Ensemble-based conditioning of reservoir models to seismic data

While 3D seismic has been the basis for geological model building for a long time, time-lapse seismic has primarily been used in a qualitative manner to assist in monitoring reservoir behavior. With the growing acceptance of assisted history matching methods has come an equally rising interest in incorporating 3D or time-lapse seismic data into the history matching process in a more quantitative manner. The common approach in recent studies has been to invert the seismic data to elastic or to dynamic reservoir properties, typically acoustic impedance or saturation changes. Here we consider the use of both 3D and time-lapse seismic amplitude data based on a forward modeling approach that does not require any inversion in the traditional sense. Advantages of such an approach may be better estimation and treatment of model and measurement errors, the combination of two inversion steps into one by removing the explicit inversion to state space variables, and more consistent dependence on the validity of assumptions underlying the inversion process. In this paper, we introduce this approach with the use of an assisted history matching method in mind. Two ensemble-based methods, the ensemble Kalman filter and the ensemble randomized maximum likelihood method, are used to investigate issues arising from the use of seismic amplitude data, and possible solutions are presented. Experiments with a 3D synthetic reservoir model show that additional information on the distribution of reservoir fluids, and on rock properties such as porosity and permeability, can be extracted from the seismic data. The role for localization and iterative methods are discussed in detail.     

煤层气藏数值模拟垂向网格优化

数值模拟是研究煤层气藏工程的一种常规方法,建立模型时人们常忽略垂向网格精细程度对模拟的影响,无法准确反映出垂向上流体流动规律、气水分异现象以及压降漏斗展布等,对模拟结果有很大影响。为了研究垂向网格划分精度对煤层气藏数值模拟过程的影响,采用不同模拟器对垂向网格的精细程度进行模拟计算,运用渗透率等效方法、局部网格加密方法和模拟器自带压裂方法模拟煤层压裂缝,总共模拟了3种方法15套方案。结果表明,垂向网格划分精度对煤层气生产影响较大,当网格步长达到1.5m时计算结果较为精确,可以满足模拟需求。网格数量及网格步长的合理划分,能够更好地呈现煤层中气水分异现象,有助于分析气水流动状态,便于历史拟合和产量预测。     

A simple and efficient approach to predict reservoir settling volume: case study of Bin El Ouidane reservoir (Morocco)

The negligence of the cumulative deposit volume over years may lead to uselessness of a pre-established and efficient reservoir management method. In this objective, this paper tries to introduce a simple approach to forecast annually the volume lost from the reservoir capacity. The suggested approach employs the modified universal soil loss equation (MUSLE) and the Dendy and Bolton (J Soil Water Conserv 31:264–266, 1976) methods, in addition to the sediment consolidation process. This process permits to follow the evolution of sediment deposit volume throughout the years. For application, we selected the reservoir of Bin El Ouidane (Morocco), for which we have tried to fit a linear regression between sediment yield and observed settling volumes. The optimization process was assured by the algorithm genetic and the OptQuest methods. The results show a high significant (R²?=?0.9513, RMSE?=?8.5428, and p value?=?0.0009) linear regression between cumulative sediment yield volume and accumulated measured lost volume from the reservoir of Bin El Ouidane. The use of a linear relation is justified by the fact that all nonlinear regressions in long term are composed of multiple linear regressions in short term. Nevertheless, this method can become more efficient, and confirmed for real forecasting applications by performing modifications essentially related to in situ measures of different variables. Finally, and considering its simplicity regarding input data and application, the proposed approach converges to efficient results. Therefore, and after validation in other reservoirs, this method can be used to forecast annual reservoir settling at short term.     

A hybrid calibration approach to Hertz-type contact parameters for discrete element models

This study aims at providing a hybrid calibration framework to estimate Hertz-type contact parameters (particle-scale shear modulus and Poisson ratio) for both two-dimensional and three-dimensional discrete element modelling (DEM). On the basis of statistically isotropic granular packings, a set of analytical formulae between macroscopic material parameters (Young modulus and Poisson ratio) and particle-scale Hertz-type contact parameters for granular systems are derived under small-strain isotropic stress conditions. However, the derived analytical solutions are only estimated values for general models. By viewing each DEM modelling as an implicit mathematical function taking the particle-level parameters as independent variables and employing the derived analytical solutions as the initial input parameters, an automatic iterative scheme is proposed to obtain the calibrated parameters with higher accuracies. Considering highly nonlinear features and discontinuities of the macro-micro relationship in Hertz-based discrete element models, the adaptive moment estimation algorithm is adopted in this study because of its capacity of dealing with noise gradients of cost functions. The proposed method is validated with several numerical cases including randomly distributed monodisperse and polydisperse packings. Noticeable improvements in terms of calibration efficiency and accuracy have been made.     

