Investigating the Fracture Network Effects on Sweep Efficiency during WAG Injection Process

In this study, the main recovery mechanisms behind oil/water/gas interactions during the water-alternating-gas (WAG) injection process, in a network of matrix/fracture, were fundamentally investigated. A visual micromodel was utilized to provide insights into the potential applications of WAG process in fractured oil-wet media as well as the possibility of observing microscopic displacement behavior of fluids in the model. The model was made of an oil-wet facture/matrix network system, comprised of four matrix blocks surrounded with fractures. Different WAG injection scenarios, such as slug arrangements and the effects of fluid injection rates on oil recovery were studied. A new equation representing the capillary number, considering the fracture viscous force and matrix capillary force, was developed to make the experimental results more similar to a real field. In general, WAG tests performed in the fractured model showed a higher oil recovery factor compared with the results of gas and water injection tests at their optimum rates. The results showed that the presence of an oil film, in all cases, was the main reason for co-current drainage and double displacement of oil under applied driving forces. Furthermore, the formation of oil liquid bridges improved the recovery efficiency, which was greatly influenced by the size of fracture connecting the two matrix blocks; these connecting paths were more stable when there was initial water remaining in the media. Analyzing different recovery curves and microscopic view of the three phases in the transparent model showed that starting an injection mode with gas (followed by repeated small slugs of water and gas), could considerably improve oil recovery by pushing water into the matrix zone and increasing the total sweep efficiency.     

An Improvement on Modeling of Forced Gravity Drainage in Dual Porosity Simulations Using a New Matrix-Fracture Transfer Function

In fractured oil reservoirs, the gravity drainage mechanism has great potentials to higher oil recovery in comparison with other mechanisms. Recently, the forced gravity drainage assisted by gas injection has also been considered; however, there are few comprehensive studies in the literature. Dual porosity model, the most common approach for simulation of fractured reservoirs, uses transfer function concept to represent the fluid exchange between matrix and its neighborhood fractures. This study compares the results of different available transfer functions with those of fine grid simulations when forced gravity drainage contributes to oil production from a single matrix block. These comparisons can lead to a more sophisticated formulation including the interplay of capillary, gravity and viscous forces. As a result, a new matrix-fracture transfer function can be developed and its results can be tested against the results of fine-grid simulations. Moreover, the reliability of this model for simulation of forced gravity drainage has been demonstrated by performing some sensitivity analysis.     

Explicit Rate–Time Solutions for Modeling Matrix–Fracture Flow of Single Phase Gas in Dual-Porosity Media

One of the widely used methods for modeling matrix–fracture fluid exchange in naturally fractured reservoirs is dual porosity approach. In this type of modeling, matrix blocks are regarded as sources/sinks in the fracture network medium. The rate of fluid transfer from matrix blocks into fracture medium may be modeled using shape factor concept (Warren and Root, SPEJ 3:245–255, 1963); or the rate–time solution is directly derived for the specific matrix geometry (de Swaan, SPEJ 16:117–122, 1976). Numerous works have been conducted to study matrix–fracture fluid exchange for slightly compressible fluids (e.g. oil). However, little attention has been taken to systems containing gas (compressible fluid). The objective of this work is to develop explicit rate–time solutions for matrix–fracture fluid transfer in systems containing single phase gas. For this purpose, the governing equation describing flow of gas from matrix block into fracture system is linearized using pseudopressure and pseudotime functions. Then, the governing equation is solved under specific boundary conditions to obtain an implicit relation between rate and time. Since rate calculations using such an implicit relation need iterations, which may be computationally inconvenient, an explicit rate–time relation is developed with the aid of material balance equation and several specific assumptions. Also, expressions are derived for average pseudopressure in matrix block. Furthermore, simplified solutions (originated from the complex general solutions) are introduced applicable in infinite and finite acting flow periods in matrix. Based on the derived solutions, expressions are developed for shape factor. An important observation is that the shape factor for gas systems is the same as that of oil bearing matrix blocks. Subsequently, a multiplier is introduced which relates rate to matrix pressure instead of matrix pseudopressure. Finally, the introduced equations are verified using a numerical simulator.     

