在储层建模中利用多点地质统计学整合地质概念模型及其解释

基于三维空间中稀疏的观测数据,地质学家和储层建模人员尝试预测井间的地质沉积相的空间非均质性时,地质概念模型和先验认识在其中扮演着重要的角色。这种整合先验模型或解释的过程有时是隐蔽或不易察觉的,正如在手工绘等值线图中的情形;它也能够被显式地运用到某种算法当中,比如数字绘图中的算法。新近兴起的多点地质统计学为地质学家和储层建模人员提供了一种有力工具,它强调使用训练图像把先验模型明确而定量地引入到储层建模当中。先验地质模型包含了被研究的真实储层中确信存在的样式,而训练图像则是该模型的定量化表达。通过再现高阶统计量,多点算法能够从训练图像中捕捉复杂的(非线性)特征样式并把它们锚定到观测的井位数据。文中描述了多点地质统计学原理,以突出训练图像概念重要性为主线,描述了多点地质统计学在建立三维储层模型中的应用。     

三维地震约束辫状河储层的多点统计建模研究:以委内瑞拉M区块为例

将地震信息引入多点统计地质建模之中,可以提高模型的井间预测功能.首先以委内瑞拉奥里诺科重油带一个辫状河沉积含油区块为例,结合该区辫状河储层的地质特点,利用井震信息结合的多点统计建模方法,研究了波阻抗的相标定、砂体概率生成曲线选定、训练图像分析、井震影响比等方面的技术细节及它们在辫状河储层多点统计建模中的作用.然后结合辫状河储层的沉积学特征,对研究区的心滩、河道、泛滥平原等微相空间分布的建模结果进行了分析.最后对于不同的储层建模结果进行了不确定性分析.研究表明:井震结合的多点统计建模方法,较好地降低了稀井网地区建模结果的不确定性;通过砂岩概率生成曲线,波阻抗数据转化为地震相的空间概率分布.这样就有效地建立起了地震数据与其地质意义的联系;相比仅用测井信息建模,井震结合建模结果对井间微相预测更具合理性,同时预测的河道、心滩的连续性也得到了更好的体现.      

迎接油气储层建模理论、应用的大发展——从2007年国际石油地质统计学大会谈起

2007年国际石油地质统计学大会的成果表明,运用地质研究、地震解释、生产动态三方面的数据并与模型相结合,是当前油气储层建模理论和应用的一个发展趋势。油藏描述、油藏表征及储层建模发展的整个过程,始终体现了这种多学科的融合。由于地质统计学的促进,储层建模技术具备了分析和处理各种主要由地下地质环境引起的不确定性的能力。地质研究对储层建模的核心作用主要体现为相控建模原则的确立和地质概念模型的应用上。最后,研究了储层建模中地震数据的参与和生产动态数据的结合等方面的发展。     

Facies Modeling Using a Markov Mesh Model Specification

The spatial continuity of facies is one of the key factors controlling flow in reservoir models. Traditional pixel-based methods such as truncated Gaussian random fields and indicator simulation are based on only two-point statistics, which is insufficient to capture complex facies structures. Current methods for multi-point statistics either lack a consistent statistical model specification or are too computer intensive to be applicable. We propose a Markov mesh model based on generalized linear models for geological facies modeling. The approach defines a consistent statistical model that is facilitated by efficient estimation of model parameters and generation of realizations. Our presentation includes a formulation of the general framework, model specifications in two and three dimensions, and details on how the parameters can be estimated from a training image. We illustrate the method using multiple training images, including binary and trinary images and simulations in two and three dimensions. We also do a thorough comparison to the snesim approach. We find that the current model formulation is applicable for multiple training images and compares favorably to the snesim approach in our test examples. The method is highly memory efficient.     

