operations and fluids. All flow regimes associated with these factors are shown for a number of continuously and discretely fractured reservoirs with different well and fracture configurations. For a few cases, these flow regimes were compared with those from the field data. We performed history matching of the pressure-transient data generated from our discretely and continuously fractured reservoir models with the Warren and Root (1963) dual-porosity-type models, and it is shown that they yield incorrect reservoir parameters.

A Sensitivity Analysis for Effective Parameters on 2D Fracture-Network Permeability

2009 ◽  
Vol 12 (03) ◽  
pp. 455-469 ◽  
Author(s):  
Alireza Jafari ◽  
Tayfun Babadagli
Keyword(s):  
Sensitivity Analysis ◽  
Experimental Design ◽  
Fractured Reservoirs ◽  
Fracture Network ◽  
Static Model ◽  
Naturally Fractured Reservoirs ◽  
Single Fracture ◽  
Data Sets ◽  
Fracture Networks ◽  
Fractal Characteristics

Summary Fracture-network mapping and estimation of its permeability constitute two major steps in static-model preparation of naturally fractured reservoirs. Although several different analytical methods were proposed in the past for calculating fracture-network permeability (FNP), different approaches are still needed for practical use. We propose a new and practical approach to estimate FNP using statistical and fractal characteristics of fracture networks. We also provide a detailed sensitivity analysis to determine the relative importance of fracture-network parameters on the FNP in comparison to single-fracture conductivity using an experimental-design approach. The FNP is controlled by many different fracture-network parameters such as fracture length, density, orientation, aperture, and single-fracture connectivity. Five different 2D fracture data sets were generated for random and systematic orientations. In each data set, 20 different combinations of fracture density and length for different orientations were tested. For each combination, 10 different realizations were generated. The length was considered as constant and variable. This yielded a total of 1,000 trials. The FNPs were computed through a commercial discrete-fracture-network (DFN) modeling simulator for all cases. Then, we correlated different statistical and fractal characteristics of the networks to the measured FNPs using multivariable-regression analysis. Twelve fractal (sandbox, box counting, and scanline fractal dimensions) and statistical (average length, density, orientation, and connectivity index) parameters were tested against the measured FNP for synthetically generated fracture networks for a wide range of fracture properties. All cases were above the percolation threshold to obtain a percolating network, and the matrix effect was neglected. The correlation obtained through this analysis using four data sets was tested on the fifth one with known permeability for verification. High-quality match was obtained. Finally, we adopted an experimental-design approach to identify the most-critical parameters on the FNP for different fracture-network types. The results are presented as Pareto charts. It is believed that the new method and results presented in this paper will be useful for practitioners in static-model development of naturally fractured reservoirs and will shed light on further studies on modeling and understanding the transmissibility characteristics of fracture networks. It should be emphasized that this study was conducted on 2D fracture networks and could be extended to 3D models. This, however, requires further algorithm development to use 2D fractal characteristics for 3D systems and/or development of fractal measurement techniques for a 3D system. This study will provide a guideline for this type of research.

Fracture network connectivity devolution monitoring using transdimensional data assimilation

2021 ◽  
Author(s):  
Márk Somogyvári ◽  
Mohammadreza Jalali ◽  
Irina Engelhardt ◽  
Sebastian Reich
Keyword(s):  
Data Assimilation ◽  
Weather Forecasting ◽  
Fractured Reservoirs ◽  
Fracture Network ◽  
Model Parameters ◽  
Fractured Aquifer ◽  
Dynamic Changes ◽  
Transport Pathways ◽  
Fractured Aquifers ◽  
Rock Characterization