A New Mathematical Model for Force Gravity Drainage in Fractured Porous Media

In force gas/oil gravity drainage process in fractured porous media, gas is flowing in both matrix and fractures leading to produce a finite gas pressure gradient. Consequently, viscous force plays an important role for displacing matrix oil toward fractures in addition to gravity force that is required to be modeled appropriately. A new analytical model for estimation of steady state oil saturation distribution with assumption of fixed gas pressure gradient throughout the matrix is presented. Moreover, based on some results of this analytical model a different numerical formulation is developed to predict the performance of oil production process. Comparison of the results obtained from this numerical model with the results of a conventional simulator demonstrates that the newly developed model can be applied with satisfactory accuracy. Numerical simulations show that the viscous displacement in fractured porous media can reduce the capillary threshold height, and thus it suggests the force gravity drainage as a favorable production mechanism when the matrix length is close to the threshold height.     

Traveling liquid bridges in unsaturated fractured porous media

Interplay between capillary, gravity and viscous forces in unsaturated fractures gives rise to a range of complex flow phenomena. Evidence of highly intermittent fluxes, preferential and sustainable flow pathways lead to potentially significant flow focusing of concern for regulatory and management of water resources in fractured rock formations. In previous work[Ghezzehei TA,Or D.: Water Resour. Res. In Review(2005)] we developed mechanistic models for formation, growth and detachment of liquid bridges in geometrical irregularities within fractures. Such discrete and intermittent flows present a challenge to standard continuum theories. Our focus here is on predicting travel velocities of detached liquid elements and their interactions with fracture walls. The scaling relationships proposed by Podgorski et al. [Podgorski, T., et al.: Phys. Rev. Lett. 8703(3), 6102-NIL_95 (2001)] provide a general framework for processes affecting travel velocities of discrete liquid elements in fractures, tubes, and in coarse porous media. Comparison of travel velocity and distance by discrete bridges relative to equivalent continuous film flow reveal significantly faster and considerably larger distances traversed by liquid bridges relative to liquid films. Coalescence and interactions between liquid bridges result in complex patterns of travel times and distances. Mass loss on rough fracture surfaces shortens travel distances of an element; however, results show that such retardation provides new opportunities for coalescence of subsequent liquid elements traveling along the same path, resulting in mass accumulation and formation of larger liquid elements traveling larger distances relative to smooth fracture surfaces. Such flow focusing processes may be amplified considering a population of liquid bridges within a fracture plane and mass accumulation in fracture intersections.     

Wetting Phase Bridges Establish Capillary Continuity Across Open Fractures and Increase Oil Recovery in Mixed-Wet Fractured Chalk

The effect of fractures on oil recovery and in situ saturation development in fractured chalk has been determined at near neutral wettability conditions. Fluid saturation development was monitored both in the matrix and in the fractures and the mechanisms of fracture crossing were determined using high spatial resolution MRI. Capillary continuity across open oil-filled fractures was verified by imaging the water bridges established within the fracture. Despite an alternate escape fracture for the water, separate water bridges were shown to be stable for the entire duration of the experiments. The established capillary contact resulted in oil recovery exceeding the spontaneous imbibition potential in the outlet-isolated cores by ca. 10% PV. This is explained by viscous recovery provided by water bridges across open fractures. The size of the bridges seemed to be controlled by the wettability of the rock and not by the differential pressure applied across the open fracture.     

