Probabilistic history matching with the capacitance-resistance model in waterfloods: A precursor to numerical modeling

Several equally probable sets of uncertain reservoir parameters can normally match a production history. Such equiprobable history-matched solutions (EPHMS) are a way to estimate the uncertainty in hydrocarbon-recovery predictions. In most cases, time and resource limitations permit evaluation of only few of the EPHMS, thereby reducing reliability of predictions of numerical models. As a precursor to comprehensive numerical simulations in a probabilistic frame, we suggest the use of capacitance-resistance model or CRM. In CRM only injection and production rates are needed.The CRM is a fast analytic tool for history matching and optimizing waterfloods. In this study, we used CRM and a Buckley-Leverett-based fractional-flow model to rapidly generate many EPHMS. The EPHMS represent a unique combination of major reservoir variables, such as residual saturations, endpoint mobility ratio, oil and water in-place volumes, and recoverable oil.We used production data from two matured waterfloods and a synthetic field (Synfield) to evaluate the EPHMS. For most cases, one thousand EPHMS and the consequent cumulative distribution functions (CDFs) for several uncertain variables, including recoverable oil, were developed. We compared the CDFs obtained from EPHMS to that of 200 finite-difference simulations performed on the Synfield by changing porosity and residual saturations. EPHMS mimicked the same uncertain range of production forecasts used earlier in the finite-difference model. This approach attested to the goodness of CRM solutions and its ability to quantify reservoir uncertainty. Two field examples illustrated applications of the proposed approach at the field and pattern levels, and provided clues about the remaining oil and its monetary value.     

A New Methodology for Assisted History Matching Using Independent Objective Functions

Abstract

History matching is a complex inverse problem for which the degree of difficulty and the computational effort (in terms of number of simulations) increase with the increasing of the number of matching parameters. This article presents a new methodology for assisted history matching based on independent objective functions that decrease the number of simulations. The proposed approach consists of the optimization of several objective functions related to each region of the reservoir to be matched, such as a well or a group of wells. Optimization processes, one for each objective function, are started simultaneously, modifying the same data file, yielding a more efficient process, allowing speedup and preserving the quality of the results. The methodology was successfully applied to an offshore field. The results show that the quality of results is practically the same when compared to the conventional procedures, i.e., matching of the wells individually or combining several wells. The advantage is a significant reduction on the number of simulations, preserving the quality of the results.     

Regional probability perturbations for history matching

Reservoir simulation is ubiquitous in the petroleum industry, and conditioning models to production data (history matching) has become an essential job of reservoir engineers. Traditional history-matching methods directly perturb reservoir properties without regard to the existing geological continuity. When the geological heterogeneity is destroyed, the result is often a history-matched model with little prediction power. This paper presents a method for matching historical production data and, at the same time, honoring large-scale geologic information that is obtained from stratigraphic and sedimentological interpretations. Geostatistical simulation methods are used to inject the interpreted geological heterogeneity into a reservoir model. In order to maintain geological continuity in the history match models, we propose a method that perturbs the probability models used to simulate the geological model. Regional perturbations are incorporated to make the method practical for field cases that have numerous wells and local geologic differences. We demonstrate that the proposed approach does not create geological artifacts at the region borders. Additionally, a new simple yet efficient optimization method that can jointly optimize the magnitude of the perturbations for a large number of regions is proposed. A number of realistic synthetic examples demonstrate the method under various geological scenarios and several production data matching criteria. A realistic 3D synthetic simulation model based on a North Sea fluvial channel-type reservoir demonstrates how the method would work in practice. The current work provides reservoir engineers with an additional tool to use in the history-matching process.     

