High-resolution facies and porosity models of the upper Jurassic Arab-D carbonate reservoir using an outcrop analogue, central Saudi Arabia

Subsurface models of hydrocarbon reservoirs are coarse and of low resolution when compared with the actual geologic characteristics. Therefore, the understanding of the three-dimensional architecture of reservoir units is often incomplete. Outcrop analogues are commonly used to understand the spatial continuity of reservoir units. In this study, a Late Jurassic outcrop analogue for the Arab-D reservoir of central Saudi Arabia was used to build a high-resolution model that captures fine geologic details. Subsurface reservoir lithofacies were matched with those from the studied outcrop, and porosity values derived from published core and well log data from the Ain Dar, Uthmanyah, and Shudgum areas of the Ghawar Field, eastern Saudi Arabia, were then applied to the equivalent lithofacies in the outcrop. Maximum, minimum, and average subsurface porosity for each lithofacies were distributed in the facies model using a geostatistical algorithm to produce nine porosity models for the field data. Several realisations were run to visualise the variability in each model and to quantitatively measure the uncertainty associated with the models. The results indicated that potential reservoir zones were associated with grainstone, packstone, and some wackestone layers. Semivariogram analysis of the lithofacies showed good continuity in the N-S direction and less continuity in the E-W direction. The high-resolution lithofacies models detected permeability barriers and isolated low porosity bodies within the potential reservoir zones. This model revealed the porosity distribution in areas smaller than one cell in the subsurface model and highlighted the uncertainty associated with several aspects of the model.     

A flow-based pattern recognition algorithm for rapid quantification of geologic uncertainty

Geologic uncertainties and limited well data often render recovery forecasting a difficult undertaking in typical appraisal and early development settings. Recent advances in geologic modeling algorithms permit automation of the model generation process via macros and geostatistical tools. This allows rapid construction of multiple alternative geologic realizations. Despite the advances in geologic modeling, computation of the reservoir dynamic response via full-physics reservoir simulation remains a computationally expensive task. Therefore, only a few of the many probable realizations are simulated in practice. Experimental design techniques typically focus on a few discrete geologic realizations as they are inherently more suitable for continuous engineering parameters and can only crudely approximate the impact of geology. A flow-based pattern recognition algorithm (FPRA) has been developed for quantifying the forecast uncertainty as an alternative. The proposed algorithm relies on the rapid characterization of the geologic uncertainty space represented by an ensemble of sufficiently diverse static model realizations. FPRA characterizes the geologic uncertainty space by calculating connectivity distances, which quantify how different each individual realization is from all others in terms of recovery response. Fast streamline simulations are employed in evaluating these distances. By applying pattern recognition techniques to connectivity distances, a few representative realizations are identified within the model ensemble for full-physics simulation. In turn, the recovery factor probability distribution is derived from these intelligently selected simulation runs. Here, FPRA is tested on an example case where the objective is to accurately compute the recovery factor statistics as a function of geologic uncertainty in a channelized turbidite reservoir. Recovery factor cumulative distribution functions computed by FPRA compare well to the one computed via exhaustive full-physics simulations.     

地震波阻抗约束下的储层地质建模方法与实践

以地质统计学为基础的三维地质建模技术已成为当今储层精细描述中的一项关键技术,但该项技术存在着一个最大的限制就是对硬数据的密度要求十分苛刻,因而多用于井网密度大的已开发区的储层精细描述。而在勘探区块,多采用地震属性资料作为软约束,来弥补资料不足的缺陷。本文以我国海上某油田为例,探讨了应用地震反演资料约束三维储层建模的几种方法,并提出"多条件、多级约束"的建模策略。研究表明,有效地应用包括地震信息在内的多学科信息进行岩相随机建模,能有效地弥补井间信息不足的缺陷,降低地质模型的不确定性,所建立的模型能很好地综合井资料的纵向高精度和地震资料的横向高精度信息,可以成功地应用三维随机建模技术解决勘探开发阶段的储层精细描述问题。     

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.      

