Calculation of Well Index for Nonconventional Wells on Arbitrary Grids

Wells are seldom modeled explicitly in large scale finite difference reservoir simulations. Instead, the well is coupled to the reservoir through the use of a well index, which relates wellbore flow rate and pressure to grid block quantities. The use of an accurate well index is essential for the detailed modeling of nonconventional wells; i.e., wells with an arbitrary trajectory or multiple branches. The determination of a well index for such problems is complicated, particularly when the simulation grid is irregular or unstructured. In this work, a general framework for the calculation of accurate well indices for general nonconventional wells on arbitrary grids is presented and applied. The method entails the use of an accurate semianalytical well model based on Green's functions as a reference single phase flow solution. This result is coupled with a finite difference calculation to provide an accurate well index for each grid block containing a well segment. The method is demonstrated on a number of homogeneous example cases involving deviated, horizontal and multilateral wells oriented skew to the grid. Both Cartesian and globally unstructured multiblock grids are considered. In all these cases, the method is shown to provide results that are considerably more accurate compared to results using standard procedures. The method is also applied to heterogeneous problems involving horizontal wells, where it is shown to be capable of approximating the effects of subgrid heterogeneity in coarse finite difference models.     

Impact of CO<Subscript>2</Subscript> injection rate on heat extraction at the HDR geothermal field of Zhacanggou,China

CO₂ is now considered as a novel heat transmission fluid to extract geothermal energy. It can achieve the goal of energy exploitation and CO₂ geological sequestration. Taking Zhacanggou as research area, a “Three-spot” well pattern (one injection with two production), “wellbore–reservoir” coupled model is built, and a constant injection rate is set up. A fully coupled wellbore–reservoir simulator—T2Well—is introduced to study the flow mechanism of CO₂ working as heat transmission fluid, the variance pattern of each physical field, the influence of CO₂ injection rate on heat extraction and the potential and sustainability of heat resource in Guide region. The density profile variance resulting from temperature differences of two wells can help the system achieve “self-circulation” by siphon phenomenon, which is more significant in higher injection rate cases. The density of CO₂ is under the effect of both pressure and temperature; moreover, it has a counter effect on temperature and pressure. The feedback makes the flow process in wellbore more complex. In low injection rate scenarios, the temperature has a dominating impact on the fluid density, while in high rate scenario, pressure plays a more important role. In most scenarios, it basically keeps stable during 30-year operation. The decline of production temperature is <5 °C. However, for some high injection rate cases (75 and 100 kg/s), due to the heat depletion in reservoir, there is a dramatic decline for production temperature and heat extraction rate. Therefore, a 50-kg/s CO₂ injection rate is more suitable for “Three-spot” well pattern in Guide region.     

A parallel, implicit, cell‐centered method for two‐phase flow with a preconditioned Newton–Krylov solver

A new parallel solution technique is developed for the fully implicit three‐dimensional two‐phase flow model. An expandedcell‐centered finite difference scheme which allows for a full permeability tensor is employed for the spatial discretization, and backwardEuler is used for the time discretization. The discrete systems are solved using a novel inexact Newton method that reuses the Krylov information generated by the GMRES linear iterative solver. Fast nonlinear convergence can be achieved by composing inexact Newton steps with quasi‐Newton steps restricted to the underlying Krylov subspace. Furthermore, robustness and efficiency are achieved with a line‐search backtracking globalization strategy for the nonlinear systems and a preconditioner for each coupled linear system to be solved. This inexact Newton method also makes use of forcing terms suggested by Eisenstat and Walker which prevent oversolving of the Jacobian systems. The preconditioner is a new two‐stage method which involves a decoupling strategy plus the separate solutions of both nonwetting‐phase pressure and saturation equations. Numerical results show that these nonlinear and linear solvers are very effective.     

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.     

空气钻井技术在柳林煤层气井的应用

空气钻井技术是煤层气高效开发的重要钻井技术,具有循环压耗低、携砂能力强、井眼净化好的特点,同时能有效防止井漏、保护储层、提高机械钻速等,但面临着井壁稳定、水动力条件等复杂的工程和地质难题,在柳林煤层气井施工中,开展了岩层特征、水文地质条件、煤层含水特性、泡沫钻井液设计等研究,针对地层特点,设计了适合空气钻井的配套工艺技术。通过柳林地区7口井的施工,钻井周期缩短50%,储层得到有效保护,直井产气量达到1000 m3/d,水平井产气量达15000 m3/d,初步取得了良好的示范效果,推广应用前景广阔。     