A quantitative approach to fluvial facies models: Methods and example results

Traditional facies models lack quantitative information concerning sedimentological features: this significantly limits their value as references for comparison and guides to interpretation and subsurface prediction. This paper aims to demonstrate how a database methodology can be used to generate quantitative facies models for fluvial depositional systems. This approach is employed to generate a range of models, comprising sets of quantitative information on proportions, geometries, spatial relations and grain sizes of genetic units belonging to three different scales of observation (depositional elements, architectural elements and facies units). The method involves a sequential application of filters to the knowledge base that allows only database case studies that developed under appropriate boundary conditions to contribute to any particular model. Specific example facies models are presented for fluvial environmental types categorized on channel pattern, basin climatic regime and water‐discharge regime; the common adoption of these environmental types allows a straightforward comparison with existing qualitative models. The models presented here relate to: (i) the large‐scale architecture of single‐thread and braided river systems; (ii) meandering sub‐humid perennial systems; (iii) the intermediate‐scale and small‐scale architecture of dryland, braided ephemeral systems; (iv) the small‐scale architecture of sandy meandering systems; and (v) individual architectural features of a specific sedimentary environment (a terminal fluvial system) and its sub‐environments (architectural elements). Although the quantification of architectural properties represents the main advantage over qualitative facies models, other improvements include the capacity: (i) to model on different scales of interest; (ii) to categorize the model on a variety of environmental classes; (iii) to perform an objective synthesis of many real‐world case studies; (iv) to include variability‐related and knowledge‐related uncertainty in the model; and (v) to assess the role of preservation potential by comparing ancient‐system and modern‐system data input to the model.     

A general approach to model interfaces using existing soil constitutive models application to hypoplasticity

The modelling of interfaces is important for the holistic simulation of geotechnical structures (e.g. piles, tunnels and geogrids). For this reason, advanced constitutive interface models and numerical techniques are needed. There are few user-friendly models, and these are rarely implemented. In this paper, a new approach for advanced interface models is proposed. This is based on the assumption that the fully rough interface can be modelled considering simple-shear behaviour at the interface. A 3D soil model is used as a constitutive driver for a frictional subroutine. This minimises the effort required, and advanced interface models are available with less effort. Two different hypoplastic models are used with the new approach. The approach was verified for several aspects (e.g. mesh size dependence), and the volumetric behaviour was studied. The user-friendliness and absence of additional parameters led to more realistic simulation results. The proposed method can be extended to other modelling techniques and will improve the modelling of contacts in soil-structure interaction analysis.     

A scalable multistage linear solver for reservoir models with multisegment wells

Wellbore flow and interactions between wells and the reservoir can be complex. Accurate modeling of these behaviors is especially important for multilateral and other advanced wells. This paper describes a new scalable linear solver for flow simulation of detailed reservoir models with advanced wells and well groups. A general purpose research simulator serves as the computational platform, in which a multisegment well (MsWell) model is used to describe wellbore flow. In the MsWell model, the wellbore is discretized into a number of segments. Hence, the MsWell model adds a large number of equations and unknowns, which are fully coupled to the reservoir model. Operating constraints on groups of wells add one more level of complexity to the system. The new linear solver is a generalized two-stage constrained pressure residual preconditioner. A global pressure system is obtained algebraically in the first stage. The system represents the pressure coupling between the reservoir and wells accurately. The well groups are disaggregated into individual multisegment wells, which then are further reduced to a standard well-like form. The two-stage scheme serves as the inner loop of a generalized minimum residual solver. Algebraic multigrid is used to compute the first-stage pressure solution; a special block-based incomplete lower–upper preconditioner is used for the second stage. We demonstrate the superior performance of this new solver compared with state-of-the-art methods using a variety of highly detailed reservoir models with complex wells and well groups.     

Interoperable processing of digital elevation models in grid infrastructures

Based on the service specifications of the Open Geospatial Consortium (OGC), Spatial Data Infrastructures (SDI) support the visualization, access to vector and raster data or managing and search for spatial data. A standard for distributed spatial data processing was missing for a long time. This issue was addressed by the development of the OpenGIS Web Processing Service (WPS) specification. However, to process and analyze massive Digital Elevation Models (DEM) computing power and disk memory are scarce commodities. Here we show that Grid Computing in combination with OGC Web Services (OWS) is well suited to accomplish high processing performance and storage capacity for large-scale processing tasks of the geo community. To process these massive amounts of geo-data we develop terrain processing services which are made available as grid services. Our results will be demonstrating how to bridge the gap between the grid world and the OGC world for more sophisticated terrain processing.     

