Ensemble clustering for efficient robust optimization of naturally fractured reservoirs     

Zhe Liu  Fahim Forouzanfar 《Computational Geosciences》2018,22(1):283-296

In the development of naturally fractured reservoirs (NFRs), the existence of natural fractures induces severe fingering and breakthrough. To manage the flooding process and improve the ultimate recovery, we propose a numerical workflow to generate optimal production schedules for smart wells, in which the inflow control valve (ICV) settings can be controlled individually. To properly consider the uncertainty introduced by randomly distributed natural fractures, the robust optimization would require a large ensemble size and it would be computationally demanding. In this work, a hierarchical clustering method is proposed to select representative models for the robust optimization in order to avoid redundant simulation runs and improve the efficiency of the robust optimization. By reducing the full ensemble of models into a small subset ensemble, the efficiency of the robust optimization algorithm is significantly improved. The robust optimization is performed using the StoSAG scheme to find the optimal well controls that maximize the net-present-value (NPV) of the NFR’s development. Due to the discrete property of a natural fracture field, traditional feature extraction methods such as model-parameter-based clustering may not be directly applicable. Therefore, two different kinds of clustering-based optimization methods, a state-based (e.g., s _w profiles) clustering and a response-based (e.g., production rates) clustering, are proposed and compared. The computational results show that the robust clustering optimization could increase the computational efficiency significantly without sacrificing much expected NPV of the robust optimization. Moreover, the performance of different clustering algorithms varies widely in correspondence to different selections of clustering features. By properly extracting model features, the clustered subset could adequately represent the uncertainty of the full ensemble.  相似文献   

Comparison between cell-centered and nodal-based discretization schemes for linear elasticity     

Halvor M. Nilsen  Jan Nordbotten  Xavier Raynaud 《Computational Geosciences》2018,22(1):233-260

In this paper, we study newly developed methods for linear elasticity on polyhedral meshes. Our emphasis is on applications of the methods to geological models. Models of subsurface, and in particular sedimentary rocks, naturally lead to general polyhedral meshes. Numerical methods which can directly handle such representation are highly desirable. Many of the numerical challenges in simulation of subsurface applications come from the lack of robustness and accuracy of numerical methods in the case of highly distorted grids. In this paper, we investigate and compare the Multi-Point Stress Approximation (MPSA) and the Virtual Element Method (VEM) with regard to grid features that are frequently seen in geological models and likely to lead to a lack of accuracy of the methods. In particular, we look at how the methods perform near the incompressible limit. This work shows that both methods are promising for flexible modeling of subsurface mechanics.  相似文献   

A numerical method for the solution of the nonlinear turbulent one-dimensional free surface flow equations     

Sujit K Bose 《Computational Geosciences》2018,22(1):81-86

Free surface flow of an incompressible fluid over a shallow plane/undulating horizontal bed is characteristically turbulent due to disturbances generated by the bed resistance and other causes. The governing equations of such flows in one dimension, for finite amplitude of surface elevation over the bed, are the Continuity Equation and a highly nonlinear Momentum Equation of order three. The method developed in this paper introduces the “discharge” variable q = η U, where η = elevation of the free surface above the bed level, and U = average stream-wise forward velocity. By this substitution, the continuity equation becomes a linear first-order PDE and the momentum equation is transformed after introduction of a small approximation in the fifth term. Next, it is shown by an invertibility argument that q can be a function of η: q = F(η), rendering the momentum equation as a first order, second degree ODE for F(η), that can be be integrated by the Runge-Kutta method. The continuity equation then takes the form of a first order evolutionary PDE that can be integrated by a Lax-Wendroff type of scheme for the temporal evolution of the surface elevation η. The method is implemented for two particular cases: when the initial elevation is triangular with vertical angle of 120 ^° and when it has a sinusoidal form. The computations exhibit the physically interesting feature that the frontal portion of the propagating wave undergoes a sharp jump followed by tumbling over as a breaker. Compared to other discretization methods, the application of the Runge-Kutta and an extended version of the Lax-Wendroff scheme is much easier.  相似文献   