油藏数值模拟历史拟合质量评价方法

文中结合油藏数值模拟的基本理论及实际工作经验,提出了一套油藏数值模拟历史拟合质量评价方法。该方法采用多个量化指标,从不同层面综合评价地质模型拟合质量,形成了用以快速确定拟合调整目标和方向的算法思路,初步实现了拟合质量评价的定量化、标准化和流程化。利用该方法对平方王油田滨8-3块精细地质模型进行了历史拟合质量评价和辅助调整,实际应用效果良好。     

油藏数值模拟自动历史拟合方法——以Nelson油田为例

针对北海中部Nelson油田,研究油藏数值模拟自动历史拟合方法。完整的油藏自动历史拟合工作流程包括选择要调整的油藏变量、选择参数调整方法、自动历史拟合、数据分析、组合最优结果得到最优的油藏模型集5个步骤。以净毛比、水平渗透率、垂直渗透率为调整参数,采用全局单变量法、区域多变量法、局部多变量法等3种油藏参数调整方法,并结合生产数据和时移地震数据,对Nelson油田进行自动历史拟合。结果表明,局部参数调整方法减少了模拟中模型的数目和计算时间,提高了模拟精度,使得油藏中油水产量拟合误差大大降低,在Nelson油田应用效果最好。全局单变量法适合于历史拟合参数相互独立的情况;对于井网密度大且井间关联性强、历史拟合参数相互影响的油藏,最好选用区域多变量法进行参数调整;对于油藏历史拟合参数相互影响但每个选定调整区域相互独立的油藏,局部多变量法更加适用。     

Evaluation of the objective functions to improve production history matching performance based on fluid flow behaviour in reservoirs

This work deals with the problem of model performance evaluation, which is a challenge in many science branches, including subsurface fluid flow modelling (e.g. reservoir characterisation using history matching algorithms).The issue is posed as a problem of estimating the model performance by comparing the simulation results with observed data. This is accomplished by defining different statistical indicator objective functions (OF) to calculate the model efficiency, i.e. how model simulation fits observed data.Several deviation-based statistics used in literature as OF are analysed and applied to two synthetic case studies related to fluid flow in reservoir. Inaccuracies that arise from using the deviation-based statistics are discussed in a comparative way to propose an appropriate approach to boost the model accuracy when selecting the best realisation from multiple equally realisations generated during the history matching algorithm.The evaluations reveal that the suitable approach requires the adoption of an OF, that combines lag time with deviation-based statistic (SSR), to enhance the history matching process. The proposed approach has proven robust in the sense that it is able to provide an accurate and faster history matching algorithm for reservoir characterisation.     

Assisted History Matching Using Streamline Simulation

The quantity and quality of the information obtained from modern reservoir characterization techniques is still not sufficient to perfectly represent the reservoir. Therefore, reservoir models must be calibrated in order to provide a more reliable production forecast. This process is called production history matching. History matching is one of the most time-consuming tasks of a reservoir study due to the complexity of the process, multiple acceptable solutions, and demand for specialist knowledge. Many times this task is still based on a trial and error procedure, which is normally very inefficient because it involves a large number of cycles. This paper shows that it is possible to integrate the experience of the professionals involved in the process with some automatic techniques to accelerate the process and to obtain better solutions. This process is called Assisted History Matching. The use of streamline simulation as a complementary technique is applied to allow a better understanding of fluid flow behavior on the reservoir, mapping heterogeneities location, and then choosing adequate geological parameters, such as permeability and porosity, according to the identified flow patterns. Reservoir parameters are modified along blocks mapped by the streamlines. Automatic procedures are then applied along with parallel computing to find the best combination of the selected parameters. The methodology was applied to a complex real field where satisfactory results were obtained.     