Compressed History Matching: Exploiting Transform-Domain Sparsity for Regularization of Nonlinear Dynamic Data Integration Problems

In this paper, we present a new approach for estimating spatially-distributed reservoir properties from scattered nonlinear dynamic well measurements by promoting sparsity in an appropriate transform domain where the unknown properties are believed to have a sparse approximation. The method is inspired by recent advances in sparse signal reconstruction that is formalized under the celebrated compressed sensing paradigm. Here, we use a truncated low-frequency discrete cosine transform (DCT) is redundant to approximate the spatial parameters with a sparse set of coefficients that are identified and estimated using available observations while imposing sparsity on the solution. The intrinsic continuity in geological features lends itself to sparse representations using selected low frequency DCT basis elements. By recasting the inversion in the DCT domain, the problem is transformed into identification of significant basis elements and estimation of the values of their corresponding coefficients. To find these significant DCT coefficients, a relatively large number of DCT basis vectors (without any preferred orientation) are initially included in the approximation. Available measurements are combined with a sparsity-promoting penalty on the DCT coefficients to identify coefficients with significant contribution and eliminate the insignificant ones. Specifically, minimization of a least-squares objective function augmented by an l ₁-norm of DCT coefficients is used to implement this scheme. The sparsity regularization approach using the l ₁-norm minimization leads to a better-posed inverse problem that improves the non-uniqueness of the history matching solutions and promotes solutions that are, according to the prior belief, sparse in the transform domain. The approach is related to basis pursuit (BP) and least absolute selection and shrinkage operator (LASSO) methods, and it extends the application of compressed sensing to inverse modeling with nonlinear dynamic observations. While the method appears to be generally applicable for solving dynamic inverse problems involving spatially-distributed parameters with sparse representation in any linear complementary basis, in this paper its suitability is demonstrated using low frequency DCT basis and synthetic waterflooding experiments.     

岩性约束反演方法及应用

本文采用非线性反演技术建立了岩性约束反演计算方法，用于地层岩性解释和储层模拟、描述等方面。文中讨论了岩性正演数学模型的建立、初始模型的选取和约束条件对反演结果的影响。给出了综合利用地震、测井和地质资料计算孔隙度和泥质含量的反演结果，并分析了反演精度。理论模型计算结果说明了岩性约束反演的可行性和正确性。并给出Ｓｕｎ工作站上应用该软件处理某油田实际资料的岩性反演结果。     

A Methodology for Establishing a Data Reliability Measure for Value of Spatial Information Problems

We propose a value of information (VOI) methodology for spatial Earth problems. VOI is a tool to determine whether purchasing a new information source would improve a decision-makers’ chances of taking the optimal action. A prior uncertainty assessment of key geologic parameters and a reliability of the data to resolve them are necessary to make a VOI assessment. Both of these elements are challenging to obtain, as this assessment is made before the information is acquired. We present a flexible prior geologic uncertainty modeling scheme that allows for the inclusion of many types of spatial parameter. Next, we describe how to obtain a physics-based reliability measure by simulating the geophysical measurement on the generated prior models and interpreting the simulated data. Repeating this simulation and interpretation for all datasets, a frequency table can be obtained that describes how many times a correct or false interpretation was made by comparing them to their respective original model. This frequency table is the reliability measure and allows a more realistic VOI calculation. An example VOI calculation is demonstrated for a spatial decision related to aquifer recharge where two geophysical techniques are considered for their ability to resolve channel orientations. As necessitated by spatial problems, this methodology preserves the structure, influence and dependence of spatial variables through the prior geological modeling and the explicit geophysical simulation and interpretations.     

Geologic uncertainty in a regulatory environment: An example from the potential Yucca Mountain nuclear waste repository site

Regulatory geologists are concerned with predicting the performance of sites proposed for waste disposal or for remediation of existing pollution problems. Geologic modeling of these sites requires large-scale expansion of knowledge obtained from very limited sampling. This expansion induces considerable uncertainty into the geologic models of rock properties that are required for modeling the predicted performance of the site.One method for assessing this uncertainty is through nonparametric geostatistical simulation. Simulation can produce a series of equiprobable models of a rock property of interest. Each model honors measured values at sampled locations, and each can be constructed to emulate both the univariate histogram and the spatial covariance structure of the measured data. Computing a performance model for a number of geologic simulations allows evaluation of the effects of geologic uncertainty. A site may be judged acceptable if the number of failures to meet a particular performance criterion produced by these computations is sufficiently low. A site that produces too many failures may be either unacceptable or simply inadequately described.The simulation approach to addressing geologic uncertainty is being applied to the potential high-level nuclear waste repository site at Yucca Mountain, Nevada, U.S.A. Preliminary geologic models of unsaturated permeability have been created that reproduce observed statistical properties reasonably well. A spread of unsaturated groundwater travel times has been computed that reflects the variability of those geologic models. Regions within the simulated models exhibiting the greatest variability among multiple runs are candidates for obtaining the greatest reduction in uncertainty through additional site characterization.     

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(英文)

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。     

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.