Oil Displacement for One-Dimensional Three-Phase Flow with Phase Change in Fractured Media

In this article, the numerical simulations for one-dimensional three-phase flows in fractured porous media are implemented. The simulation results show that oil displacement in matrix is dominated by oil–water capillary pressure only under certain conditions. When conditions are changed to decrease the amount of water entering into the fractured media from the boundary of the flow field, water in fracture may be vaporized to superheated steam. In these cases, the appearance of superheated steam in fracture rather than in matrix will decrease the fracture pressure and generate the pressure difference between matrix and fracture, which results in oil flowing from matrix to fracture. Assuming that oil is wetting to steam, the matrix steam–oil capillary pressure will decrease the matrix oil-phase pressure as the matrix steam saturation increases. After the steam–oil capillary pressure finally exceeds the pressure difference due to the appearance of superheated steam in fracture, the oil displacement in matrix will stop. It is also shown that variations of the water relative permeability curve in matrix do not result in different mechanisms for oil displacement in matrix. The simulation results suggest that the amount of liquid water supply from the boundary of flow field fundamentally influence the mechanisms for oil displacement in matrix.     

An Analytical Model for Determination of the Solvent Convective Dispersion Coefficient in the Vapor Extraction Heavy Oil Recovery Process

In this article, a new model is developed to determine the solvent convective dispersion coefficient in a solvent vapor extraction (VAPEX) heavy oil recovery process. It is assumed that solvent mass transfer by convective dispersion takes place along the transition zone between the solvent chamber and untouched heavy oil, whereas solvent mass transfer by molecular diffusion occurs in the direction normal to the transition zone. It is also assumed that the solvent-diluted heavy oil gravity drainage through the transition zone has a linear or quadratic velocity profile in order to obtain analytical solutions of the solvent convective dispersion coefficients for the solvent chamber spreading and falling phases. As a result, this analytical model correlates the solvent convective dispersion coefficient to the maximum apparent oil gravity drainage velocity at the interface between the solvent chamber and transition zone, solvent molecular diffusion coefficient, transition-zone thickness, and porosity of the porous medium. To determine the solvent convective dispersion coefficient, the maximum apparent oil gravity drainage velocity is calculated by using Darcy’s law and the transition-zone thickness is obtained either from a previous study or by using a time similarity between the solvent molecular diffusion and oil gravity drainage. It is found that such a determined solvent convective dispersion coefficient is two to five orders larger than the solvent molecular diffusion coefficient, depending on the detailed experimental conditions of a specific VAPEX test.     

Displacement of Cr(III)–Partially Hydrolyzed Polyacrylamide Gelling Solution in a Fracture in Porous Media

During waterflooding of a fractured formation, water may channel through the fracture or interconnected network of fractures, leaving a large portion of oil bearing rock unswept. One remedial practice is injection of a gelling solution into the fracture. Such placement of a gelling mixture is associated with leak-off from the fracture face into the adjoining matrix. Design of a gel treatment needs understanding of the flow of gelling mixture in and around the fracture. This flow is addressed here for Cr(III)–partially hydrolyzed polyacrylamide formulation through experiments and conceptual model. A fractured slab was used to develop a lab-model, where the flow along the fracture and simultaneous leak-off into the matrix can be controlled. Also, the fracture and matrix properties had to be evaluated individually for a meaningful analysis of the displacement of gelling solution. During this displacement, the gelling fluid leaked off from the fracture into the matrix as a front, resulting in a decreasing velocity (and pressure gradient) along the fracture. With pressure in the fracture held constant with time, the leak-off rate decreased as the viscous front progressed into the matrix. The drop in leak-off rate was rapid during the initial phase of displacement. A simple model, based on the injection of a viscous solution into the dual continua, could explain the displacement of Cr(III)–polyacrylamide gelling mixture through the fractured slab. This study rules out any major complication from the immature gelling fluid, e.g., build-up of cake layer on the fracture face. The model, due to its simplicity may become useful for quick sizing of gel treatment, and any regression-based evaluation of fluid properties in a fracture for other applications.     

