Controllability,observability and identifiability in single-phase porous media flow

Over the past few years, more and more systems and control concepts have been applied in reservoir engineering, such as optimal control, Kalman filtering, and model reduction. The success of these applications is determined by the controllability, observability, and identifiability properties of the reservoir at hand. The first contribution of this paper is to analyze and interpret the controllability and observability of single-phase flow reservoir models and to investigate how these are affected by well locations, heterogeneity, and fluid properties. The second contribution of this paper is to show how to compute an upper bound on the number of identifiable parameters when history matching production data and to present a new method to regularize the history matching problem using a reservoir’s controllability and observability properties.     

A system-theoretical approach to selective grid coarsening of reservoir models

From a system-theoretical point of view and for a given configuration of wells, there are only a limited number of degrees of freedom in the input–output dynamics of a reservoir system. This means that a large number of combinations of the state variables (pressure and saturation values) are not actually controllable and observable from the wells, and accordingly, they are not affecting the input–output behavior of the system. In an earlier publication, we therefore proposed a control-relevant upscaling methodology that uniformly coarsens the reservoir. Here, we present a control-relevant selective (i.e. non-uniform) coarsening (CRSC) method, in which the criterion for grid size adaptation is based on ranking the grid block contributions to the controllability and observability of the reservoir system. This multi-level CRSC method is attractive for use in iterative procedures such as computer-assisted flooding optimization for a given configuration of wells. In contrast to conventional flow-based coarsening techniques our method is independent of the specific flow rates or pressures imposed at the wells. Moreover the system-theoretical norms employed in our method provide tight upper bounds to the ‘input–output energy’ of the fine and coarse systems. These can be used as an a priori error-estimate of the performance of the coarse model. We applied our algorithm to two numerical examples and found that it can accurately reproduce results from the corresponding fine-scale simulations, while significantly speeding up the simulation.     

岩溶热储井间连通性的示踪研究

岩溶热储储层的不均匀性强,采灌井之间的连通性不易确定。示踪技术可以将运移参数量化,有效刻画储层流体的特征,研究回灌井和开采井之间的水力联系,包括导水通道,流体流速等信息,对长期回灌可能引起的开采井的冷却进行预测,是岩溶热储井间连通性研究十分有效的技术。本文以华北牛驼镇地热田雄县地区为例,针对蓟县系雾迷山组岩溶热储,采用荧光素钠示踪剂,进行了1口井注入,10口井观测的群井示踪试验。采用裂隙介质溶质运移模型,对示踪试验数据进行了解释,得到优势通道的长度、渗透流速、纵向弥散度、回收率等储层性质,获得了试验区内采灌井之间的连通特征。对调整采灌井布局提出了建议。     

A scalable multistage linear solver for reservoir models with multisegment wells

Wellbore flow and interactions between wells and the reservoir can be complex. Accurate modeling of these behaviors is especially important for multilateral and other advanced wells. This paper describes a new scalable linear solver for flow simulation of detailed reservoir models with advanced wells and well groups. A general purpose research simulator serves as the computational platform, in which a multisegment well (MsWell) model is used to describe wellbore flow. In the MsWell model, the wellbore is discretized into a number of segments. Hence, the MsWell model adds a large number of equations and unknowns, which are fully coupled to the reservoir model. Operating constraints on groups of wells add one more level of complexity to the system. The new linear solver is a generalized two-stage constrained pressure residual preconditioner. A global pressure system is obtained algebraically in the first stage. The system represents the pressure coupling between the reservoir and wells accurately. The well groups are disaggregated into individual multisegment wells, which then are further reduced to a standard well-like form. The two-stage scheme serves as the inner loop of a generalized minimum residual solver. Algebraic multigrid is used to compute the first-stage pressure solution; a special block-based incomplete lower–upper preconditioner is used for the second stage. We demonstrate the superior performance of this new solver compared with state-of-the-art methods using a variety of highly detailed reservoir models with complex wells and well groups.     