两种沉积相建模方法的对比分析

在油田开发方案设计阶段,基础地质资料尤其是钻井资料相对较少,因此对储层分布的认识具有较大的不确定性。沉积相建模为储层分布不确定性的定量表征提供了技术手段,但每种沉积相建模方法具有各自的适应性。以渤海P油田为例,分别应用布尔模拟和示性点过程模拟方法,以河道带和河道内砂体为描述对象建立了2种沉积相模型,定量表征2种储层分布模式,分析2种模拟结果的储层分布规律,指出以河道内砂体为描述对象的建模方法提供了该油田储层分布的最可能模式,而以河道带为描述对象的建模方法提供了储层分布的另一种可能模式,为油藏数值模拟方案设计和敏感性分析提供了地质依据。     

Multiple-Point Simulation with an Existing Reservoir Model as Training Image

The multiple-point simulation (MPS) method has been increasingly used to describe the complex geologic features of petroleum reservoirs. The MPS method is based on multiple-point statistics from training images that represent geologic patterns of the reservoir heterogeneity. The traditional MPS algorithm, however, requires the training images to be stationary in space, although the spatial distribution of geologic patterns/features is usually nonstationary. Building geologically realistic but statistically stationary training images is somehow contradictory for reservoir modelers. In recent research on MPS, the concept of a training image has been widely extended. The MPS approach is no longer restricted by the size or the stationarity of training images; a training image can be a small geometrical element or a full-field reservoir model. In this paper, the different types of training images and their corresponding MPS algorithms are first reviewed. Then focus is placed on a case where a reservoir model exists, but needs to be conditioned to well data. The existing model can be built by process-based, object-based, or any other type of reservoir modeling approach. In general, the geologic patterns in a reservoir model are constrained by depositional environment, seismic data, or other trend maps. Thus, they are nonstationary, in the sense that they are location dependent. A new MPS algorithm is proposed that can use any existing model as training image and condition it to well data. In particular, this algorithm is a practical solution for conditioning geologic-process-based reservoir models to well data.     

Using Sequential Indicator Simulation as a Tool in Reservoir Description: Issues and Uncertainties

Flow simulation studies require an accurate model of the reservoir in terms of its sedimentological architecture. Pixel-based reservoir modeling techniques are often used to model this architecture. There are, however, two problem areas with such techniques. First, several statistical parameters have to be provided whose influence on the resulting model is not readily inferable. Second, conditioning the models to relevant geological data that carry great uncertainty on their own adds to the difficulty of obtaining reliable models and assessing model reliability. The Sequential Indicator Simulation (SIS) method has been used to examine the impact of such uncertainties on the final reservoir model. The effects of varying variogram types, frequencies of lithology occurrence, and the gridblock model orientation with respect to the sedimentological trends are illustrated using different reservoir modeling studies. Results indicate, for example, that the choice of variogram type can have a significant impact on the facies model. Also, reproduction of sedimentological trends and large geometries requires careful parameter selection. By choosing the appropriate modeling strategy, sedimentological principles can be translated into the numerical model. Solutions for dealing with such issues and the geological uncertainties are presented. In conclusion, each reservoir modeling study should begin by developing a thorough quantitative sedimentological understanding of the reservoir under study, followed by detailed sensitivity analyses of relevant statistical and geological parameters.     

Adaptive Conditioning of Multiple-Point Statistical Facies Simulation to Flow Data with Probability Maps

Multiple-point statistics (MPS) provides a flexible grid-based approach for simulating complex geologic patterns that contain high-order statistical information represented by a conceptual prior geologic model known as a training image (TI). While MPS is quite powerful for describing complex geologic facies connectivity, conditioning the simulation results on flow measurements that have a nonlinear and complex relation with the facies distribution is quite challenging. Here, an adaptive flow-conditioning method is proposed that uses a flow-data feedback mechanism to simulate facies models from a prior TI. The adaptive conditioning is implemented as a stochastic optimization algorithm that involves an initial exploration stage to find the promising regions of the search space, followed by a more focused search of the identified regions in the second stage. To guide the search strategy, a facies probability map that summarizes the common features of the accepted models in previous iterations is constructed to provide conditioning information about facies occurrence in each grid block. The constructed facies probability map is then incorporated as soft data into the single normal equation simulation (snesim) algorithm to generate a new candidate solution for the next iteration. As the optimization iterations progress, the initial facies probability map is gradually updated using the most recently accepted iterate. This conditioning process can be interpreted as a stochastic optimization algorithm with memory where the new models are proposed based on the history of the successful past iterations. The application of this adaptive conditioning approach is extended to the case where multiple training images are proposed as alternative geologic scenarios. The advantages and limitations of the proposed adaptive conditioning scheme are discussed and numerical experiments from fluvial channel formations are used to compare its performance with non-adaptive conditioning techniques.     

