Integration of Markov mesh models and data assimilation techniques in complex reservoirs

We present a methodology that allows conditioning the spatial distribution of geological and petrophysical properties of reservoir model realizations on available production data. The approach is fully consistent with modern concepts depicting natural reservoirs as composite media where the distribution of both lithological units (or facies) and associated attributes are modeled as stochastic processes of space. We represent the uncertain spatial distribution of the facies through a Markov mesh (MM) model, which allows describing complex and detailed facies geometries in a rigorous Bayesian framework. The latter is then embedded within a history matching workflow based on an iterative form of the ensemble Kalman filter (EnKF). We test the proposed methodology by way of a synthetic study characterized by the presence of two distinct facies. We analyze the accuracy and computational efficiency of our algorithm and its ability with respect to the standard EnKF to properly estimate model parameters and assess future reservoir production. We show the feasibility of integrating MM in a data assimilation scheme. Our methodology is conducive to a set of updated model realizations characterized by a realistic spatial distribution of facies and their log permeabilities. Model realizations updated through our proposed algorithm correctly capture the production dynamics.     

Bayesian Gaussian Mixture Linear Inversion for Geophysical Inverse Problems

A Bayesian linear inversion methodology based on Gaussian mixture models and its application to geophysical inverse problems are presented in this paper. The proposed inverse method is based on a Bayesian approach under the assumptions of a Gaussian mixture random field for the prior model and a Gaussian linear likelihood function. The model for the latent discrete variable is defined to be a stationary first-order Markov chain. In this approach, a recursive exact solution to an approximation of the posterior distribution of the inverse problem is proposed. A Markov chain Monte Carlo algorithm can be used to efficiently simulate realizations from the correct posterior model. Two inversion studies based on real well log data are presented, and the main results are the posterior distributions of the reservoir properties of interest, the corresponding predictions and prediction intervals, and a set of conditional realizations. The first application is a seismic inversion study for the prediction of lithological facies, P- and S-impedance, where an improvement of 30% in the root-mean-square error of the predictions compared to the traditional Gaussian inversion is obtained. The second application is a rock physics inversion study for the prediction of lithological facies, porosity, and clay volume, where predictions slightly improve compared to the Gaussian inversion approach.     

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.      

塔河油气田AT1区块凝析气藏三维地质建模研究

以随机函数理论为基础,采用相控-多参数协同的随机建模方法,建立塔河油气田AT1区块凝析气藏三维地质模型,实现气藏精细三维表征。首先,以钻井和岩芯资料为基础构建储层构造模型;然后,以小层界面为控制条件建立储层结构模型;接着,在沉积相、地质条件的约束下,采用序贯指示模拟法来建立砂体骨架模型;随后,在砂体骨架模型内进行优势相计算,形成最终有效砂体骨架模型;最后,以有效砂体骨架模型为约束,采用序贯高斯模拟法建立储层物性参数模型。结果表明：将物性参数变量与微相分布结合的序贯高斯模拟法建立孔隙度等物性参数的分布模型,以及采用地质分析类比、地质统计分析等方法优选最佳模型是有效的地质建模方法;所建地质模型精确细致地表征了塔河油气田AT1区块凝析气藏构造格架及储层、流体三维分布,反映了辫状水道复合连片,东北向展布,储层物性受相控较明显,非均质性较强。     

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.     

井震联合建模技术在萨尔图油田B1DD区块的应用及其效果

为解决以往油藏描述工作单孔资料在深度和广度上存在明显局限性的问题,提出了一套井震联合地质建模的方法：首先以地震精细解释的层位数据和断层数据为约束,结合测井资料建立构造模型;然后采用地震反演体的概率面在平面上作为约束,纵向上在测井曲线上分类统计各微相的概率分布曲线,在变差函数分析的基础上,采用序贯指示模拟算法模拟出储层微相的空间展布,建立沉积相模型;最后采用相控技术和地质统计学理论,分析参数区域化变量的特征,建立储层属性模型。在大庆萨尔图油田的B1DD区块进行验证的结果表明,井震资料的联合应用揭示了大量的小断层,使断点组合率提高了15%,大于2 m的砂岩预测符合率达到90%以上,提高了井间断层和砂岩的预测精度,进而提高了地质模型、尤其是井间模型的精度。     

Maximum likelihood classification for facies inference from reservoir attributes

A cluster analysis methodology is developed to recover facies realizations from observed reservoir attributes. A maximum likelihood estimator allows us for identifying the most probable underlying facies using a spatial clustering algorithm. In seismic characterization, this algorithm can yield relevant geological models for subsequent history-matching studies. In history-matching procedures, it provides informative facies maps as well as starting points for further studies.     