无限大三层越流油气藏井底压力的精确解及典型曲线

在考虑表皮效应和井筒储存的影响的条件下，采用最大有效井径的概念，建立无限三层越流油藏井底压力的动态模型。通过拉氏变换得到拉氏空间下以Bessel函数表示的井底压力和分层流量的精确解。运用Crump数值反演方法，得到实空间的解；分析了压力动态特征。该模型不但适合于表皮系数为正的情况，也适合于表皮系数为负的情形。用新模型绘制的典型曲线进行拟合，得到更加准确的结果。     

A mathematical model of permeability alteration around wells

This paper presents an analytical solution of the permeability alteration problem around the wellbore. This alteration may be a permeability reduction due to drilling fluid invasion or mudcake formation around the wellbore. On the other hand, the alteration may be a permeability increase resulting from stimulation by acidizing the formation matrix around the well. This permeability discontinuity in a reservoir forms a composite reservoir system. With the composite model, both the degree and the radial extent of permeability alteration can be adequately predicted. The conventional skin concept is inadequate and physically unrealistic in most of these cases. This paper describes the application of an automatic weighted constrained least-squares parameter estimation technique and the analytical model for pressure transient analysis. The parameters of the composite reservoir system are determined from a match of the pressure transient data. The behaviour of the pressure transient in such composite systems is presented using the analytical solution.     

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。      

Role of Geomechanics in Assessing the Feasibility of CO2 Sequestration in Depleted Hydrocarbon Sandstone Reservoirs

Carbon dioxide (CO₂) sequestration in depleted sandstone hydrocarbon reservoirs could be complicated by a number of geomechanical problems associated with well drilling, completions, and CO₂ injection. The initial production of hydrocarbons (gas or oil) and the resulting pressure depletion as well as associated reduction in horizontal stresses (e.g., fracture gradient) narrow the operational drilling mud weight window, which could exacerbate wellbore instabilities while infill drilling. Well completions (casing, liners, etc.) may experience solids flowback to the injector wells when injection is interrupted due to CO₂ supply or during required system maintenance. CO₂ injection alters the pressure and temperature in the near wellbore region, which could cause fault reactivation or thermal fracturing. In addition, the injection pressure may exceed the maximum sustainable storage pressure, and cause fracturing and fault reactivation within the reservoirs or bounding formations. A systematic approach has been developed for geomechanical assessments for CO₂ storage in depleted reservoirs. The approach requires a robust field geomechanical model with its components derived from drilling and production data as well as from wireline logs of historical wells. This approach is described in detail in this paper together with a recent study on a depleted gas field in the North Sea considered for CO₂ sequestration. The particular case study shows that there is a limitation on maximum allowable well inclinations, 45° if aligning with the maximum horizontal stress direction and 65° if aligning with the minimum horizontal stress direction, beyond which wellbore failure would become critical while drilling. Evaluation of sanding risks indicates no sand control installations would be needed for injector wells. Fracturing and faulting assessments confirm that the fracturing pressure of caprock is significantly higher than the planned CO₂ injection and storage pressures for an ideal case, in which the total field horizontal stresses increase with the reservoir re-pressurization in a manner opposite to their reduction with the reservoir depletion. However, as the most pessimistic case of assuming the total horizontal stresses staying the same over the CO₂ injection, faulting could be reactivated on a fault with the least favorable geometry once the reservoir pressure reaches approximately 7.7 MPa. In addition, the initial CO₂ injection could lead to a high risk that a fault with a cohesion of less than 5.1 MPa could be activated due to the significant effect of reduced temperature on the field stresses around the injection site.     

The flow and heat transfer characteristics of compressed air in high-pressure air injection wells

High-pressure air injection (HPAI) is a significant enhanced oil recovery (EOR) technology of light oils especially in deep, thin, low-permeability reservoirs. The flow and heat transfer behaviors of compressed air in wellbore is essential to maximize performance of air in EOR. Due to strong compressibility of air and high injection pressure, wellbore temperature and pressure are greatly affected by friction and gas compression. However, the available models of wellbore flow and heat transfer are only accurate for thermal fluid, such as saturated steam and superheated steam, injected at relatively low pressure and high temperature. In this paper, a novel model is proposed to characterize wellbore pressure and temperature distribution for HPAI wells with consideration of dynamic behaviors of injected air. Flow and heat transfer in depth direction are coupled with air properties by iterative technique, and heat transfer in radial direction is treated as steady state in wellbore and transient state in formation. The mathematical model is solved by employing finite difference method and it is validated by field data. Then, integrated analyses of flowing pressure, heat transfer mechanism, and interaction between pressure and temperature are conducted. Results indicate that (1) as well depth increases, temperature difference between formation and air tends to become constant, and the radial heat transfer tends to reach an equilibrium state. The higher the flow rate is, the deeper the equilibrium depth is. (2) Air temperature is dominated by heat transmission from formation at low flow rates and dominated by frictional heat and gas compression effect at high flow rates. Fictional heat begins to affect air temperature at an injection rate beyond the critical value, while gas compression effect can increase air temperature in the whole calculated injection rate range. (3) Interaction between wellbore temperature and pressure is mainly achieved by altering air density. The effect of injection pressure on air temperature can be negligible, while the influence of injection temperature shows strong dependency on injection rate.     