基于干扰试井的煤层气储层优势渗流方向研究

为获得晋城矿区某区块3号煤层的储层连通性及其优势渗流方向,为矿区煤层气规模开发方案制定与调整提供依据,利用干扰试井技术对该区块井网内的煤层气井进行井间干扰测试。选定一口井为激动井,其周围5口井为观测井,组成干扰试井测试井组,测试并分析煤层气储层的连通性及其优势渗流方向。结果表明:激动井W-160井与观测井W-156井、W-166井间的煤层气储层连通性,优于其与观测井W-161井、W-157井以及W-164井间的储层连通性,即该区块煤层气储层的优势渗流方向为NE-SW向。将测试成果与生产实际相比对,验证了其正确性。试验证明了干扰试井测试可有效识别煤层气储层的连通性及优势渗流方向。      

Coherence mapping—An automated approach to display goodness-of-correlation between wells in a field

Patterns of inter-well correlations in map view can yield insight into the architecture of an area such as a petroleum reservoir. Preferred directions of fluid communications, discontinuities, and structural or depositional “grain” of an area often can be identified. In coherence mapping, large numbers of wells are compared in pairs, using a similarity coefficient. Sliding cross-correlation techniques of sections can be used to adjust for some normal stratigraphic inconsistencies. The calculated parameters are mapped as vector spider plots for each well, or as link-lines between well pairs with line thickness proportional to the strength of correlation. The resulting maps display areas of coherence and lines of discontinuities which can be interpreted according to the geologic style of the region. The method works best for areas with relatively great density of wells and uniform distribution. The database should contain logs digitized over the interval of interest and at least one stratigraphic marker. A pilot study of a carbonate reservoir with some 150 wells provided useful suggestions for reinterpretation of the field in terms of steeply dipping clinoforms of basin margin deposits.     

应用遗传神经网络研究碎屑岩储集层流动单元

应用遗传神经网络模式识别方法,以文72块沙三中为例,在取芯关键井流动单元聚类分析的基础上,选用流动层指数、孔隙度、渗透率、粒度中值、泥质含量、最大孔喉半径6项参数,将取芯井流动单元划分为4类,采用神经网络模式识别方法,通过建立遗传神经网络的学习及预测模型,对文72块沙三中油藏进行了流动单元识别,阐述了各类流动单元的特征,并应用序贯指示模拟,获得了流动单元的时空展布.流动单元与沉积微相空间分布的对比表明,物性和储集能力都较好的流动单元大部分位于水下分支水道微相中部及河口坝微相,水道和河口坝沉积是控制物性较好流动单元的主要沉积微相.储集层流动单元比沉积微相更精细地刻画了影响储集层流体流动的地下结构,通过流动单元研究可以预测剩余油的可能分布.     

Calculation of the Inverse of the Covariance

In reservoir characterization, the covariance is often used to describe the spatial correlation and variation in rock properties or the uncertainty in rock properties. The inverse of the covariance, on the other hand, is seldom discussed in geostatistics. In this paper, I show that the inverse is required for simulation and estimation of Gaussian random fields, and that it can be identified with the differential operator in regularized inverse theory. Unfortunately, because the covariance matrix for parameters in reservoir models can be extremely large, calculation of the inverse can be a problem. In this paper, I discuss four methods of calculating the inverse of the covariance, two of which are analytical, and two of which are purely numerical. By taking advantage of the assumed stationarity of the covariance, none of the methods require inversion of the full covariance matrix.     

低渗透储层水平井—直井联合布井极限注采井距研究

低渗透储层水平井—直井联合布井技术具有广泛的应用前景,其布井方式至关重要。首先利用劈分流场的方法直观地给出常规储层水平井—直井联合布井的产能评价方法;然后针对低渗透储层的渗流特点,在考虑启动压力梯度条件下建立新的井网渗流物理模型并求解得到产能评价公式;最后经分析计算给出启动压力梯度影响的面积井网极限注采井距关系曲线。研究结果为低渗透储层部署水平井—直井联合井网提供理论依据。     

Analysis of a more realistic well representation during secondary recovery in 3-D continuum models

