Dynamic data integration for structural modeling: model screening approach using a distance-based model parameterization

This paper proposes a novel history-matching method where reservoir structure is inverted from dynamic fluid flow response. The proposed workflow consists of searching for models that match production history from a large set of prior structural model realizations. This prior set represents the reservoir structural uncertainty because of interpretation uncertainty on seismic sections. To make such a search effective, we introduce a parameter space defined with a “similarity distance” for accommodating this large set of realizations. The inverse solutions are found using a stochastic search method. Realistic reservoir examples are presented to prove the applicability of the proposed method.     

Bayesian estimation of reservoir properties—effects of uncertainty quantification of 4D seismic data

This paper shows a history matching workflow with both production and 4D seismic data where the uncertainty of seismic data for history matching comes from Bayesian seismic waveform inversion. We use a synthetic model and perform two seismic surveys, one before start of production and the second after 1 year of production. From the first seismic survey, we estimate the contrast in slowness squared (with uncertainty) and use this estimate to generate an initial estimate of porosity and permeability fields. This ensemble is then updated using the second seismic survey (after inversion to contrasts) and production data with an iterative ensemble smoother. The impact on history matching results from using different uncertainty estimates for the seismic data is investigated. From the Bayesian seismic inversion, we get a covariance matrix for the uncertainty and we compare using the full covariance matrix with using only the diagonal. We also compare with using a simplified uncertainty estimate that does not come from the seismic inversion. The results indicate that it is important not to underestimate the noise in seismic data and that having information about the correlation in the error in seismic data can in some cases improve the results.     

An approximate dynamic programming approachto decision making in the presence of uncertainty for surfactant-polymer flooding

The least squares Monte Carlo method is a decision evaluation method that can capture the effect of uncertainty and the value of flexibility of a process. The method is a stochastic approximate dynamic programming approach to decision making. It is based on a forward simulation coupled with a recursive algorithm which produces the near-optimal policy. It relies on the Monte Carlo simulation to produce convergent results. This incurs a significant computational requirement when using this method to evaluate decisions for reservoir engineering problems because this requires running many reservoir simulations. The objective of this study was to enhance the performance of the least squares Monte Carlo method by improving the sampling method used to generate the technical uncertainties used in obtaining the production profiles. The probabilistic collocation method has been proven to be a robust and efficient uncertainty quantification method. By using the sampling methods of the probabilistic collocation method to approximate the sampling of the technical uncertainties, it is possible to significantly reduce the computational requirement of running the decision evaluation method. Thus, we introduce the least squares probabilistic collocation method. The decision evaluation considered a number of technical and economic uncertainties. Three reservoir case studies were used: a simple homogeneous model, the PUNQ-S3 model, and a modified portion of the SPE10 model. The results show that using the sampling techniques of the probabilistic collocation method produced relatively accurate responses compared with the original method. Different possible enhancements were discussed in order to practically adapt the least squares probabilistic collocation method to more realistic and complex reservoir models. Furthermore, it is desired to perform the method to evaluate high-dimensional decision scenarios for different chemical enhanced oil recovery processes using real reservoir data.     

薄窄砂体地震跟踪预测方法

大庆长垣西部地区葡萄花油层主要发育水下分流河道和小片席状砂,砂体厚度1~3 m,横向变化快,分布零散,地震储层预测精度受到限制,给油藏评价和开发带来较大风险。为了提高薄窄砂体预测精度,以古龙油田为例,提出了分步逐级井震联合反演方法:以岩石物理响应特征分析为基础,优选反演方法,优化流程参数,不断增加滚动井数,通过5批161口开发井的优选及调整,砂体预测精度不断提高,确保了该油田初步开发方案实施效果,形成了可以推广应用的滚动预测跟踪调整的工作流程。     

An integrative approach to robust design and probabilistic risk assessment for CO<Subscript>2</Subscript> storage in geological formations