识别水力裂缝参数的自动拟合模型和方法

为认识和了解地层、分析和评估压裂施工质量,分别考虑裂缝导流能力随生产过程变化和不变化的情形,提出了以生产过程中实测的产量或井底压力为拟合目标,识别水力裂缝参数的生产历史自动拟合模型和方法,用逐步二次规划法进行了数值求解。最后通过文献对比和实例计算说明模型和方法的可靠性和适用性     

An Automatic History Matching Module with Distributed and Parallel Computing

Abstract

The data assimilation process of adjusting variables in a reservoir simulation model to honor observations of field data is known as history matching and has been extensively studied for a few decades. However, limited success has been achieved due to the high complexity of the problem and the large computational effort required in the real fields. Successful applications of the ensemble Kalman filter (EnKF) to reservoir history matching have been reported in various publications. The EnKF is a sequential method: once new data are available, only these data are used to update all the unknown reservoir properties while previous geological information is unused directly. In this method, multiple reservoir models rather than one single model are implemented, and each model is called a member. Conventionally, the impact of each member on the updating is equally treated. Another approach is the weighted EnKF. During the updating, the method weighs the contribution of each member through the comparison between the simulation response and the measurements. Better matching performance has been found in the weighted EnKF than in the conventional EnKF. To improve computational efficiency, two-level high-performance computing for reservoir history matching process is implemented in this research, distributing ensemble members simultaneously while simulating each member in a parallel style.

An automatic history-matching module based on the weighted EnKF and high-performance computing is developed and validated through a synthetic case operating from primary, waterflooding to flooding of water alternating with gas. The study shows that the weighted EnKF improves the matching results, and the high-performance computing process significantly reduces the history matching execution time.     

An Investigation of and Comparison Between the Simulation of Miscible and Immiscible Gas Injection in an Undersaturated Fractured Reservoir in the South of Iran

M-Reservoir is a dual porosity fractured reservoir having active aquifer and heterogenous production zones. It had had only a total oil recovery of 8.4% with the total production of 240 MMSTB up to 2008. By simulation of slime tube experiment using Eclipse 300 software, minimum miscibility pressure of 3700 psia was obtained, which was below its average pressure. Production optimization and final recovery increment were performed via analyzing and matching of fluid reservoir, history matching of past reservoir performance, and investigating on different location of gas injected well. The best location of injected well was selected based on the recovery coefficient and gas injection method of miscible and immiscible at various rates and were compared with natural depletion in selected locations. The results represent that the miscible gas injection has more recovery coefficient than natural depletion and there is somewhat recovery coefficient in comparison with immiscible gas injection.     

基于数据空间反演的油藏实时生产优化方法

油藏开发实时优化调控技术是智能油藏研究的核心内容。提出了基于数据空间反演的油藏实时生产优化新方法,仅需若干油藏模型先验生产动态,基于贝叶斯理论构建代理模型,根据随机极大似然原理拟合历史观测数据进行模型训练,反演得到符合实际观测数据的生产动态后验估计。采用同步扰动随机逼近算法建立生产优化数学模型,实现注采参数实时优化,提高经济开发效益。该方法基于代理模型在拟合阶段避免了重复数值模拟计算,得到正确生产动态后验估计同时兼顾了油藏模型实际地质特征,优化所得方案考虑了目标油藏的不确定性,降低了实际生产开发风险。油藏实例应用表明:该方法能得到与常规多模型数据同化方法相一致的生产动态预测结果,拟合过程计算效率提高了5倍,且注采优化方案能取得良好的驱油效果。提出的油藏开发生产优化设计方法为油田实时生产优化提供了新的思路。     

基于数据空间反演的油藏实时生产优化方法

油藏开发实时优化调控技术是智能油藏研究的核心内容。提出了基于数据空间反演的油藏实时生产优化新方法,仅需若干油藏模型先验生产动态,基于贝叶斯理论构建代理模型,根据随机极大似然原理拟合历史观测数据进行模型训练,反演得到符合实际观测数据的生产动态后验估计。采用同步扰动随机逼近算法建立生产优化数学模型,实现注采参数实时优化,提高经济开发效益。该方法基于代理模型在拟合阶段避免了重复数值模拟计算,得到正确生产动态后验估计同时兼顾了油藏模型实际地质特征,优化所得方案考虑了目标油藏的不确定性,降低了实际生产开发风险。油藏实例应用表明:该方法能得到与常规多模型数据同化方法相一致的生产动态预测结果,拟合过程计算效率提高了5倍,且注采优化方案能取得良好的驱油效果。提出的油藏开发生产优化设计方法为油田实时生产优化提供了新的思路。     