Conditioning of Multiple-Point Statistics Facies Simulations to Tomographic Images

Geophysical tomography captures the spatial distribution of the underlying geophysical property at a relatively high resolution, but the tomographic images tend to be blurred representations of reality and generally fail to reproduce sharp interfaces. Such models may cause significant bias when taken as a basis for predictive flow and transport modeling and are unsuitable for uncertainty assessment. We present a methodology in which tomograms are used to condition multiple-point statistics (MPS) simulations. A large set of geologically reasonable facies realizations and their corresponding synthetically calculated cross-hole radar tomograms are used as a training image. The training image is scanned with a direct sampling algorithm for patterns in the conditioning tomogram, while accounting for the spatially varying resolution of the tomograms. In a post-processing step, only those conditional simulations that predicted the radar traveltimes within the expected data error levels are accepted. The methodology is demonstrated on a two-facies example featuring channels and an aquifer analog of alluvial sedimentary structures with five facies. For both cases, MPS simulations exhibit the sharp interfaces and the geological patterns found in the training image. Compared to unconditioned MPS simulations, the uncertainty in transport predictions is markedly decreased for simulations conditioned to tomograms. As an improvement to other approaches relying on classical smoothness-constrained geophysical tomography, the proposed method allows for: (1) reproduction of sharp interfaces, (2) incorporation of realistic geological constraints and (3) generation of multiple realizations that enables uncertainty assessment.     

Bayesian model selection for complex geological structures using polynomial chaos proxy

Different interpretation of sedimentary environments lead to “scenario uncertainty” where the prior reservoir model has a high level of discrete uncertainty. In a real field application, the scenario uncertainty has a considerable effect on flow response uncertainty and makes the uncertainty quantification problem highly nonlinear. We use clustering methods to address the scenario uncertainty. Our approach to cluster analysis is based on the posterior probabilities of models, known as “Bayesian model selection.” Accordingly, we integrate overall possible parameters in each scenario with respect to their corresponding priors to give the measure of how well a model is supported by observations. We propose a cluster-based reduced terms polynomial chaos proxy to efficiently estimate the posterior probability density function under each cluster and calculate the posterior probability of each model. We demonstrate that the convergence rate of the reduced terms polynomial chaos proxy is significantly improved under each cluster comparing to the non-clustered case. We apply the proposed cluster-based polynomial chaos proxy framework to study the plausibility of three training images based on different geological interpretation of the second layer of synthetic Stanford VI reservoir. We demonstrate that the proposed workflow can be efficiently used to calculate the posterior probability of each scenario and also sample from the posterior facies models within each scenario.     

Lithofacies modeling by multipoint statistics and economic evaluation by NPV volume for the early Cretaceous Wabiskaw Member in Athabasca oilsands area,Canada

The static modeling and dynamic simulation are essential and critical processes in petroleum exploration and development. In this study, lithofacies models for Wabiskaw Member in Athabasca, Canada are generated by multipoint statistics(MPS) and then compared with the models built by sequential indicator simulation(SIS). Three training images(Tls) are selected from modern depositional environments;the Orinoco River Delta estuary, Cobequid bay-Salmon River estuary, and Danube River delta environment. In order to validate lithofacies models, average and variance of similarity in lithofacies are calculated through random and zonal blind-well tests.In random six-blind-well test, similarity average of MPS models is higher than that of SIS model. The Salmon MPS model closely resembles facies pattern of Wabiskaw Member in subsurface. Zonal blind-well tests show that successful lithofacies modeling for transitional depositional setting requires additional or proper zonation information on horizontal variation, vertical proportion, and secondary data.As Wabiskaw Member is frontier oilsands lease, it is impossible to evaluate the economics from production data or dynamic simulation. In this study, a dynamic steam assisted gravity drainage(SAGD)performance indicator(SPIDER) on the basis of reservoir characteristics is calculated to build 3 D reservoir model for the evaluation of the SAGD feasibility in Wabiskaw Member. SPIDER depends on reservoir properties, economic limit of steam-oil ratio, and bitumen price. Reservoir properties like porosity,permeability, and water saturation are measured from 13 cores and calculated from 201 well-logs. Three dimensional volumes of reservoir properties are constructed mostly based on relationships among properties. Finally, net present value(NPV) volume can be built by equation relating NPV and SPIDER. The economic area exceeding criterion of US$ 10,000 is identified, and the ranges of reservoir properties are estimated. NPV-volume-generation workflow from reservoir parameter to static model provides costand time-effective method to evaluate the oilsands SAGD project.     