Controllability and observability in two-phase porous media flow

Reservoir simulation models are frequently used to make decisions on well locations, recovery optimization strategies, etc. The success of these applications is, among other aspects, determined by the controllability and observability properties of the reservoir model. In this paper, it is shown how the controllability and observability of two-phase flow reservoir models can be analyzed and quantified with aid of generalized empirical Gramians. The empirical controllability Gramian can be interpreted as a spatial covariance of the states (pressures or saturations) in the reservoir resulting from input perturbations in the wells. The empirical observability Gramian can be interpreted as a spatial covariance of the measured bottom-hole pressures or well bore flow rates resulting from state perturbations. Based on examples in the form of simple homogeneous and heterogeneous reservoir models, we conclude that the position of the wells and of the front between reservoir fluids, and to a lesser extent the position and shape of permeability heterogeneities that impact the front, are the most important factors that determine the local controllability and observability properties of the reservoir.     

基于连续损伤的水平井射孔-近井筒三维破裂模拟

射孔作为井筒与储层之间的液流通道,是水力压裂过程中的重要可控性参数。为研究水平井射孔-近井筒破裂机制,采用岩层变形-流体渗流方程描述应力状态变化,应用连续损伤破裂单元表征三维破裂位置与形态演化,并开发有限元求解程序模拟分析了射孔对水平井初始破裂压力、破裂位置及近井筒裂缝复杂性的调控作用。通过与解析模型及射孔压裂物理模型试验结果对比,验证了模型及有限元程序的有效性;水平井破裂压力数值分析结果与现场测试数据吻合较好。研究表明：射孔可调控水平井破裂压力与初始破裂位置,同时对近井筒区域裂缝扩展形态影响显著。通过优化射孔参数可以引导初始破裂向最优破裂面扩展、有效降低破裂压力,减小由于螺旋射孔空间排布引起的水平井近井筒裂缝迂曲与复杂程度,提高致密油气藏压裂改造效果。     

Effects of fractures on the well production in a coalbed methane reservoir

A water-gas two-phase flow model of a fractured vertical well in a coalbed methane (CBM) reservoir is developed based on the Buckley-Leverett equation. A program is developed based on the proposed model to predict the production of a CBM well. Compared with the monitoring results of an actual vertical fractured well, the accuracy and reliability of the analytical model are approved. The impact of reservoir parameters and fracture parameters on the CBM production are quantitatively studied. The results indicate that the production is affected by the three major factors: gas supply capacity of the matrix (viz., CBM volume released by unit volume of matrix during unit time), supply capacity of the fracture network to the major fracture, and gas exhausting ability of the major fracture to the wellbore. The permeability, matrix radius, and coal seam thickness with larger values are good for the gas supply capacity of the matrix. Higher flow conductivity of major fracture shows a stronger impact on the gas exhausting ability of the major fracture to the wellbore. A smaller fracture interval is beneficial to the supply capacity of the fracture network to the major fracture to obtain higher production. To improve the efficiency of the actual well, the flow conductivity of the major fracture should be no more than 200 mD m and the crack interval should be between 20 and 30 m. The achievements of this study provide a case reference for the production prediction of vertical fractured wells and the optimization design of hydraulic fracture parameters of CBM reservoirs.     

高温热田井筒热力学及地层参数计算方法

在高温热田的井孔施工及测试实践中,通常由于高温热水在地层或井简内闪蒸汽化,形成复杂的两相流动而无法直接从单井放喷资料中计算地层参数。西藏羊八井属于高温热水型地热田,第四系热储内热液温度约介于140—155℃之间,埋藏深度大略为70—200米左右,井口闭井压力大多在2—4个大气压之间。热储流体在上述深度、温度和压力的配置下,在地层内处于单相液态,而在开发动态下则在大部分井筒上部达到饱和点而汽化,形成相对稳定的汽化面,构成双相流和单相流之间的界面。     