The effectiveness of secondary recovery methods in reservoir development studies depends on the knowledge about how fluid-carrying regions (i.e. good-quality rock types) are connected between injection and production wells. To estimate reservoir performance uncertainty, comprehensive simulations on many reservoir model realisations are necessary, which is very CPU consuming and time demanding. Alternatively, we can use much simpler and physically based methods such as percolation approach. Classic percolation assumes connectivity between opposite 2-D faces of a 3-D system; whereas, hydrocarbon production is achieved through active wells that are one-dimensional lines (e.g. vertical, horizontal or deviated wells). The main contribution of this study is to analyse the percolation properties of 3-D continuum percolation models with more realistic well representations during secondary recovery. In particular, the connection of randomly distributed sands (i.e. good-quality rock types) between two lines (representing two wells) located at two corners of the system are modelled by Monte Carlo simulations. Subsequently, the connectivity and conductivity of such a line-to-line well representation is compared with that of face-to-face well representations in the previously published results. The critical percolation properties of those systems as well as the universality concept are also investigated. As there are many rooms for connections in 3-D models, we found that the principal percolation properties will not be altered significantly when the problem with a face-to-face connection is transformed to a line-to-line connection model.     

低渗透储层水平井-直井联合布井极限注采井距研究

低渗透储层水平井-直井联合布井技术具有广泛的应用前景,其布井方式至关重要。首先利用劈分流场的方法直观地给出常规储层水平井-直井联合布井的产能评价方法;然后针对低渗透储层的渗流特点,在考虑启动压力梯度条件下建立新的井网渗流物理模型并求解得到产能评价公式;最后经分析计算给出启动压力梯度影响的面积井网极限注采井距关系曲线。研究结果为低渗透储层部署水平井-直井联合井网提供理论依据。     

Waterflooding using closed-loop control

To fully exploit the possibilities of “smart” wells containing both measurement and control equipment, one can envision a system where the measurements are used for frequent updating of a reservoir model, and an optimal control strategy is computed based on this continuously updated model. We developed such a closed-loop control approach using an ensemble Kalman filter to obtain frequent updates of a reservoir model. Based on the most recent update of the reservoir model, the optimal control strategy is computed with the aid of an adjoint formulation. The objective is to maximize the economic value over the life of the reservoir. We demonstrate the methodology on a simple waterflooding example using one injector and one producer, each equipped with several individually controllable inflow control valves (ICVs). The parameters (permeabilities) and dynamic states (pressures and saturations) of the reservoir model are updated from pressure measurements in the wells. The control of the ICVs is rate-constrained, but the methodology is also applicable to a pressure-constrained situation. Furthermore, the methodology is not restricted to use with “smart” wells with down-hole control, but could also be used for flooding control with conventional wells, provided the wells are equipped with controllable chokes and with sensors for measurement of (wellhead or down hole) pressures and total flow rates. As the ensemble Kalman filter is a Monte Carlo approach, the final results will vary for each run. We studied the robustness of the methodology, starting from different initial ensembles. Moreover, we made a comparison of a case with low measurement noise to one with significantly higher measurement noise. In all examples considered, the resulting ultimate recovery was significantly higher than for the case of waterflooding using conventional wells. Furthermore, the results obtained using closed-loop control, starting from an unknown permeability field, were almost as good as those obtained assuming a priori knowledge of the permeability field.     

高含硫气藏非稳态水平井产量预测模型研究

元素硫从含硫天然气中析出沉降会影响流体流动,常规的水平井产量预测模型无法用于高含硫气藏水平井非稳态产量预测。本文基于非稳态椭圆流理论,耦合基质内的椭圆流动和裂缝内的非达西流动,考虑元素硫沉积及缝间干扰效应的影响,建立了适用于酸化水平井与酸压水平井的非稳态产量预测模型。分析了硫沉积对渗透率、孔隙度的影响,计算了不同裂缝参数对产能的影响,该模型适用于变井底流压生产条件。计算结果表明：科学准确的元素硫溶解度模型能较好地预测高含硫气藏水平井产量。酸压改造后缝间干扰现象会降低气井产能,且随着时间逐渐增强。硫沉积会降低储层渗透率和孔隙度,使得产量下降。增大裂缝导流能力,增加裂缝半长或者裂缝数量都能有效提高水平井产量,与裂缝导流能力相比,裂缝半长和裂缝数量对产量的影响更大。     