A percolation-type fracture criterion for composites with randomly oriented fibres

A fracture model is built up for a solid composed of brittle fibres randomly oriented in the matrix volume. The fracture process includes a stable growth of microcracks caused by fibre breaking under the load and formation of an infinite cluster of the microcracks. Both upper and lower bounds for ultimate stress in a fibre system are found as functions of the fibre volume fraction. The calculation of the ultimate stresses are performed by using the percolation theory and the theory of branching processes. At the present stage of the theory under consideration, only two types of the microcracks are appraised, namely that of a delamination type which corresponds to a weak fibre/matrix interface, and that of a penny shape which corresponds to a strong fibre/matrix interface. A particular solid contains only one type of the microcracks. In both cases, non-linear dependencies of the ultimate composite strength on fibre volume fraction are obtained.     

基于XFEM-MBEM的嵌入式离散裂缝模型流固耦合数值模拟方法

离散缝网的表征与模拟是目前国内外研究的热点. 在非常规油气开发过程中, 由于地应力场的存在会对裂缝的流动属性产生显著影响, 若将裂缝视为静态对象, 与矿场数据会出现极大偏差, 因此要基于动态裂缝做更深入的研究. 本文针对致密油藏应力场?渗流场耦合力学问题, 提出了一种高效的混合数值离散化方法, 其中采用扩展有限元法 (XFEM) 求解岩石的弹性形变, 采用了混合边界元法 (MBEM) 精确计算基岩与裂缝间的非稳态窜流, 这两种数值格式是完全耦合的, 并对整体计算格式的时间项进行了全隐式求解, 可准确表征致密油藏开采过程中的裂缝变形及流体流动机理. 此外, 本文采用了嵌入式离散裂缝前处理算法显式表征大尺度水力压裂缝, 并考虑了支撑剂的作用; 采用了双孔有效应力原理和双重介质隐式裂缝表征方法, 可捕捉基质与小尺度天然裂缝的动态信息; 由此, 本文所提出的混合模型综合表征了基质?天然裂缝?水力压裂缝共同组成的致密油藏复杂渗流环境, 并通过几个实例论证了模型的准确性, 研究表明: 对致密油藏压裂水平井进行产能评价时, 应力场所引起渗流参数的改变及裂缝开度降低的影响不可忽略. 本文研究可为非常规油气资源的开发提供理论指导.      

Experiments on melting of a vertical ice layer immersed in immiscible liquid

Experiments on the melting of a vertical ice layer immersed in immiscible liquid yielded quantitative results both for the timewise evolution of the melting front and the heat transfer. Vegetable oil, which was contained in a rectangular vessel, was adopted as a testing liquid. A bubble-free ice block stuck on a cooled wall was installed vertically in the vessel. The experiments were carried out for the immiscible liquid temperatures from 7.6 to 30.0 ^°C, while for the cooled wall temperatures from 0 to ?11.5 ^°C. The flow structure of the liquid and the melting front were extensively observed and recorded photographically. It was found that the heat transfer and the rate of melting are significantly affected by a couple of fluid motions of both the water melt induced by melting of ice and the immiscible liquid based on free convection.     

Computational analysis of convective instabilities in a liquid layer subjected to an inclined gradient of temperature

A 3D numerical study of convective instabilities in a horizontal liquid layer (silicone oil with a Prandtl number Pr = 102) with an upper free surface is presented. The liquid layer is subjected to an inclined gradient of temperature. The influence of both gravity and thermocapillary forces on the formation of convective patterns is studied for different values of the liquid layer depth. Numerical results are found to be in good agreement with experimental data of other authors.     

一种利用岩块特征长度估算二维渗吸量的新方法

 对于存在大量亲水疏油岩块的天然裂缝性油藏,自发渗吸是基质岩块和裂缝系统油水交换的重要驱动机制．对于一维渗吸问题,前期存在自相似解析解,后期可以用近似解析解描述,从而可以很方便地估算出岩块剩余油饱和度和岩块出油速率．本文研究了二维矩形岩块在不同边界条件下渗吸过程的近似解析解,通过引入特征长度,将二维岩块渗吸问题等效为一维,从而可以有效利用一维近似解析解来估算出二维岩块渗吸过程中剩余油饱和度和岩块出油速率随时间的变化．本文提出了一个新的混合特征长度,在渗吸前期取岩块面积与岩块开放边界长度之比;在渗吸后期,特征长度根据前期特征长度和Ma 等提出的特征长度按饱和度插值确定．通过数值检验比较了几种常见的特征长度取法和本文提出的混合特征长度取法,结果表明新的混合特征长度总体性能优于其他已有的特征长度取法,并且适用于本文列举的所有边界条件．     