Sedimentary Microfacies and Porosity Modeling of Deep-Water Sandy Debris Flows by Combining Sedimentary Patterns with Seismic Data: An Example from Unit I of Gas Field A, South China Sea

Sandy debris flow deposits are present in Unit I during Miocene of Gas Field A in the Baiyun Depression of the South China Sea. The paucity of well data and the great variability of the sedimentary microfacies make it difficult to identify and predict the distribution patterns of the main gas reservoir, and have seriously hindered further exploration and development of the gas field. Therefore, making full use of the available seismic data is extremely important for predicting the spatial distribution of sedimentary microfacies when constructing three-dimensional reservoir models. A suitable reservoir modeling strategy or workflow controlled by sedimentary microfacies and seismic data has been developed. Five types of seismic attributes were selected to correlate with the sand percentage, and the root mean square (RMS) amplitude performed the best. The relation between the RMS amplitude and the sand percentage was used to construct a reservoir sand distribution map. Three types of main sedimentary microfacies were identified: debris channels, fan lobes, and natural levees. Using constraints from the sedimentary microfacies boundaries, a sedimentary microfacies model was constructed using the sequential indicator and assigned value simulation methods. Finally, reservoir models of physical properties for sandy debris flow deposits controlled by sedimentary microfacies and seismic inversion data were established. Property cutoff values were adopted because the sedimentary microfacies and the reservoir properties from well-logging interpretation are intrinsically different. Selection of appropriate reservoir property cutoffs is a key step in reservoir modeling when using simulation methods based on sedimentary microfacies control. When the abnormal data are truncated and the reservoir properties probability distribution fits a normal distribution, microfacies-controlled reservoir property models are more reliable than those obtained from the sequence Gauss simulation method. The cutoffs for effective porosity of the debris channel, fan lobe, and natural levee facies were 0.2, 0.09, and 0.12, respectively; the corresponding average effective porosities were 0.24, 0.13, and 0.15. The proposed modeling method makes full use of seismic attributes and seismic inversion data, and also makes the property data of single-well depositional microfacies more conformable to a normal distribution with geological significance. Thus, the method allows use of more reliable input data when we construct a model of a sandy debris flow.     

地震波形指示反演在珠江口盆地A油田薄层预测中的应用

珠江口盆地A油田主要发育三角洲前缘沉积,砂泥岩互层严重,且储层薄、横向连续性差,分布规律难以掌握,随着开发进程的加快,其对储层预测的要求越来越精细,而常规反演方法很难满足高精度储层预测的要求。针对这一难题,结合该油田沉积相分布稳定的特征,这里在地震波形相控反演思想的基础上,将地震波形指示反演方法应用到A油田的薄层预测中,研究表明:①该方法的预测结果既在空间上体现了地震相约束,平面上也更符合该油田的地质沉积规律;②三维地震波形特征直接反映沉积相信息,减小了常规人工划分沉积相约束的工作量和主观认识的不确定性;③地震波形指示反演突破常规基于空间域插值算法的限制,对井位分布的均匀性没有严格要求,大大提高了储层反演的适用领域。该方法首次应用于珠江口盆地,并且在A油田的薄储层及薄隔夹层反演预测中,为该油田的开采提供了可靠的资料基础,取得了很好的应用效果,实现了井震协同的高分辨率储层预测,落实了薄层的空间展布。     

马朗凹陷牛东地区卡拉岗组火山岩储层建模研究

火山岩储层比碎屑岩具有更强的非均质性,储层的地质建模工作变得非常复杂。针对马朗凹陷牛东地区卡拉岗组玄武岩和火山岩的储层地质特征,运用petrel建模软件对储层进行三维地质建模。首先利用钻井、测井、录井、地震、岩心分析化验等资料完成了地层对比,建立地层格架。在此基础上,综合测井与地震资料,建立该地区的构造模型、岩相模型和含油饱和度模型,应用蚂蚁体示踪的方法建立了裂缝分布模型。建模结果检验与实际情况相吻合,为油藏开发方案控制提供了主要依据。     