基于物质平衡反演法的致密砂岩气藏地层压力计算

压力是气藏的“灵魂”,地层压力是评价气井产能,分析气藏潜力的基础。然而,受到资料完整程度、方法适用条件等因素的限制,大部分气井无法准确获取地层压力。为了评价致密砂岩气藏地层压力,基于少量压力监测资料,采用数学反演思维,提出物质平衡反演法。首先,利用拟稳定流动状态下气井生产数据,拟合Blasingame图版,计算气井动态储量。而后,通过动态储量及一个测压数据进行反演,建立物质平衡方程,代入累产气量,评价地层压力,最后,以大宁–吉县区块致密砂岩气井为例,进行地层压力计算。结果表明:(1) 物质平衡反演法仅需一个测压点,可以评价气井的地层压力变化。(2) 气井原始地层压力差异大,单井地层压力变化复杂,存在多个压力系统。(3) 压力系统不一致与储层非均质性强有关。研究结果对于致密气单井压力计算和致密气藏压力评价提供了可靠的方法,为致密气藏开发方案调整和效益开发奠定了基础。      

Near-well upscaling for three-phase flows

Large-scale flow models constructed using standard coarsening procedures may not accurately resolve detailed near-well effects. Such effects are often important to capture, however, as the interaction of the well with the formation can have a dominant impact on process performance. In this work, a near-well upscaling procedure, which provides three-phase well-block properties, is developed and tested. The overall approach represents an extension of a recently developed oil–gas upscaling procedure and entails the use of local well computations (over a region referred to as the local well model (LWM)) along with a gradient-based optimization procedure to minimize the mismatch between fine and coarse-scale well rates, for oil, gas, and water, over the LWM. The gradients required for the minimization are computed efficiently through solution of adjoint equations. The LWM boundary conditions are determined using an iterative local-global procedure. With this approach, pressures and saturations computed during a global coarse-scale simulation are interpolated onto LWM boundaries and then used as boundary conditions for the fine-scale LWM computations. In addition to extending the overall approach to the three-phase case, this work also introduces new treatments that provide improved accuracy in cases with significant flux from the gas cap into the well block. The near-well multiphase upscaling method is applied to heterogeneous reservoir models, with production from vertical and horizontal wells. Simulation results illustrate that the method is able to accurately capture key near-well effects and to provide predictions for component production rates that are in close agreement with reference fine-scale results. The level of accuracy of the procedure is shown to be significantly higher than that of a standard approach which uses only upscaled single-phase flow parameters.     

http://www.sciencedirect.com/science/article/pii/S1674987114001649

Hydrocarbon production from shale has attracted much attention in the recent years. When applied to this prolific and hydrocarbon rich resource plays, our understanding of the complexities of the flow mechanism(sorption process and flow behavior in complex fracture systems- induced or natural) leaves much to be desired. In this paper, we present and discuss a novel approach to modeling, history matching of hydrocarbon production from a Marcellus shale asset in southwestern Pennsylvania using advanced data mining, pattern recognition and machine learning technologies. In this new approach instead of imposing our understanding of the flow mechanism, the impact of multi-stage hydraulic fractures, and the production process on the reservoir model, we allow the production history, well log, completion and hydraulic fracturing data to guide our model and determine its behavior. The uniqueness of this technology is that it incorporates the so-called "hard data" directly into the reservoir model, so that the model can be used to optimize the hydraulic fracture process. The "hard data" refers to field measurements during the hydraulic fracturing process such as fluid and proppant type and amount, injection pressure and rate as well as proppant concentration. This novel approach contrasts with the current industry focus on the use of "soft data"(non-measured, interpretive data such as frac length, width,height and conductivity) in the reservoir models. The study focuses on a Marcellus shale asset that includes 135 wells with multiple pads, different landing targets, well length and reservoir properties. The full field history matching process was successfully completed using this data driven approach thus capturing the production behavior with acceptable accuracy for individual wells and for the entire asset.     