GANSim: Conditional Facies Simulation Using an Improved Progressive Growing of Generative Adversarial Networks (GANs)

Conditional facies modeling combines geological spatial patterns with different types of observed data, to build earth models for predictions of subsurface resources. Recently, researchers have used generative adversarial networks (GANs) for conditional facies modeling, where an unconditional GAN is first trained to learn the geological patterns using the original GAN’s loss function, then appropriate latent vectors are searched to generate facies models that are consistent with the observed conditioning data. A problem with this approach is that the time-consuming search process needs to be conducted for every new conditioning data. As an alternative, we improve GANs for conditional facies simulation (called GANSim) by introducing an extra condition-based loss function and adjusting the architecture of the generator to take the conditioning data as inputs, based on progressive growing of GANs. The condition-based loss function is defined as the inconsistency between the input conditioning value and the corresponding characteristics exhibited by the output facies model, and forces the generator to learn the ability of being consistent with the input conditioning data, together with the learning of geological patterns. Our input conditioning factors include global features (e.g., the mud facies proportion) alone, local features such as sparse well facies data alone, and joint combination of global features and well facies data. After training, we evaluate both the quality of generated facies models and the conditioning ability of the generators, by manual inspection and quantitative assessment. The trained generators are quite robust in generating high-quality facies models conditioned to various types of input conditioning information.

     

A Stochastic Object Model Conditioned to High-Quality Seismic Data

We present an approach for modeling facies bodies in which a highly constrained stochastic object model is used to integrate detailed seismic interpretation of the reservoir’s sedimentological architecture directly in a three-dimensional reservoir model. The approach fills the gap between the use of seismic data in a true deterministic sense, in which the facies body top and base are resolved and mapped directly, and stochastic methods in which the relationship between seismic attributes and facies is defined by conditional probabilities. The lateral geometry of the facies bodies is controlled by seismic interpretations on horizon slices or by direct body extraction, whereas facies body thickness and cross-sectional shape are defined by a mixture of seismic data, well data, and user defined object shapes. The stochastic terms in the model are used to incorporate local geometric variability, which is used to increase the geological realism of the facies bodies and allow for correct, flexible well conditioning. The result is a set of three-dimensional facies bodies that are constrained to the seismic interpretations and well data. Each body is defined as a parametric object that includes information such as location of the body axis, depositional direction, axis-to-margin normals, and external body geometry. The parametric information is useful for defining geologically realistic intrabody petrophysical trends and for controlling connectivity between stacked facies bodies.     

A Multiple Training Image Approach for Spatial Modeling of Geologic Domains

Characterization of complex geological features and patterns remains one of the most challenging tasks in geostatistics. Multiple point statistics (MPS) simulation offers an alternative to accomplish this aim by going beyond classical two-point statistics. Reproduction of features in the final realizations is achieved by borrowing high-order spatial statistics from a training image. Most MPS algorithms use one training image at a time chosen by the geomodeler. This paper proposes the use of multiple training images simultaneously for spatial modeling through a scheme of data integration for conditional probabilities known as a linear opinion pool. The training images (TIs) are based on the available information and not on conceptual geological models; one image comes from modeling the categories by a deterministic approach and another comes from the application of conventional sequential indicator simulation. The first is too continuous and the second too random. The mixing of TIs requires weights for each of them. A methodology for calibrating the weights based on the available drillholes is proposed. A measure of multipoint entropy along the drillholes is matched by the combination of the two TIs. The proposed methodology reproduces geologic features from both TIs with the correct amount of continuity and variability. There is no need for a conceptual training image from another modeling technique; the data-driven TIs permit a robust inference of spatial structure from reasonably spaced drillhole data.     

Stochastic simulation of categorical variables using a classification algorithm and simulated annealing

An important step of reservoir characterization is the stochastic modeling of the geometry of lithofacies which control large-scale heterogeneities of petrophysical properties. Although multiple realizations are necessary to appreciate the uncertainty in the spatial distribution of facies, a common short cut consists of retaining the first realization drawn. This paper presents an alternative to this potentially hazardous selection: (1) a categorical map is generated by allocating a single facies to each grid node according to the local probabilities of occurrence of the facies, and (2) the map then is post-processed using a steepest descent-type algorithm so as to improve reproduction of spatial continuity and transition probabilities between facies. The procedure is illustrated using a synthetic dataset. A waterflood simulation shows that retaining a single realization would yield, in average, larger errors in production forecasts (water cuts and recovered oil) than the single postprocessed facies map.     