<p>In fractured aquifers, the permeability of open fractures could change over time due to precipitation effects and hydrothermal mineral growth. These processes could lead to the clogging of individual fractures and to the complete rearrangement of flow and transport pathways. Existing fractured rock characterization techniques often neglect this dynamicity and treat the reconstruction as a static inversion problem. The dynamic changes then later added to the model as an independent forward modeling task. In this research we provide a new data assimilation-based methodology to monitor and predict the dynamic changes of fractured aquifers due to mineralization in a quasi-real-time manner.</p><p>We formulate the inverse problem as a dynamic ‘hidden Markov process’ where the underlying model dynamicity is just partly known. Data assimilation methods are specifically designed to model such systems with strong uncertainties. A typical example for such problems is weather forecasting, where the combination of nonlinear processes and the partial observations make the forecasting challenging. To handle the strong random behavior, data assimilation approaches use stochastic algorithms. In this study we combine DFN-based stochastic aquifer reconstruction techniques with data assimilation algorithms to provide a dynamic inverse modelling framework for fractured reservoirs. We use the transdimensional DFN inversion of (Somogyvári et al., 2017) to initialize the data assimilation. This method uses a transdimensional MCMC approach to identify the most probable DFN geometries given the observations. Because the method is transdimensional it can adjust the number of model parameters, the number of fractures within the DFN. We developed this idea further by enhancing a particle filter algorithm with transdimensional model updates, allowing us to infer DFN models with changing fracture numbers.</p><p>We demonstrate the applicability of this new approach on outcrop-based synthetic fractured aquifer models. To create a dynamic DFN example, we simulate solute transport in a 2-D fracture network model using an advection-dispersion algorithm. We simulate fracture sealing in a stochastic way: we define a limit concentration above which the fractures could seal with a predefined probability at any timestep. At the initial timestep, a hydraulic tomography experiment is performed to capture the initial aquifer structure, which is then reconstructed by the transdimensional DFN inversion. At predefined timesteps hydraulic tests are performed at different parts of the aquifer, to obtain information about new state of the synthetic model. These observations are then processed by the data assimilation algorithm, which updates the underlying DFN models to better fit to the observations.</p>

scholarly journals New algorithm to simulate fracture network propagation using stationary and moving coordinates in naturally fractured reservoirs

2020 ◽  
Vol 8 (11) ◽  
pp. 4025-4042
Author(s):  
Zhiqiang Li ◽  
Zhilin Qi ◽  
Wende Yan ◽  
Xiaoliang Huang ◽  
Qianhua Xiao ◽  
...  
Keyword(s):  
Fractured Reservoirs ◽  
Fracture Network ◽  
Naturally Fractured Reservoirs ◽  
Naturally Fractured ◽  
Network Propagation

scholarly journals Evaluation of an uncertainty reduction methodology based on Iterative Sensitivity Analysis (ISA) applied to naturally fractured reservoirs

2019 ◽  
Vol 74 ◽  
pp. 40 ◽  
Author(s):  
Luís Augusto Nagasaki Costa ◽  
Célio Maschio ◽  
Denis José Schiozer
Keyword(s):  
Sensitivity Analysis ◽  
History Matching ◽  
Flow Behavior ◽  
Fractured Reservoirs ◽  
Search Space ◽  
Naturally Fractured Reservoirs ◽  
Reservoir Modeling ◽  
Naturally Fractured ◽  
Geostatistical Techniques

History matching for naturally fractured reservoirs is challenging because of the complexity of flow behavior in the fracture-matrix combination. Calibrating these models in a history-matching procedure normally requires integration with geostatistical techniques (Big Loop, where the history matching is integrated to reservoir modeling) for proper model characterization. In problems involving complex reservoir models, it is common to apply techniques such as sensitivity analysis to evaluate and identify most influential attributes to focus the efforts on what most impact the response. Conventional Sensitivity Analysis (CSA), in which a subset of attributes is fixed at a unique value, may over-reduce the search space so that it might not be properly explored. An alternative is an Iterative Sensitivity Analysis (ISA), in which CSA is applied multiple times throughout the iterations. ISA follows three main steps: (a) CSA identifies Group i of influential attributes (i = 1, 2, 3, …, n); (b) reduce uncertainty of Group i, with other attributes with fixed values; and (c) return to step (a) and repeat the process. Conducting CSA multiple times allows the identification of influential attributes hidden by the high uncertainty of the most influential attributes. In this work, we assess three methods: Method 1 – ISA, Method 2 – CSA, and Method 3 – without sensitivity analysis, i.e., varying all uncertain attributes (larger searching space). Results showed that the number of simulation runs for Method 1 dropped 24% compared to Method 3 and 12% to Method 2 to reach a similar matching quality of acceptable models. In other words, Method 1 reached a similar quality of results with fewer simulations. Therefore, ISA can perform as good as CSA demanding fewer simulations. All three methods identified the same five most influential attributes of the initial 18. Even with many uncertain attributes, only a small percentage is responsible for most of the variability of responses. Also, their identification is essential for efficient history matching. For the case presented in this work, few fracture attributes were responsible for most of the variability of the responses.

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