CO₂ storage in geological formations is currently being discussed intensively as a technology with a high potential for mitigating CO₂ emissions. However, any large-scale application requires a thorough analysis of the potential risks. Current numerical simulation models are too expensive for probabilistic risk analysis or stochastic approaches based on a brute-force approach of repeated simulation. Even single deterministic simulations may require parallel high-performance computing. The multiphase flow processes involved are too non-linear for quasi-linear error propagation and other simplified stochastic tools. As an alternative approach, we propose a massive stochastic model reduction based on the probabilistic collocation method. The model response is projected onto a higher-order orthogonal basis of polynomials to approximate dependence on uncertain parameters (porosity, permeability, etc.) and design parameters (injection rate, depth, etc.). This allows for a non-linear propagation of model uncertainty affecting the predicted risk, ensures fast computation, and provides a powerful tool for combining design variables and uncertain variables into one approach based on an integrative response surface. Thus, the design task of finding optimal injection regimes explicitly includes uncertainty, which leads to robust designs with a minimum failure probability. We validate our proposed stochastic approach by Monte Carlo simulation using a common 3D benchmark problem (Class et al., Comput Geosci 13:451–467, 2009). A reasonable compromise between computational efforts and precision was reached already with second-order polynomials. In our case study, the proposed approach yields a significant computational speed-up by a factor of 100 compared with the Monte Carlo evaluation. We demonstrate that, due to the non-linearity of the flow and transport processes during CO₂ injection, including uncertainty in the analysis leads to a systematic and significant shift of the predicted leakage rates toward higher values compared with deterministic simulations, affecting both risk estimates and the design of injection scenarios.     

Representing Spatial Uncertainty Using Distances and Kernels

Assessing uncertainty of a spatial phenomenon requires the analysis of a large number of parameters which must be processed by a transfer function. To capture the possibly of a wide range of uncertainty in the transfer function response, a large set of geostatistical model realizations needs to be processed. Stochastic spatial simulation can rapidly provide multiple, equally probable realizations. However, since the transfer function is often computationally demanding, only a small number of models can be evaluated in practice, and are usually selected through a ranking procedure. Traditional ranking techniques for selection of probabilistic ranges of response (P10, P50 and P90) are highly dependent on the static property used. In this paper, we propose to parameterize the spatial uncertainty represented by a large set of geostatistical realizations through a distance function measuring “dissimilarity” between any two geostatistical realizations. The distance function allows a mapping of the space of uncertainty. The distance can be tailored to the particular problem. The multi-dimensional space of uncertainty can be modeled using kernel techniques, such as kernel principal component analysis (KPCA) or kernel clustering. These tools allow for the selection of a subset of representative realizations containing similar properties to the larger set. Without losing accuracy, decisions and strategies can then be performed applying a transfer function on the subset without the need to exhaustively evaluate each realization. This method is applied to a synthetic oil reservoir, where spatial uncertainty of channel facies is modeled through multiple realizations generated using a multi-point geostatistical algorithm and several training images.     

History matching and uncertainty quantification of facies models with multiple geological interpretations

Uncertainty quantification is currently one of the leading challenges in the geosciences, in particular in reservoir modeling. A wealth of subsurface data as well as expert knowledge are available to quantify uncertainty and state predictions on reservoir performance or reserves. The geosciences component within this larger modeling framework is partially an interpretive science. Geologists and geophysicists interpret data to postulate on the nature of the depositional environment, for example on the type of fracture system, the nature of faulting, and the type of rock physics model. Often, several alternative scenarios or interpretations are offered, including some associated belief quantified with probabilities. In the context of facies modeling, this could result in various interpretations of facies architecture, associations, geometries, and the way they are distributed in space. A quantitative approach to specify this uncertainty is to provide a set of alternative 3D training images from which several geostatistical models can be generated. In this paper, we consider quantifying uncertainty on facies models in the early development stage of a reservoir when there is still considerable uncertainty on the nature of the spatial distribution of the facies. At this stage, production data are available to further constrain uncertainty. We develop a workflow that consists of two steps: (1) determining which training images are no longer consistent with production data and should be rejected and (2) to history match with a given fixed training image. We illustrate our ideas and methodology on a test case derived from a real field case of predicting flow in a newly planned well in a turbidite reservoir off the African West coast.     

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.     