Streamline-Based History Matching Constrained to Reservoir Geostatistics Using Gradual Deformation Technique

Abstract

A new and general procedure for history matching that uses streamline simulation and a gradual deformation technique has been proposed. Streamline trajectories define the major flow paths and help the algorithm to modify the reservoir model only in the regions that cause the mismatch between simulation results and field observations. The use of a gradual deformation technique enables the algorithm to remain constrained to reservoir geostatistics. It also reduces the number of independent variables in the optimization problem. In our algorithm, effective conductivities are defined along each streamline. The effective streamline conductivities are then adjusted using the values of measured and computed breakthrough times of individual streamlines. Then an intermediate objective function is defined to minimize the difference between adjusted (desired) and computed effective streamline conductivities. The algorithm continues until a satisfactory match is obtained. In order to examine the quality of our history matching procedure, it is applied to a synthetic reservoir.     

A framework to integrate history matching and geostatistical modeling using genetic algorithm and direct search methods

History matching is an inverse problem where the reservoir model is modified in order to reproduce field observed data. Traditional history matching processes are executed separately from the geological and geostatistical modeling stage due to the complexity of each area. Changes made directly on the reservoir properties generally yield inconsistent geological models. This work presents a framework to integrate geostatistical modeling and history matching process, where geostatistical images are treated as matching parameters. The traditional optimization methods normally applied in history matching generally use gradient information. The treatment of geostatistical images as matching parameters is difficult for these methods due to the strong non-linearities in the solution space. Therefore, another objective of this work is to investigate the application of two optimization methods: genetic algorithm and direct search method in the proposed framework. In order to accelerate the optimization process, two additional techniques are used: upscaling and distributed computing. Results are presented showing the viability of the genetic algorithm in the type of problem addressed in this work and also that direct search method can be used with some restriction. Finally, the benefits of distributed computing and the consistence of the upscaling process are shown.     

流动单元约束的油藏数值模拟研究

油藏数值模拟在油田开发方案的编制和确定、油田开采中生产措施的调整和优化、剩余油形成与分布以及提高油藏采收率方面,已逐渐成为一种不可欠缺的研究手段。油藏数值模拟的精度主要受油藏地质模型的精细程度和模拟模型的求解精度的影响。从提高油藏地质模型精度入手,将流动单元与油藏数值模拟相结合,通过利用流动单元细分模拟层系和针对不同的流动单元选取相应的相对渗透率曲线,提高油藏数值模拟的精度。模拟结果表明,流动单元约束的油藏数值模拟模型具有初始拟合程度高、模型修改程度低、能够更精确的反映层内和平面剩余油分布的特点。     

Risk Assessment of Petroleum Fields—Use of Numerical Simulation and Proxy Models

Abstract

The development of petroleum fields is a complex task due to the high influence of uncertainties on E&P projects. During the appraisal and development phases, uncertainties related to geologic and fluid models play an important role, especially in offshore heavy oil fields due to the low economic return, limited flexibility, and importance of reservoir modeling. The flexibility is limited because of the necessity to design the production facilities based on a low amount of information. The reservoir modeling process is important because risk of field development projects is normally caused by a high uncertainty on the recovery factor. Due to the necessity of a more robust evaluation of recovery factor, risk assessment methodologies normally are integrated with reservoir simulation, which is the best available tool to predict reservoir performance. However, higher precision on prediction of reservoir behavior is normally associated with fine simulation grid and high computation effort. In this article, some alternatives are presented to improve the efficiency of risk assessment, considering precision and computation effort. Among these alternatives are (1) use of coarse models, (2) use of coarse models modified to reproduce fine grid results, (3) simplifications on the risk assessment procedure, and (4) use of proxy models based on statistical (experimental) design and response surface methodology. A general discussion, including each alternative, use of upscaling techniques, reduction of grid size, number of attributes, use of parallel computing, and use of proxy models are made based on previous publications and results of a case study.