Passing the Editorial Baton     

George W. LutherIII 《Aquatic Geochemistry》2018,24(1):1-2

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Identifying influence areas with connectivity analysis – application to the local perturbation of heterogeneity distribution for history matching     

Véronique Gervais  Mickaële Le Ravalec 《Computational Geosciences》2018,22(1):3-28

Numerical representations of a target reservoir can help to assess the potential of different development plans. To be as predictive as possible, these representations or models must reproduce the data (static, dynamic) collected on the field. However, constraining reservoir models to dynamic data – the history-matching process – can be very time consuming. Many uncertain parameters need to be taken into account, such as the spatial distribution of petrophysical properties. This distribution is mostly unknown and usually represented by millions of values populating the reservoir grid. Dedicated parameterization techniques make it possible to investigate many spatial distributions from a small number of parameters. The efficiency of the matching process can be improved from the perturbation of specific regions of the reservoir. Distinct approaches can be considered to define such regions. For instance, one can refer to streamlines. The leading idea is to identify areas that influence the production behavior where the data are poorly reproduced. Here, we propose alternative methods based on connectivity analysis to easily provide approximate influence areas for any fluid-flow simulation. The reservoir is viewed as a set of nodes connected by weighted links that characterize the distance between two nodes. The path between nodes (or grid blocks) with the lowest cumulative weight yields an approximate flow path used to define influence areas. The potential of the approach is demonstrated on the basis of 2D synthetic cases for the joint integration of production and 4D saturation data, considering several formulations for the weights attributed to the links.  相似文献   

A method of alternating characteristics with application to advection-dominated environmental systems     

Katerina Georgiou  John Harte  Ali Mesbah  William J. Riley 《Computational Geosciences》2018,22(3):851-865

We present a numerical method for solving a class of systems of partial differential equations (PDEs) that arises in modeling environmental processes undergoing advection and biogeochemical reactions. The salient feature of these PDEs is that all partial derivatives appear in linear expressions. As a result, the system can be viewed as a set of ordinary differential equations (ODEs), albeit each one along a different characteristic. The method then consists of alternating between equations and integrating each one step-wise along its own characteristic, thus creating a customized grid on which solutions are computed. Since the solutions of such PDEs are generally smoother along their characteristics, the method offers the potential of using larger time steps while maintaining accuracy and reducing numerical dispersion. The advantages in efficiency and accuracy of the proposed method are demonstrated in two illustrative examples that simulate depth-resolved reactive transport and soil carbon cycling.  相似文献   

Seasonal variability of oxygen and hydrogen isotopes in a wetland system of the Yunnan-Guizhou Plateau,southwest China: a quantitative assessment of groundwater inflow fluxes     

Xingxing Cao  Pan Wu  Shaoqi Zhou  Han Tu  Shui Zhang 《Hydrogeology Journal》2018,26(1):215-231

The Caohai Wetland serves as an important ecosystem on the Yunnan–Guizhou Plateau and as a nationally important nature reserve for migratory birds in China. In this study, surface water, groundwater and wetland water were collected for the measurement of environmental isotopes to reveal the seasonal variability of oxygen and hydrogen isotopes (δ¹⁸O, δD), sources of water, and groundwater inflow fluxes. Results showed that surface water and groundwater are of meteoric origin. The isotopes in samples of wetland water were well mixed vertically in seasons of both high-flow (September) and low-flow (April); however, marked seasonal and spatial variations were observed. During the high-flow season, the isotopic composition in surface wetland water varied from ?97.13 to ?41.73‰ for δD and from ?13.17 to ?4.70‰ for δ¹⁸O. The composition of stable isotopes in the eastern region of this wetland was lower than in the western region. These may have been influenced by uneven evaporation caused by the distribution of aquatic vegetation. During the low-flow season, δD and δ¹⁸O in the more open water with dead aquatic vegetation ranged from ?37.11 to ?11.77‰, and from ?4.25 to ?0.08‰, respectively. This may result from high evaporation rates in this season with the lowest atmospheric humidity. Groundwater fluxes were calculated by mass transfer and isotope mass balance approaches, suggesting that the water sources of the Caohai Wetland were mainly from groundwater in the high-flow season, while the groundwater has a smaller contribution to wetland water during the low-flow season.  相似文献   

