Modeling Hysteresis in Porous Media Flow via Relaxation

Two-phase flow in a porous medium can be modeled, using Darcy's law, in terms of the relative permeability functions of the two fluids (say, oil and water). The relative permeabilities generally depend not only on the fluid saturations but also on the direction in which the saturations are changing. During water injection, for example, the relative oil permeability k _ro falls gradually until a threshold is reached, at which stage the k _ro begins to decrease sharply. The latter stage is termed imbibition. If oil is subsequently injected, then k _ro does not recover along the imbibition path, but rather increases only gradually until another threshold is reached, whereupon it rises sharply. This second stage is called drainage, and the type of flow that occurs between the imbibition and drainage stages is called scanning flow. Changes in permeability during scanning flow are approximately reversible, whereas changes during drainage and imbibition are irreversible. Thus there is hysteresis, or memory, exhibited by the two-phase flow in the porous medium. In this work, we describe two models of permeability hysteresis. Common to both models is that the scanning flow regime is modeled with a family of curves along which the flow is reversible. In the Scanning Hysteresis Model (SHM), the scanning curves are bounded by two curves, the drainage and imbibition curves, where the flow can only occur in a specific direction. The SHM is a heuristic model consistent with experiments, but it does not have a nice mathematical specification. For instance, the algorithm for constructing solutions of Riemann problems involves several ad hoc assumptions. The Scanning Hysteresis Model with Relaxation (SHMR) augments the SHM by (a) allowing the scanning flow to extend beyond the drainage and imbibition curves and (b) treating these two curves merely as attractors of states outside the scanning region. The attraction, or relaxation, occurs on a time scale that corresponds to the redistribution of phases within the pores of the medium driven by capillary forces. By means of a formal Chapman–Enskog expansion, we show that the SHM with additional viscosity arises from the SHMR in the limit of vanishing relaxation time, provided that the diffusion associated with capillarity exceeds that induced by relaxation. Moreover, through a rigorous study of traveling waves in the SHMR, we show that the shock waves used to solve Riemann problems in the SHM are precisely those that have diffusive profiles. Thus the analysis of the SHMR justifies the SHM model. Simulations based on a simple numerical method for the simulation of flow with hysteresis confirm our analysis.     

Water requirements for germination and early seedling establishment in four African savanna woody plant species

The aim of this study was to determine the water requirements for germination and early seedling establishment of four African savanna tree species, namelyAcacia karroo, A. nilotica, A. tortilisandMundulea sericea. The acacias are characteristic of nutrient-rich, andM. sericeaof nutrient-poor savannas. Imbibition times of scarified seeds ofA. karroo(4 h),M. sericea(6 h) andA. tortilis(8 h) were rapid relative toA. nilotica(28 h) and were inversely correlated with seed size. Imbibed water is lost in about 2 h after drying at 25°C for all species exceptA. nilotica(only 70% moisture loss). Seeds ofA. karrooandM. sericeakept at 40°C dried to below their original moisture contents within 2 h. Seeds ofA. niloticaandA. tortilisdried at 40°C lost viability relative to (undried) control seeds, while there was no significant loss of viability forA. karrooandM. sericea. For fully imbibed seeds to germinate in sandy savanna soils, all four species required at least the equivalent of 3 mm rainfall every 2 days under mild greenhouse conditions. However, most ungerminated seeds were still viable despite drying-out from a fully imbibed state. Maintenance of soil at 50% field capacity (FC), or watering to FC every 9th day is the maintenance requirements for 2-week-old seedlings ofA. niloticaandM. sericeato continue growth for a further 5 weeks under greenhouse conditions, althoughA. niloticamostly survived 25% FC with one seedling surviving 12·5% FC. Root penetration was rapid in sandy soils, withA. niloticaandM. sericeaattaining a depth of 40 cm within 15 days. Frequent, but not necessarily high, rainfall appears to be essential for germination and seedling survival over the first 7 weeks.     

低渗储层多孔介质渗吸系数的分形分析

水自发渗吸驱油是低渗裂缝性油藏的重要采油机理,分析渗吸影响因素,研究油藏渗吸潜力,有效地利用渗吸效应,对提高石油采收率具有重要意义.系统分析了油藏渗吸及渗吸系数的研究现状,进而基于储层岩石孔隙结构的分形特征,推导了平均实际流速与平均直线流速的关系,考虑原始水饱和度的影响,建立了低渗油藏多孔介质渗吸系数的分形模型.结果表...     

The importance of the petrophysical properties and external factors in the stone decay on monuments

In this paper it is proposed to quantify the importance of some physical parameters responsible for stone decay on monuments. The most common decay process is the crystallisation of salt near the surface of the rocks or inside their porous network. Therefore, the water balance in rocks submitted to these special saturation and position conditions has been studied specifically, using the general concepts of water transfer in unsaturated porous media, and using the capillary imbibition kinetics of different rocks. Different parameters have been taken into account for the calculation of the salt crystallisation position: on one hand, several external parameters such as relative humidity, air convection and the presence of solute in solution, and on the other hand, the intrinsic water transfer properties of the rocks. Their relative importance is discussed, considering the potential values that each parameter can reach in nature.     