The methodology applied to quantify risk involves a sensitivity analysis in order to reduce the number of critical attributes and simulation of reservoir models obtained through the combination of these attributes. Afterward, a statistic treatment is used to evaluate the risk involved in the process. Based on a case study, it is shown that the use of faster simulation models and proxies can speed up risk assessment, but a few steps must be performed to guarantee the quality of the results.     

复杂裂缝性油藏历史拟合中的特殊做法

克拉玛依油田八区 上二叠统下乌尔禾组油藏是一个具有边底水的特低渗透裂缝性巨厚砾岩油藏,在油藏数值模拟研究过程中,针对油藏的具体特点,对“非油层”出油问题、注入水漏失问题、水淹水窜井问题、地层水侵入问题以及不同水驱油模式问题采取了一些特殊做法,对400多口井、23年的生产历史进行了精细拟合,单井的压力、含水率拟合符合率达85%以上。获得了很好的拟合结果,为类似油藏的数值模拟提供了可供借鉴的经验,这些做法可推广应用于其它低渗透裂缝性油藏。     

砂岩成岩过程中的孔隙演化定量模拟———以鄂尔多斯盆地安塞地区长 8 油层组储层为例

孔隙度在埋藏成岩过程中的变化是一个连续的过程,对油气成藏和区域储层评价具有重要意义。 目 前大部分实测孔隙度在深度上都是断续的,针对这一现状,以鄂尔多斯盆地安塞地区长 ₈ 油层组储层砂 岩为例,应用数理统计和数字模拟方法来定量模拟整个埋藏成岩过程中的孔隙演化。 在岩石学特征、成岩 作用特征以及地层埋藏史和成岩史研究的基础上,以现今孔隙度为约束条件,以埋藏深度和埋藏时间为 变量,将研究区长 ₈ 油层组孔隙演化进程分为孔隙度减小和孔隙度增大 2 个过程,并分别建立了相应的 从埋藏初始至今的孔隙演化定量模型。 结果表明,机械压实作用阶段的孔隙度减小过程是以埋藏深度为 自变量的连续函数;压实胶结作用阶段的孔隙度减小过程、增孔窗口阶段（65～100 ℃）及次生孔隙度保持 阶段均是埋藏深度和埋藏时间的连续函数。 因此,分段模型叠加得到的总孔隙演化模型为一个四段式函 数。 利用研究区实际地质资料对孔隙演化定量模型进行的实例验证表明,该模型在砂岩孔隙演化模拟方 面有较好的应用效果。     

页岩气井间干扰分析及井距优化

页岩气井距设计与优化是评价页岩气开发效果的重要指标。在理论认识的基础上,根据类比法、数值模拟、经济评价方法论证,形成了从井间干扰模拟、动态数据诊断到多井生产模拟、井距优化的完整工作流程：①通过建立压力探测边界传播模型,模拟不同连通条件下井间干扰响应程度;②基于井间干扰响应规律,根据气井生产动态数据演绎识别、诊断井间干扰;③以地质解释和动态分析结果为基础参数,建立气藏体积压裂多井数值模型,模拟气田生产动态,结合净现值模型优化井距。以长宁国家级页岩气示范区宁201井区为例,模拟表明,减小井距可使得井间干扰提前发生,同时也提高区块整体采收率;基于目前的压裂规模和参数体系,300~400 m井距可进一步优化至260~320 m,单位面积内井数增加20%~30%,区块储量采收率提高10%左右;区块整体净现值随着生产年限不断增加,但对应的最优井距结果不随生产周期的改变而改变。