Computing derivative information of sequentially coupled subsurface models     

Rafael J. de Moraes  José R. P. Rodrigues  Hadi Hajibeygi  Jan Dirk Jansen 《Computational Geosciences》2018,22(6):1527-1541

A generic framework for the computation of derivative information required for gradient-based optimization using sequentially coupled subsurface simulation models is presented. The proposed approach allows for the computation of any derivative information with no modification of the mathematical framework. It only requires the forward model Jacobians and the objective function to be appropriately defined. The flexibility of the framework is demonstrated by its application in different reservoir management studies. The performance of the gradient computation strategy is demonstrated in a synthetic water-flooding model, where the forward model is constructed based on a sequentially coupled flow-transport system. The methodology is illustrated for a synthetic model, with different types of applications of data assimilation and life-cycle optimization. Results are compared with the classical fully coupled (FIM) forward simulation. Based on the presented numerical examples, it is demonstrated how, without any modifications of the basic framework, the solution of gradient-based optimization models can be obtained for any given set of coupled equations. The sequential derivative computation methods deliver similar results compared to FIM methods, while being computationally more efficient.  相似文献   

Numerical solution and convergence analysis of steam injection in heavy oil reservoirs     

H. Hajinezhad  Ali R. Soheili  Mohammad R. Rasaei  F. Toutounian 《Computational Geosciences》2018,22(6):1433-1444

In this paper, the numerical methods for solving the problem of steam injection in the heavy oil reservoirs are presented. We consider a 3-dimensional model of 3-phase flow, oil, water, and steam, with the effect of 3-phase relative permeability. Interphase mass transfer of water and steam is considered; oil is assumed nonvolatile. We apply the simultaneous solution approach to solve the corresponding nonlinear discretized partial differential equation in the fully implicit form. The convergence of finite difference scheme is proved by the Rosinger theorem. The heuristic Jacobian-Free-Newton-Krylov (HJFNK) method is proposed for solving the system of algebraic equations. The result of this proposed numerical method is well compared with some experimental results. Our numerical results show that the first iteration of the full approximation scheme (FAS) provides a good initial guess for the Newton method. Therefore, we propose a new hybrid-FAS-HJFNK method while there is no steam in the reservoir. The numerical results show that the hybrid-FAS-HJFNK method converges faster than the HJFNK method.  相似文献   

Sensitivity of the Gravity Recovery and Climate Experiment (GRACE) to the complexity of aquifer systems for monitoring of groundwater     

Yashwant B. Katpatal  C. Rishma  Chandan K. Singh 《Hydrogeology Journal》2018,26(3):933-943

The Gravity Recovery and Climate Experiment (GRACE) satellite mission is aimed at assessment of groundwater storage under different terrestrial conditions. The main objective of the presented study is to highlight the significance of aquifer complexity to improve the performance of GRACE in monitoring groundwater. Vidarbha region of Maharashtra, central India, was selected as the study area for analysis, since the region comprises a simple aquifer system in the western region and a complex aquifer system in the eastern region. Groundwater-level-trend analyses of the different aquifer systems and spatial and temporal variation of the terrestrial water storage anomaly were studied to understand the groundwater scenario. GRACE and its field application involve selecting four pixels from the GRACE output with different aquifer systems, where each GRACE pixel encompasses 50–90 monitoring wells. Groundwater storage anomalies (GWSA) are derived for each pixel for the period 2002 to 2015 using the Release 05 (RL05) monthly GRACE gravity models and the Global Land Data Assimilation System (GLDAS) land-surface models (GWSA_GRACE) as well as the actual field data (GWSA_Actual). Correlation analysis between GWSA_GRACE and GWSA_Actual was performed using linear regression. The Pearson and Spearman methods show that the performance of GRACE is good in the region with simple aquifers; however, performance is poorer in the region with multiple aquifer systems. The study highlights the importance of incorporating the sensitivity of GRACE in estimation of groundwater storage in complex aquifer systems in future studies.  相似文献