Conditioning generative adversarial networks on nonlinear data for subsurface flow model calibration and uncertainty quantification

Conditioning complex subsurface flow models on nonlinear data is complicated by the need to preserve the expected geological connectivity patterns to maintain solution plausibility. Generative adversarial networks (GANs) have recently been proposed as a promising approach for low-dimensional representation of complex high-dimensional images. The method has also been adopted for low-rank parameterization of complex geologic models to facilitate uncertainty quantification workflows. A difficulty in adopting these methods for subsurface flow modeling is the complexity associated with nonlinear flow data conditioning. While conditional GAN (CGAN) can condition simulated images on labels, application to subsurface problems requires efficient conditioning workflows for nonlinear data, which is far more complex. We present two approaches for generating flow-conditioned models with complex spatial patterns using GAN. The first method is through conditional GAN, whereby a production response label is used as an auxiliary input during the training stage of GAN. The production label is derived from clustering of the flow responses of the prior model realizations (i.e., training data). The underlying assumption of this approach is that GAN can learn the association between the spatial features corresponding to the production responses within each cluster. An alternative method is to use a subset of samples from the training data that are within a certain distance from the observed flow responses and use them as training data within GAN to generate new model realizations. In this case, GAN is not required to learn the nonlinear relation between production responses and spatial patterns. Instead, it is tasked to learn the patterns in the selected realizations that provide a close match to the observed data. The conditional low-dimensional parameterization for complex geologic models with diverse spatial features (i.e., when multiple geologic scenarios are plausible) performed by GAN allows for exploring the spatial variability in the conditional realizations, which can be critical for decision-making. We present and discuss the important properties of GAN for data conditioning using several examples with increasing complexity.

     

Data Assimilation in Truncated Plurigaussian Models: Impact of the Truncation Map

Assimilation of production data into reservoir models for which the distribution of porosity and permeability is largely controlled by facies has become increasingly common. When the locations of the facies bodies must be conditioned to observations, the truncated plurigaussian model has been often shown to be a useful method for modeling as it allows gaussian variables to be updated instead of facies types. Previous experience has also shown that ensemble Kalman filter-like methods are particularly effective for assimilation of data into truncated plurigaussian models. In this paper, some limitations are shown of the ensemble-based or gradient-based methods when applied to truncated plurigaussian models of a certain type that is likely to occur for modeling channel facies. It is also shown that it is possible to improve the data match and increase the ensemble spread by modifying the updating step using an approximate derivative of the truncation map.     

Training Images from Process-Imitating Methods

The lack of a suitable training image is one of the main limitations of the application of multiple-point statistics (MPS) for the characterization of heterogeneity in real case studies. Process-imitating facies modeling techniques can potentially provide training images. However, the parameterization of these process-imitating techniques is not straightforward. Moreover, reproducing the resulting heterogeneous patterns with standard MPS can be challenging. Here the statistical properties of the paleoclimatic data set are used to select the best parameter sets for the process-imitating methods. The data set is composed of 278 lithological logs drilled in the lower Namoi catchment, New South Wales, Australia. A good understanding of the hydrogeological connectivity of this aquifer is needed to tackle groundwater management issues. The spatial variability of the facies within the lithological logs and calculated models is measured using fractal dimension, transition probability, and vertical facies proportion. To accommodate the vertical proportions trend of the data set, four different training images are simulated. The grain size is simulated alongside the lithological codes and used as an auxiliary variable in the direct sampling implementation of MPS. In this way, one can obtain conditional MPS simulations that preserve the quality and the realism of the training images simulated with the process-imitating method. The main outcome of this study is the possibility of obtaining MPS simulations that respect the statistical properties observed in the real data set and honor the observed conditioning data, while preserving the complex heterogeneity generated by the process-imitating method. In addition, it is demonstrated that an equilibrium of good fit among all the statistical properties of the data set should be considered when selecting a suitable set of parameters for the process-imitating simulations.