Optimization of nonconventional wells under uncertainty using statistical proxies

The determination of the optimal type and placement of a nonconventional well in a heterogeneous reservoir represents a challenging optimization problem. This determination is significantly more complicated if uncertainty in the reservoir geology is included in the optimization. In this study, a genetic algorithm is applied to optimize the deployment of nonconventional wells. Geological uncertainty is accounted for by optimizing over multiple reservoir models (realizations) subject to a prescribed risk attitude. To reduce the excessive computational requirements of the base method, a new statistical proxy (which provides fast estimates of the objective function) based on cluster analysis is introduced into the optimization process. This proxy provides an estimate of the cumulative distribution function (CDF) of the scenario performance, which enables the quantification of proxy uncertainty. Knowledge of the proxy-based performance estimate in conjunction with the proxy CDF enables the systematic selection of the most appropriate scenarios for full simulation. Application of the overall method for the optimization of monobore and dual-lateral well placement demonstrates the performance of the hybrid optimization procedure. Specifically, it is shown that by simulating only 10% or 20% of the scenarios (as determined by application of the proxy), optimization results very close to those achieved by simulating all cases are obtained.     

Assessing the risk of soil vulnerability to wind erosion through conditional simulation of soil water content in Sistan plain, Iran

Surface soil water content (SWC) is one of the key factors controlling wind erosion in Sistan plain, southeast of Iran. Knowledge of the spatial variability of surface SWC is then important to identify high-risk areas over the region. Sequential Gaussian simulation (SGSIM) is used to produce a series of equiprobable models of SWC spatial distribution across the study area. The simulated realizations are used to model the uncertainty attached to the surface SWC estimates through producing a probability map of not exceeding a specified critical threshold when soil becomes vulnerable to wind erosion. The results show that SGSIM is a suitable approach for modelling SWC uncertainty, generating realistic representations of the spatial distribution of SWC that honour the sample data and reproduce the sample semivariogram model. The uncertainty model obtained using SGSIM is compared with the model achieved through sequential indicator simulation (SISIM). According to accuracy plots, goodness statistics and probability interval width plots, SGSIM performs better for modelling local uncertainty than SISIM. Sequential simulation provided a probabilistic approach to assess the risk that SWC does not exceed a critical threshold that might cause soil vulnerability to wind erosion. The resulted risk map can be used in decision-making to delineate “vulnerable” areas where a treatment is needed.     

Series Expansion-Based Genetic Inversion of Wireline Logging Data

An evolutionary approach is applied to solve the nonlinear well logging inverse problem. In the framework of the proposed interval inversion method, nuclear, sonic, and laterolog resistivity data measured at an arbitrary depth interval are jointly inverted, where the depth variation of porosity, water saturation, and shale volume is expanded into series using Legendre polynomials as basis functions. In the interval inversion procedure, the series expansion coefficients are estimated by using an adaptive float-encoded genetic algorithm. Since the solution of the inverse problem using traditional linear optimization tools highly depends on the selection of the initial model, a heuristic search is necessary to reduce the initial model dependence of the interval inversion procedure. The genetic inversion strategy used in interval inversion seeks the global extreme of the objective function and provides an estimate of the vertical distribution of petrophysical parameters, even starting the inversion procedure from extremely high distances from the optimum. For a faster computational process, after a couple of thousand generations, the genetic algorithm is replaced by some linear optimization steps. The added advantage of using the Marquardt algorithm is the possibility to characterize the accuracy of the series expansion coefficients and derived petrophysical properties. A Hungarian oil field example demonstrates the feasibility and stability of the improved interval inversion method. As a significance, the genetic inversion method does not require prior knowledge or strong restrictions on the values of petrophysical properties and gives highly reliable estimation results practically independent of the initial model and core information.