基于地震信息的歧口18-1稀井网区储层预测

针对歧口18-1区块沙河街组扇三角洲储层砂体横向变化快的地质特征和稀井网的资料条件,应用工区的三维地震资料,采用地震属性分析、测井约束反演等方法,分层次开展歧口18-1沙河街组储层砂体空间分布的预测,确定了区块优质储层的分布规律。通过提取各种地震属性,在单井地震属性岩性标定的基础上,优选均方根振幅属性作为参数,确定了歧口18-1区块沙河街组扇三角洲有利相带的空间分布;据此,在扇三角洲内部应用测井约束反演技术预测优质储层的分布规律及其内部结构,为断块有利勘探目标的确定和开发方案的制定提供了地质依据。这种精度逐级提高的层次性储层预测技术,尤其适合稀井网、大井距条件下的海上油田优质储层的确定,可有效地降低开发风险。     

综合应用测井及地震资料建立复杂断块地质模型

针对滩海油田具有完钻井少,以地震资料为主的特点,采用井震结合的方法进行地质建模。复杂断块油藏具有许多内部断层,充分利用地震解释层位和断层成果建立合理的构造模型。采用“多步建模”的思路,选用序贯高斯同位协同模拟算法建立储层参数模型。以测井资料为硬数据,地震反演数据为软数据,先后建立自然伽玛模型、泥质含量模型和砂泥岩相模型,然后以砂泥岩相模型为约束,建立储层参数模型。经研究表明,综合使用地震解释成果和三维地震数据体,有助于建立准确、合理的构造模型;而采用“多步建模”的思路,利用序贯高斯同位协同模拟算法,并综合测井资料、地震资料建立储层参数模型,有助于从地质的角度对储层参数模拟进行约束,提高储层随机建模精度,保证储层参数模型的准确和可靠性。     

应用多尺度资料研究川西大邑构造上三叠统须家河组成岩储集相*

利用丰富的岩心、测井和地震资料,以薄片镜下观察、岩心物性分析、测井曲线交会、地震速度反演等作为手段,对大邑构造上三叠统须家河组储集层成岩储集相的类型、成岩储集相的地质与测井响应特征、以及优质成岩储集相的演化序列与平面分布开展了半定量—定量研究,以期深化低渗透砂岩储集层的地质理论和指导该地区气田的高效开发。结果表明,研究区砂岩可划分为4类成岩储集相,即强破裂杂基溶孔—微孔—裂缝成岩储集相、强压实微孔成岩储集相、强压实致密成岩储集相和强胶结致密成岩储集相。采用声波、密度、电阻率和自然伽马曲线交会的方法可有效识别各类成岩储集相。强破裂杂基溶孔—微孔—裂缝成岩储集相物性最好,为优质成岩储集相,其岩石类型以石英砂岩为主,经历了强烈的压实作用和破裂作用,孔隙度3％～8％,渗透率大于0.5×10^-3 μm²,主要发育在构造高部位的分流河道和水下分流河道砂体中,沉积因素和构造因素对其平面分布起到了重要控制作用。     

地震油藏地质研究及其在大港滩海地区的应用

针对滩海地区油藏评价阶段"井点少,以地震资料为主,面向水平井、大斜度井开发需要"的特点和要求,提出地震油藏地质研究的思路、方法和技术,其涉及的内容包括地震地层划分对比、地震构造精细解释、地震沉积相研究、地震储层预测、地震油藏流体识别以及油气分布的不均一性研究。以地震沉积学的原理及方法为指导,以单井相分析为基础,将地震高阶信息应用于沉积相平面分析;利用地层切片技术在地震数据体中提取等时地层单元信息,结合各种地震属性参数的分布研究不同地层单元的沉积相分布及其演化史。在对储集层特征进行重构基础上的随机模拟地震反演是储层表征与预测的有效方法。地震油藏地质研究的主要目的是揭示油藏的非均质性及油气分布的不均一性,进而较准确地评价油藏。实现这一目的的关键一方面是依据地质模式减少地震信息的多解性和提高地震信息的纵向分辨率;二是探索如何将地震信息与测井、录井、地质等多种信息真正融合起来,综合分析和解决地质问题。通过大港滩海地区地震油藏地质研究,发现研究区油气分布的不均一现象,这对认识复杂油藏具有重要意义。     