混合润湿孔隙介质中油自吸实验研究

混合润湿孔隙介质普遍存在, 使得多相流体渗流过程十分复杂, 但对其研究和认识至今仍很肤浅, 是油气运移成藏、剩余油气分布等方面研究中必须解决的关键难题。本文通过对饱和水的混合润湿模型进行油自吸实验, 观察不同混合润湿程度条件下油自吸运移过程, 分析认识混合润湿孔隙介质中多相渗流的机理。实验结果表明, 在混合润湿孔隙介质中油是否能够自发地运移与介质中亲油颗粒的比例关系密切, 但并非简单的单调变化关系。研究认为, 亲油颗粒与亲水颗粒随机分布, 导致多种与喉道配位颗粒的亲油-亲水关系, 当亲油颗粒比例占优才表现为亲油喉道。机理上, 混合润湿孔隙介质中油自吸运移的发生与否及程度取决于亲油喉道在空间上的连通程度, 后者与孔隙介质中亲油颗粒比例相当。仅有当孔隙介质中亲油颗粒足够多, 且组成的亲油喉道能够相互接触形成连续亲油通道时, 油才能够通过自吸运移进入多孔介质。     

不同驱替方式下岩石电阻率与饱和度的关系

针对高含水期老区调整井饱和度评价过程中存在的问题,通过模拟油田开发过程的岩石物理实验,研究水驱油方式下电阻率与含水饱和度之间的关系。与油驱水不同,水驱油方式下电阻增大率与含水饱和度在双对数坐标系中的关系不再是一条直线,而呈现出明显的与高、低含水饱和度区间相关的两段式;岩石的润湿特征不同,两段式拐点所对应的含水饱和度S_wp不同,水驱方式下所能达到的最终采收率也不同。水驱油方式下的I－S_w曲线特征表明,用勘探阶段及开发初期油驱水实验得到的饱和度公式对开发中后期的饱和度进行评价不太合适,尤其是在高含水期,电阻率对高含水饱和度反映能力的局限性严重制约了这一阶段水淹层的评价精度。     

裂缝性致密砂岩气藏水相毛管自吸调控

钻井、完井、增产改造工作液滤液、边底水或凝析水在井筒或裂缝面附近发生毛管自吸行为和滞留效应诱发水相圈闭损害,妨碍气藏的及时发现、准确评价和经济开发.以我国四川、鄂尔多斯盆地典型致密砂岩气藏为例,基于致密气藏天然气产出机理,分析了致密气藏经济开发的水平井钻井完井、水力压裂、采气等作业环节中水相自吸过程及其对作业效果的影响.钻井完井过程中水相快速自吸进入基块,驱替出非润湿相油气,打破裂缝壁面力学—化学平衡,诱发井壁失稳;进入裂缝的工作液要快速返排,以免自吸侵入基块降低基块—裂缝传质效率;裂缝中水相高速流动,不易毛管自吸进入基块,造成边底水沿裂缝快速推进,造成水淹.矿场工程技术实践证明,裂缝致密气藏勘探开发全过程,选用合理水基工作流体体系,改善采气工艺措施,调控毛管自吸,进而达到防治水相圈闭损害的目的,是经济开发致密气藏的关键.     

缝洞型碳酸盐岩油藏自吸驱油作用及其在开发中的利用

缝洞型碳酸盐岩油藏的多孔基质岩块是主要的储集空间,裂缝为主要的渗流通道,储油层具有非常复杂的孔隙空间结构,影响油层的注水驱油效率,从而影响油藏的最终采收率。实验表明在不具渗透性的多孔基质岩块内,毛管自吸驱油是改善基质岩块内石油动用程度的重要作用;储层在不同含水饱和度下均存在自吸作用,毛管自吸驱油系数随自吸时间延长而提高,最高可达35%;周期注水是利用毛管自吸驱油改善开发效果的有效开发方式,实验中最佳压力变化幅度为1.5倍～2倍,且投注初期即实施周期注水的效果最好;塔河油田数值模拟研究表明周期注水开发效果明显好于依靠天然能量、连续注水的效果,其优点是既保持地层能量,避免注入水的突进,同时又充分利用毛管自吸驱油作用,周期注水是很好的提高采收率方法。     

致密气藏压后关井压裂液静态渗吸实验研究——以大庆油田徐家围子区块为例

影响致密储层渗吸的因素较多,但系统的因素划分和敏感性分析依然具有很大挑战。为了高效开采致密气藏,为致密气藏压后焖井时间即开井制度优化提供依据,选取大庆油田徐家围子区块致密砂岩天然岩心,结合压汞、电镜扫描和X射线衍射等实验,在室内开展了静态渗吸实验,研究了致密储层静态渗吸的规律及其影响因素,包括渗吸时间、致密储层的渗透率、孔隙类型、润湿性和压裂液的离子浓度。实验结果表明:致密砂岩岩心静态渗吸气水置换主要作用在静态渗吸过程的早期阶段;在致密气藏的储层渗透率范围内,静态渗吸采出程度随渗透率增大而增大;原生孔为储气空间,与原生粒间孔相连的次生溶蚀孔、粒间溶蚀缝和颗粒边缘溶蚀缝为渗吸提供了畅通的通道;静态渗吸速度和最终采出程度随岩心亲水性的增强而增加;压裂时所用的压裂液浓度越低,储层的渗吸效果越好。研究结果可为致密气井压裂后排采制度设计提供基础。