     

基于解析雅克比矩阵的E-E_x广域电磁法一维并行约束反演

对于野外实测数据的反演解释,一维反演仍然占据着重要地位。提出一种使用探测深度和等对数域剖分的方式来剖分层厚、只进行电阻率单参数反演的方案。反演时,先使用MT反演来建立初始模型,之后采用MATLAB自带的parfor循环和最优化工具箱来进行最优化计算,使用解析法来计算雅克比矩阵,从而大大提高了计算速度。对于实际地电模型,充分考虑到已有的先验信息,通过使用井震约束反演有效降低了反演多解性,使反演结果更加接近真实的地层情况。     

基于岩石物理模型的页岩储层裂缝属性及各向异性参数反演

针对富有机质页岩储层复杂的矿物组分与微观孔缝结构,本文提出基于岩石物理模型和改进粒子群算法的页岩储层裂缝属性及各向异性参数反演方法。应用自相容等效介质理论与Chapman多尺度孔隙理论建立裂缝型页岩双孔隙系统岩石物理模型。开发基于岩石物理模型的反演流程,引入模拟退火优化粒子群算法解决多参数同时反演问题,反演算法能够避免陷入局部极值且收敛速度快。将本文方法应用于四川盆地龙马溪组页岩气储层,反演得到的孔隙纵横比、裂缝密度等物性参数和各向异性参数与已有研究结果一致,能为页岩储层的评价提供多元化信息。     

边坡可靠度分析的一种新的优化求解方法

介绍了Low & Tang提出的一种新的可靠度优化求解方法,并将之用于边坡可靠度分析中：该方法适用于任何概率分布的相关变量,不必计算当量正态均值和方差、相关变量独立变换,直接在变量的原始空间内搜索边坡的最小可靠指标和概率临界滑面,可采用任何合适的约束优化方法进行求解,方法清晰简洁。边坡可靠度分析常用的滑面有2个：最小安全系数（变量均值处）对应的确定性临界滑面和最小可靠指标对应的概率临界滑面,但这2个滑面在有些情况下差别较大,Hassan & Wolff提出了一种简化方法可以方便地获得概率临界滑面,但由于方法简单,受到质疑。通过一系列算例分析,优化求解方法得到的概率临界滑面和Hassan & Wolff的简化方法滑面非常接近,显示了简化方法的有效性,值得在工程实践中推广。     

Seismic characterization and reconstruction of reference ground motion at accelerometric sites of the Italian national accelerometric network (RAN)

We present a field procedure that has been extensively used in Italy to characterize local seismic response at accelerometric sites and to retrieve ground motion at reference soil conditions by deconvolution analysis. To allow a generalized application to large areas where borehole data are generally lacking or inadequate for the seismic characterization for soils down to the reference seismic bedrock, cost-effectiveness of the considered procedures is a main issue. Thus, major efforts have been devoted to optimize available information and exploit fast and cheap surface geophysical prospecting. In particular, geological/geomorphological survey and passive seismic prospecting (both in single- and multi-station configurations) were jointly considered to reconstruct seismo-stratigraphical site conditions. This information was then used to feed numerical modeling aiming at computing the local seismic response and performing a deconvolution analysis to reconstruct ground motion at reference soil conditions. Major attention was devoted to evaluate and manage uncertainty involved in the procedure and to quantify its effect on final outcomes. An application of this procedure to a set of sites included in the Italian Accelerometric Network is presented.     

Seismic characterization and reconstruction of reference ground motion at accelerometric sites of the Italian national accelerometric network (RAN)

We present a field procedure that has been extensively used in Italy to characterize local seismic response at accelerometric sites and to retrieve ground motion at reference soil conditions by deconvolution analysis. To allow a generalized application to large areas where borehole data are generally lacking or inadequate for the seismic characterization for soils down to the reference seismic bedrock, cost-effectiveness of the considered procedures is a main issue. Thus, major efforts have been devoted to optimize available information and exploit fast and cheap surface geophysical prospecting. In particular, geological/geomorphological survey and passive seismic prospecting (both in single- and multi-station configurations) were jointly considered to reconstruct seismo-stratigraphical site conditions. This information was then used to feed numerical modeling aiming at computing the local seismic response and performing a deconvolution analysis to reconstruct ground motion at reference soil conditions. Major attention was devoted to evaluate and manage uncertainty involved in the procedure and to quantify its effect on final outcomes. An application of this procedure to a set of sites included in the Italian Accelerometric Network is presented.