Real-time reservoir management: A multiscale adaptive optimization and control approach

We propose a decision-making approach for optimizing the profitability of hydrocarbon reservoirs. The proposed approach addresses the overwhelming complexity of the overall optimization problem by suggesting an oilfield operations hierarchy that entails different time scales. We discuss system identification, optimization, and control that are appropriate at various levels of the hierarchy and capitalize on the abilities of permanently instrumented and remotely actuated fields. Optimization is performed in real-time and is based on feedback. We provide details on real-time identification of hybrid models and their use at the scheduling and supervisory control levels. Case studies using field-calibrated simulation data demonstrate the applicability and value of the proposed approach. Directions for future development are given.     

基于角点网格的煤层三维建模与可视化研究

在煤层气排采分析及数值模拟研究中,煤储层结构的三维建模是数值模拟和结果分析的起点,具有关键作用。三维长方体等传统网格,难以表达地层的起伏变化,角点网格具有表达起伏变化地层的优势。从煤层气动态可视化的角度出发,基于角点网格建立了煤储层三维地质模型。研究了角点网格模型的数据特点及生成角点网格的方法,采用C#编程语言并结合OpenGL图形接口,开发了煤储层三维可视化软件模型,利用该模型表达了山西省沁水盆地潘庄区块的煤储层地质构造。结果表明,角点网格适用于煤储层三维模型的构建,能较好的表达煤层的结构特征。     

储层建模中几种原型模型的建立

储层地质知识库的建立是储层建模过程中极为重要的一步，它为建模提供基本的条件数据及各种统计参数。本文总结了建立地质知识库的主要步骤及基本内容。在资料较少的情况下，需要借助原型模型来提供一些无法直接获得但对建模十分重要的参数，如砂体宽厚比、水平方向变差函数等。文中用3个实例较详细的介绍了建立原型模型的3种主要方法，分别是利用露头、成熟油田和沉积模拟实验建立原型模型，并比较了各自的优缺点。     

Virtual element method for geomechanical simulations of reservoir models

In this paper, we study the use of virtual element method (VEM) for geomechanics. Our emphasis is on applications to reservoir simulations. The physical processes behind the formation of the reservoirs, such as sedimentation, erosion, and faulting, lead to complex geometrical structures. A minimal representation, with respect to the physical parameters of the system, then naturally leads to general polyhedral grids. Numerical methods which can directly handle this representation will be highly favorable, in particular in the setting of advanced work-flows. The virtual element method is a promising candidate to solve the linear elasticity equations on such models. In this paper, we investigate some of the limits of the VEM method when used on reservoir models. First, we demonstrate that care must be taken to make the method robust for highly elongated cells, which is common in these applications, and show the importance of calculating forces in terms of traction on the boundary of the elements for elongated distorted cells. Second, we study the effect of triangulations on the surfaces of curved faces, which also naturally occur in subsurface models. We also demonstrate how a more stable stabilization term for reservoir application can be derived.     

A Bayesian approach to calibrating apatite fission track annealing models for laboratory and geological timescales

We present a new approach for modelling annealing of fission tracks in apatite, aiming to address various problems with existing models. We cast the model in a fully Bayesian context, which allows us explicitly to deal with data and parameter uncertainties and correlations, and also to deal with the predictive uncertainties. We focus on a well-known annealing algorithm [Laslett, G.M., Green, P.F., Duddy, I.R., Gleadow. A.J.W., 1987. Thermal annealing of fission tracks in apatite. 2. A quantitative-analysis. Chem. Geol., 65 (1), 1-13], and build a hierachical Bayesian model to incorporate both laboratory and geological timescale data as direct constraints. Relative to the original model calibration, we find a better (in terms of likelihood) model conditioned just on the reported laboratory data. We then include the uncertainty on the temperatures recorded during the laboratory annealing experiments. We again find a better model, but the predictive uncertainty when extrapolated to geological timescales is increased due to the uncertainty on the laboratory temperatures. Finally, we explictly include a data set [Vrolijk, P., Donelick, R.A., Quenq, J., Cloos. M., 1992. Testing models of fission track annealing in apatite in a simple thermal setting: site 800, leg 129. In: Larson, R., Lancelet, Y. (Eds.), Proceedings of the Ocean Drilling Program, Scientific Results, vol. 129, pp. 169-176] which provides low-temperature geological timescale constraints for the model calibration. When combined with the laboratory data, we find a model which satisfies both the low-temperature and high-temperature geological timescale benchmarks, although the fit to the original laboratory data is degraded. However, when extrapolated to geological timescales, this combined model significantly reduces the well-known rapid recent cooling artifact found in many published thermal models for geological samples.     