     

地质统计学反演及其在吉林扶余油田储层预测中的应用

地质统计学反演方法将随机建模技术与常规地震反演相结合,有效地综合地质、测井和三维地震数据,可以更加精确地描述储层的变化.在执行地质统计学反演前,首先应用稀疏脉冲约束反演,了解储层的大致分布,以求取子波和水平变差函数.地质统计学反演从井点出发,井间以原始地震数据作为硬数据,通过随机模拟的产生井间波阻抗,然后将波阻抗转换成反射系数,并用确定性反演方法求得的子波褶积产生地震道,通过反复迭代直至合成地震道与原始地震数据达到一定程度的匹配,反演结果是多个等概率的波阻抗数据体实现.反演结果符合输入数据的地质统计学特征并受地质模型的约束,它综合了测井的垂向分辨率高和地震的横向分辨率高的优势,结果的多个实现用于不确定性评价.     

Spectral Simulation and Conditioning to Local Continuity Trends in Geologic Modeling

Spectral simulation has gained application in building geologic models due to the advantage of better honoring the spatial continuity of petrophysical properties, such as reservoir porosity and shale volume. Distinct from sequential simulation methods, spectral simulation is a global algorithm in the sense that a global density spectrum is calculated once and the inverse Fourier transform is performed on the Fourier coefficient also only once to generate a simulation realization. The generated realizations honor the spatial continuity structure globally over the whole field instead of only within a search neighborhood, as with sequential simulation algorithms. However, the disadvantage of global spectral simulation is that it traditionally cannot account for the local information such as the local continuity trends, which are often observed in reservoirs and hence are important to be accounted for in geologic models. This disadvantage has limited wider application of spectral simulation in building geologic models. In this paper, we present ways of conditioning geologic models to the relevant local information. To account for the local continuity trends, we first scale different frequency components of the original model with local-amplitude spectrum ratios that are specific to the local trend. The sum of these scaled frequency components renders a new model that displays the desired local continuity trend. The implementation details of this new method are discussed and examples are provided to illustrate the algorithm.     

Inverse trishear modeling of bedding dip data using Markov chain Monte Carlo methods

We present a method for fitting trishear models to surface profile data, by restoring bedding dip data and inverting for model parameters using a Markov chain Monte Carlo method. Trishear is a widely-used kinematic model for fault-propagation folds. It lacks an analytic solution, but a variety of data inversion techniques can be used to fit trishear models to data. Where the geometry of an entire folded bed is known, models can be tested by restoring the bed to its pre-folding orientation. When data include bedding attitudes, however, previous approaches have relied on computationally-intensive forward modeling. This paper presents an equation for the rate of change of dip in the trishear zone, which can be used to restore dips directly to their pre-folding values. The resulting error can be used to calculate a probability for each model, which allows solution by Markov chain Monte Carlo methods and inversion of datasets that combine dips and contact locations. These methods are tested using synthetic and real datasets. Results are used to approximate multimodal probability density functions and to estimate uncertainty in model parameters. The relative value of dips and contacts in constraining parameters and the effects of uncertainty in the data are investigated.     

三维地质结构模型精度评估理论与误差修正方法研究

三维地质模型精度评估与误差修正问题已成为制约三维地质模拟技术深入发展应用的瓶颈。在综合国内外研究现状与发展趋势的基础上,提出了三维地质结构模型精度评估、误差检测、动态修正的总体研究框架。在模型精度评估方面,提出分别构建三维地质结构模型精度评估的一般理论模型、面向特定地质体的实际操作模型和地质结构构造不确定性的三维空间分布模型的研究思路,指出应重点研究地质实体自身特性、三维地质建模方法对三维地质结构模型精度的影响,解决由一般地质界面的内插误差和特殊地质体的外推误差引起的精度评估问题。在模型误差修正方面,提出基于建模初始数据的模型误差修正方法和基于建模中间结果的模型误差修正方法,在具体实现时,引入“数据 模型的可视化交互技术”。这些研究成果为建立一套完整的三维地质结构模型精度评估与误差修正的理论体系和方法体系奠定了基础,有助于完善复杂地质条件下三维地质模拟的方法与技术。     

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.     

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.     

Sensitivity and uncertainty analyses for performance assessment modeling

Sensitivity and uncertainty analyses methods for computer models are being applied in performance assessment modeling in the geologic high-level radioactive-waste repository program. The models used in performance assessment tend to be complex physical/chemical models with large numbers of input variables. There are two basic approaches to sensitivity and uncertainty analyses: deterministic and statistical. The deterministic approach to sensitivity analysis involves numerical calculation or employs the adjoint form of a partial differential equation to compute partial derivatives; the uncertainty analysis is based on Taylor series expansions of the input variables propagated through the model to compute means and variances of the output variable. The statistical approach to sensitivity analysis involves a response surface approximation to the model with the sensitivity coefficients calculated from the response surface parameters; the uncertainty analysis is based on simulation. The methods each have strengths and weaknesses.     

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.