     

A genetic meta-algorithm-assisted inversion approach: hydrogeological study for the determination of volumetric rock properties and matrix and fluid parameters in unsaturated formations

An evolutionary inversion approach is suggested for the interpretation of nuclear and resistivity logs measured by direct-push tools in shallow unsaturated sediments. The efficiency of formation evaluation is improved by estimating simultaneously (1) the petrophysical properties that vary rapidly along a drill hole with depth and (2) the zone parameters that can be treated as constant, in one inversion procedure. In the workflow, the fractional volumes of water, air, matrix and clay are estimated in adjacent depths by linearized inversion, whereas the clay and matrix properties are updated using a float-encoded genetic meta-algorithm. The proposed inversion method provides an objective estimate of the zone parameters that appear in the tool response equations applied to solve the forward problem, which can significantly increase the reliability of the petrophysical model as opposed to setting these parameters arbitrarily. The global optimization meta-algorithm not only assures the best fit between the measured and calculated data but also gives a reliable solution, practically independent of the initial model, as laboratory data are unnecessary in the inversion procedure. The feasibility test uses engineering geophysical sounding logs observed in an unsaturated loessy-sandy formation in Hungary. The multi-borehole extension of the inversion technique is developed to determine the petrophysical properties and their estimation errors along a profile of drill holes. The genetic meta-algorithmic inversion method is recommended for hydrogeophysical logging applications of various kinds to automatically extract the volumetric ratios of rock and fluid constituents as well as the most important zone parameters in a reliable inversion procedure.     

Prior model identification during subsurface flow data integration with adaptive sparse representation techniques

Construction of predictive reservoir models invariably involves interpretation and interpolation between limited available data and adoption of imperfect modeling assumptions that introduce significant subjectivity and uncertainty into the modeling process. In particular, uncertainty in the geologic continuity model can significantly degrade the quality of fluid displacement patterns and predictive modeling outcomes. Here, we address a standing challenge in flow model calibration under uncertainty in geologic continuity by developing an adaptive sparse representation formulation for prior model identification (PMI) during model calibration. We develop a flow-data-driven sparsity-promoting inversion to discriminate against distinct prior geologic continuity models (e.g., variograms). Realizations of reservoir properties from each geologic continuity model are used to generate sparse geologic dictionaries that compactly represent models from each respective prior. For inversion initially the same number of elements from each prior dictionary is used to construct a diverse geologic dictionary that reflects a wide range of variability and uncertainty in the prior continuity. The inversion is formulated as a sparse reconstruction problem that inverts the flow data to identify and linearly combine the relevant elements from the large and diverse set of geologic dictionary elements to reconstruct the solution. We develop an adaptive sparse reconstruction algorithm in which, at every iteration, the contribution of each dictionary to the solution is monitored to replace irrelevant (insignificant) elements with more geologically relevant (significant) elements to improve the solution quality. Several numerical examples are used to illustrate the effectiveness of the proposed approach for identification of geologic continuity in practical model calibration problems where the uncertainty in the prior geologic continuity model can lead to biased inversion results and prediction.     

Estimation of volcanic hazards based on Cox stochastic processes

Assessments of the probability and the consequences of future volcanic activity can be critical aspects when evaluating the safety of the population and of industrial plants. A new methodology has been developed for the probabilistic modelling of volcanic hazards based on regional volcanic data that facilitates the production of probabilistic hazard maps for various volcanic scenarios (lava flows, tephra). The stochastic model is based on Cox processes and allows account to be taken of the observed temporal and spatial correlation inherent in volcanic eruptions. The model is applied to the Quaternary field of the Osteifel region where the forecast number of future eruptions and the probabilities related to the different scenarios are estimated using a Monte Carlo approach. The obtained hazard maps of future volcanic events are part of a comprehensive hazard analysis and serve as a major input for the risk analysis that will determine the consequences of forecast volcanic activity at the site.     

Method for Stochastic Inverse Modeling of Fault Geometry and Connectivity Using Flow Data

This paper focuses on fault-related uncertainties in the subsurface, which can significantly affect the numerical simulation of physical processes. Our goal is to use dynamic data and process-based simulation to update structural uncertainty in a Bayesian inverse approach. We propose a stochastic fault model where the number and features of faults are made variable. In particular, this model samples uncertainties about connectivity between the faults. The stochastic three dimensional fault model is integrated within a stochastic inversion scheme in order to reduce uncertainties about fault characteristics and fault zone layout, by minimizing the mismatch between observed and simulated data.