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。     

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。     

新场气田分段压裂水平井裂缝布局优化

新场气田属于大型多层致密砂岩异常高压气藏,储层物性差,非均质性强,气井动用储量低。目前,为大幅度提高气井产能,提高储量动用长度,该气藏多采用多段压裂水平井开发。因此,迫切需要论证裂缝参数及其组合对多段压裂水平井开发效果的影响,为气藏下步科学高效开发和持续高产稳产提供理论基础。以川西新场气田为研究对象,采用数值模拟法深入研究了压裂水平井裂缝几何布局对气井产能的影响,包括非均匀裂缝长度、非均匀裂缝间距、压裂规模与裂缝数量、裂缝长度与间距的匹配、裂缝夹角与间距的匹配。结果表明:对于多段压裂水平井,U型模式的裂缝长度布局最优;均匀裂缝间距开发效果优于非均匀裂缝间距;水力压裂时,少段数长缝能取得更佳的开发效果;0. 67~1倍缝长的裂缝间距布局、垂直于井筒的正交裂缝布局有利于改善压裂水平井开发效果,裂缝间距的增大能有效降低非正交裂缝低夹角对产量的影响。     

实验室尺度高地温梯度模拟地层的实现方法研究

地热井与周围热储层的传热过程对地热井产热性能研究有重要意义。由于实际工程中在地热井周边布置测点较难,无法获取地热井周围热储层的参数变化,进而为地热热储模拟结果提供验证,故以往大多地热热储模拟仅将地热井作为源项处理,未考虑地热流体和储层的耦合流动换热。实验室条件下的模拟试验方便布置测点,可为热储-井筒耦合流动传热模型提供试验验证,其中如何实现实验室尺度下有温度梯度的模拟地层是试验研究的关键,目前尚未有类似研究。基于传热学基本原理,研究了实验室条件下有较高温度梯度多孔地层的快速实现方法,通过确定模拟热储层和热储盖层几何尺寸、优选填充多孔介质和实现恒定温度的模拟热储层,设计了一套实验室尺度下有高温度梯度的模拟地层系统,通过分层加热与边界动态热补偿方法,较快实现了热储层温度分别为60,65,70°C下模拟地层的线性温度分布,采用有限体积法得到的数值模拟与试验结果的相对误差在±2.5%范围内,二者吻合较好。文章设计搭建的模拟地层系统可为开展地热井筒-热储耦合模拟试验提供条件,进而为开发的地热热储-井筒耦合传热数值软件提供试验验证。     

Modeling semi-steady state near-well flow performance for horizontal wells in anisotropic reservoirs

This paper presents a novel methodology to model semi-steady state horizontal well flow performance in an anisotropic reservoir taking into account flow in the near-well region for an arbitrary well trajectory. It is based on an analytical productivity model describing coupled axial reservoir flow and radial well inflow. In order to apply this model in an anisotropic reservoir, the permeability field relative to the radial direction perpendicular to the well trajectory and the axial direction along the well trajectory must first be determined. A classical space transformation is used in concert with rotational transforms to obtain a virtual isotropic model. The transformation preserves the volumes and pressures. It is not a novel concept, but different from previous approaches in the sense that it is only applied in the near-well domain to formulate an equally isotropic media. As a result, the use of this virtual isotropic model requires the Dietz shape factor for an ellipse, transformed from the original cylindrical near-well domain. The Dietz shape factors are determined numerically in this research. The semi-steady state well/near-well model is implemented in a numerical simulator incorporating formation anisotropy and wellbore hydraulics. The specific productivity index along the well trajectory is generated using the virtual configuration. Numerical results for different anisotropy ratios and also incorporating frictional losses in the well are presented. Furthermore, the well/near-well model is applied in coupling with streamline reservoir model for a water flooding case. This appears to be the first coupling of a well hydraulics model and a streamline simulator. It presents the application of the well/near-well model in integrated reservoir simulation in an efficient and accurate manner. The results demonstrate that the coupling approach with a streamline reservoir model and the well/near-well is of great potential for advanced well simulation efficiently.     

Permeability determination of porous media using large‐scale finite elements and iterative solver

The problem of finite element simulation of incompressible fluid flow in porous medium is considered. The porous medium is characterized by the X‐ray microtomography technique in three dimensions. The finite calculus‐based stabilization technique is reviewed to implement the equal order finite element interpolation functions for both velocity and pressure. A noble preconditioner, the nodal block diagonal preconditioner, is considered whose performance is thoroughly investigated. Combining this preconditioner with a standard iterative solver during the computational homogenization procedure, it is possible to carry out the large‐scale fluid flow simulation for estimating permeability of the porous medium with reasonable accuracy and reliability. Copyright © 2013 John Wiley & Sons, Ltd.