秦家屯油田松南142 区块储层流动单元研究

秦家屯油田松南142 区块经多年开采已经进入高含水阶段,为分析注采关系、预测剩余油分布和提高原油采收率,在本区开展了储层流动单元研究。结合岩心、录井、测井资料,确定本区主要发育扇三角洲前缘水下分流河道、水下分流河道间、河口坝、席状砂4 种沉积微相,农Ⅷ ～农V 整体表现为一套扇三角洲前缘的进积式沉积。运用多参数模糊聚类分析将本区储层划分为由好至差的A、B、 C、D、E5 类储层流动单元,并依此确定了研究区储层流动单元类型的回判标准。在储层流动单元展布特征研究的基础上,对区内油、水井之间的注采关系进行了分析,并对剩余油分布的有利区带进行了预测。利用研究区生产动态资料对该研究成果进行检验,证明分析结果与油田实际生产状况吻合。     

安塞油田坪桥水平井区沉积微相三维建模研究

以安塞油田坪桥水平井区为例,探讨了应用水平井和露头资料及标点过程(示性点过程)方法进行沉积微相三维建模的思路与方法,同时对研究区三角洲前缘分流河道的定量结构模式进行了深入的研究。研究表明,坪桥水平井区三角洲分流河道单砂体宽度一般为40～100m左右。砂体结构呈两种模式,其一为“迷宫状”,砂体离散地分布于湖相泥岩中,其二为“拼合板状”,多个砂体在侧向上叠置而形成连片分布的砂体,但部分单砂体间可被泥质或钙质薄层侧积层所隔挡。应用水平井资料和露头资料,可有效地提取三维建模所必须的地质统计学参数。研究表明,采用标点过程方法,可建立符合地质实际的沉积微相三维模型。     

低渗致密气井分类评价方法研究 ——以子洲气田为例

由于子洲气田低渗致密气储层地质情况复杂,储层物性差异大,造成子洲气田各井的产量、压力等生产特征不同。为了更好地指导低渗致密气井高效合理的开发,需要基于各井的静态特征和动态规律,对其进行合理的分类。采用储能系数和地层系数两个储层物性参数,作为静态评价指标;采用稳产期累产气量、稳产期日均产气量、平均日产气和单位压降产气量四个动态参数,作为动态评价指标。创造性地提出依据各评价指标频率分布直方图的特征,对气井进行各指标分级。基于正交矩阵的思路,建立了动静结合的低渗致密气井分类评价方法,最终形成了静-动结合的气井分类结果：子洲气田152口低渗致密气井中I类井（储层物性好,实际产量高）占11.2%、II类井（储层物性较差,实际产量高）占8.5%、III类井（储层物性好,实际产量低）占30.3%、IV类井（储层物性差,实际产量低）占50.0%。其中,III类井是今后生产开发的研究重点,明确III类井的范围,可为将来措施提产指明方向。建立的动静结合低渗致密气井分类评价方法,可为类似区块低渗致密气井的分类提供借鉴。     

Numerical well model for non-Darcy flow through isotropic porous media[*]This work was supported in part by the EPA under grant # R 825207-01-1, by the State of Texas under ARP/ATP grant # 010366-168 and by a gift grant from Mobil Oil Corp.

Numerical simulation of fluid flow in a hydrocarbon reservoir has to account for the presence of wells. The pressure of a grid cell containing a well is different from the average pressure in that cell and different from the bottom-hole pressure for the well [17]. This paper presents a study of grid pressures obtained from the simulation of single phase flow through an isotropic porous medium using different numerical methods. Well equations are proposed for Darcy flow with Galerkin finite elements and mixed finite elements. Furthermore, high velocity (non-Darcy) flow well equations are developed for cell-centered finite difference, Galerkin finite element and mixed finite element techniques.