Using the DPFT approach to improve flash flood forecasting models

DPFT is a lumped approach for operational flash flood forecasting, based on the unit hydrograph. Using a multi-event alternating iterative algorithm, it identifies a robust and stable average transfer function and a consistent set of effective rainfall series associated with each event at the same time. This key ingredient allows an objective calibration of different loss functions, relating gauged precipitation and effective rainfall. A case study based on an operational French basin (545 km²) is presented. Three lumped production functions have been calibrated and compared. The results show that more elaborate models of loss functions must be proposed, and some possible directions for this are pointed out.Presently at the Institut de Ciences de la Terra Jaume Almera, Apartat 30102, 08080 Barcelona, Spain.Presently at EDF-DTG. Service de Ressources en Eau, BP 4348, 31029 Toulouse Cedex, France.     

Using the DPFT approach to improve flash flood forecasting models

DPFT is a lumped approach for operational flash flood forecasting, based on the unit hydrograph. Using a multi-event alternating iterative algorithm, it identifies a robust and stable average transfer function and a consistent set of effective rainfall series associated with each event at the same time. This key ingredient allows an objective calibration of different loss functions, relating gauged precipitation and effective rainfall. A case study based on an operational French basin (545 km²) is presented. Three lumped production functions have been calibrated and compared. The results show that more elaborate models of loss functions must be proposed, and some possible directions for this are pointed out.     

Evaluation of Gaussian approximations for data assimilation in reservoir models

The Bayesian framework is the standard approach for data assimilation in reservoir modeling. This framework involves characterizing the posterior distribution of geological parameters in terms of a given prior distribution and data from the reservoir dynamics, together with a forward model connecting the space of geological parameters to the data space. Since the posterior distribution quantifies the uncertainty in the geologic parameters of the reservoir, the characterization of the posterior is fundamental for the optimal management of reservoirs. Unfortunately, due to the large-scale highly nonlinear properties of standard reservoir models, characterizing the posterior is computationally prohibitive. Instead, more affordable ad hoc techniques, based on Gaussian approximations, are often used for characterizing the posterior distribution. Evaluating the performance of those Gaussian approximations is typically conducted by assessing their ability at reproducing the truth within the confidence interval provided by the ad hoc technique under consideration. This has the disadvantage of mixing up the approximation properties of the history matching algorithm employed with the information content of the particular observations used, making it hard to evaluate the effect of the ad hoc approximations alone. In this paper, we avoid this disadvantage by comparing the ad hoc techniques with a fully resolved state-of-the-art probing of the Bayesian posterior distribution. The ad hoc techniques whose performance we assess are based on (1) linearization around the maximum a posteriori estimate, (2) randomized maximum likelihood, and (3) ensemble Kalman filter-type methods. In order to fully resolve the posterior distribution, we implement a state-of-the art Markov chain Monte Carlo (MCMC) method that scales well with respect to the dimension of the parameter space, enabling us to study realistic forward models, in two space dimensions, at a high level of grid refinement. Our implementation of the MCMC method provides the gold standard against which the aforementioned Gaussian approximations are assessed. We present numerical synthetic experiments where we quantify the capability of each of the ad hoc Gaussian approximation in reproducing the mean and the variance of the posterior distribution (characterized via MCMC) associated to a data assimilation problem. Both single-phase and two-phase (oil–water) reservoir models are considered so that fundamental differences in the resulting forward operators are highlighted. The main objective of our controlled experiments was to exhibit the substantial discrepancies of the approximation properties of standard ad hoc Gaussian approximations. Numerical investigations of the type we present here will lead to the greater understanding of the cost-efficient, but ad hoc, Bayesian techniques used for data assimilation in petroleum reservoirs and hence ultimately to improved techniques with more accurate uncertainty quantification.     

Geostatistically consistent history matching of 3D oil-and-gas reservoir models

An approach for geostatistically consistent matching of 3D flow simulation models and 3D geological models is proposed. This approach uses an optimization algorithm based on identification of the parameters of the geostatistical model (for example, the variogram parameters, such as range, sill, and nugget effect). Here, the inverse problem is considered in the greatest generality taking into account facies heterogeneity and the variogram anisotropy. The correlation dependence parameters (porosity-to-log permeability) are clarified for each single facies.