A probabilistic parametrization for geological uncertainty estimation using the ensemble Kalman filter (EnKF)

In the past years, many applications of history-matching methods in general and ensemble Kalman filter in particular have been proposed, especially in order to estimate fields that provide uncertainty in the stochastic process defined by the dynamical system of hydrocarbon recovery. Such fields can be permeability fields or porosity fields, but can also fields defined by the rock type (facies fields). The estimation of the boundaries of the geologic facies with ensemble Kalman filter (EnKF) was made, in different papers, with the aid of Gaussian random fields, which were truncated using various schemes and introduced in a history-matching process. In this paper, we estimate, in the frame of the EnKF process, the locations of three facies types that occur into a reservoir domain, with the property that each two could have a contact. The geological simulation model is a form of the general truncated plurigaussian method. The difference with other approaches consists in how the truncation scheme is introduced and in the observation operator of the facies types at the well locations. The projection from the continuous space of the Gaussian fields into the discrete space of the facies fields is realized through in an intermediary space (space with probabilities). This space connects the observation operator of the facies types at the well locations with the geological simulation model. We will test the model using a 2D reservoir which is connected with the EnKF method as a data assimilation technique. We will use different geostatistical properties for the Gaussian fields and different levels of the uncertainty introduced in the model parameters and also in the construction of the Gaussian fields.     

利用地震资料进行沉积相分析

沉积相揭示了目的层段的沉积环境、储集岩成因及其分布规律。通过沉积相研究，可以帮助油藏工程师建立油藏地质概念模型，为地震资料的数字处理解释奠定了基础。从在地质、测井分析的基础上，分析了地震属性与沉积相的关系，选取了敏感的属性，利用反射强度平面图，清晰地展现了分流河道、曲流河道等相特征，采用神经网络的方法对沉积相作精细划分，使井与井之间的结果更为客观，克服了以往人为推断划分的随意性。     

Multimodal ensemble Kalman filtering using Gaussian mixture models

In this paper we present an extension of the ensemble Kalman filter (EnKF) specifically designed for multimodal systems. EnKF data assimilation scheme is less accurate when it is used to approximate systems with multimodal distribution such as reservoir facies models. The algorithm is based on the assumption that both prior and posterior distribution can be approximated by Gaussian mixture and it is validated by the introduction of the concept of finite ensemble representation. The effectiveness of the approach is shown with two applications. The first example is based on Lorenz model. In the second example, the proposed methodology combined with a localization technique is used to update a 2D reservoir facies models. Both applications give evidence of an improved performance of the proposed method respect to the EnKF.     

Stratimagic波形地震相分析在层序地层岩性分析中的应用

应用波阻抗反演以及常规地震属性预测储层时,在钻井资料较少、储层较薄的情况下多解性较强。Stratimagic波形地震相分析技术采用神经网络算法对某一层间的地震数据道进行逐道对比分类,细致刻画地震信号的横向变化,从而得到与地质相对应的地震相图,并以此用于储层砂体和地层岩性油藏的预测。以东营凹陷八面河地区滩坝砂体岩性油藏为例,说明应用该方法进行滩坝砂体和岩性油藏分布预测,是行之有效的。      

地震相控非线性随机反演在海上薄互层储层预测中的应用——以K油田沙河街组为例

针对渤海中深层薄互层储层普遍存在的埋藏深、地震资料品质差、储层厚度薄,薄互层沉积,储层横向变化快等特点,以及开发程度的加深对地震分辨率精度要求越来越高的情况,在分析储层组合和地震沉积学基础上,提出地震相控非线性反演方法,以期提高储层预测精度。该方法通过非线性最优化理论综合约束反演与模型反演的优点,根据实际地震资料建立反演目标层段的宏观相控模型,在测井资料约束下采用非线性随机算法逐道、逐次进行外推反演,有效提高地震资料的分辨率,充分考虑地质条件的随机特性,使反演结果更符合实际地质情况。在K油田应用表明,该技术提高了薄互层储层预测精度,为类似油田的储层预测、注采连通、井网部署提供可靠依据。