Effects of the dimensional and geometrical errors on the cylinder block tilt of a high-speed EHA pump

The speed of Electro-Hydrostatic Actuator pump can recently reach 20,000 rpm and the cylinder block within such high-speed pump is more likely to tilt away from the valve plate, which results in wedge-shape oil film between cylinder block and valve plate and thus increase in leakage flow. In order to realize the cylinder block balance at high speed, more attentions should be given to the dimensional and geometrical errors of cylinder block since unreasonable dimensional and geometrical errors may significantly contribute to cylinder block tilt through inertial forces of piston-slipper assemblies, especially in high speed condition. This paper analyzes the influence of dimensional and geometrical errors on the cylinder block tilt. A detailed set of relevant equations is developed, which takes into account three typical types of dimensional and geometrical errors of the cylinder block. The maximum and minimum of the extra cylinder block tilting moments produced by these dimensional and geometrical errors are examined and compared with each other using rotating vector method. According to the analytical results, some valuable suggestion is given to decrease the extra cylinder block tilting moments and inhibit the tilting effect.     

Preliminary drop-tower experiments on liquid-interface geometry in partially filled containers at zero gravity

Plexiglass containers with rounded trapezoidal cross sections were designed and built to test the validity of Concus and Finn's existence theorem (1974, 1983) for a bounded free liquid surface at zero gravity. Experiments were carried out at the NASA Lewis two-second drop tower. Dyed ethanol-water solutions and three immiscible liquid pairs, with one liquid dyed, were tested. High-speed movies were used to record the liquid motion. Liquid rose to the top of the smaller end of the containers when the contact angle was small enough, in agreement with the theory. Liquid interface motion demonstrated a strong dependence on physical properties, including surface roughness and contamination.     

Experimental study of the stability of long axisymmetric liquid bridges between solid supports at different temperatures

The stability of axisymmetric, long liquid bridges held captive between two coaxial, circular solid disks kept at different temperatures is considered. Because of the temperature difference between the supporting disks, a thermally-induced surface tension gradient and its associated flow (Marangoni convection) appear in the liquid column, modifying (decreasing) the capillary stability of the bridge. The influence on the stability limits of long, axisymmetric liquid bridges of the combined effect of gravity acceleration and thermally induced surface tension gradients was experimentally analyzed by using very small size liquid bridges (between disks 1 mm in diameter). Experimental results are compared with available analytical results.     

Compositional gravity drainage 1. Equilibrium solutions and controlling Bond numbers for a two-phase,three-component system

The amount of wetting phase that is recovered by gravity drainage is determined by an interplay of gravitational and capillary forces. The relative importance of those forces is often expressed in terms of a Bond number. For compositional gravity drainage, where the initial and displacing fluids are not in chemical equilibrium, there is no single Bond number, as phases that form during a displacement will be associated with a different interfacial tension and density for each equilibrium tie line encountered as the compositions change during flow. We study vertical compositional displacements to determine how the Bond numbers of the initial and displacing fluids control the ultimate recovery. We find analytical solutions to the capillary/gravity equilibrium for a simplified model three-component, two-phase system. The equilibrium phase composition versus distance profiles are different than those predicted from standard viscous dominated displacements. We calculate the recovery as a function of the Bond numbers of the initial and displacing phases, and the degree of diffusion for this simple system. We discuss the important role of molecular diffusion in the ultimate recovery for condensing displacements. Finally, we find that the simple numerical average of the Bond numbers provides a reasonable estimate of an effective Bond number for calculating the retained wetting phase for many compositional gravity drainages.