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1.
《Advances in water resources》1998,21(6):451-461
In this paper we consider one-dimensional capillary redistribution of two immiscible and incompressible fluids in a porous medium with a single discontinuity. We study a special time-dependent solution, a similarity solution, which is found when the initial saturation is discontinuous at the same point as the permeability and porosity, and is constant elsewhere. The similarity solution can be used to validate numerical algorithms describing two-phase flow in porous media with discontinuous heterogeneities. We discuss the construction of the similarity solution, in which we pay special attention to the interface conditions at the discontinuity, both for media with positive and zero entry pressure. Moreover, we discuss some qualitative properties of the solution, and outline a numerical procedure to determine its graph. Examples are given for the Brooks-Corey and Van Genuchten model. We also consider similarity solutions for unsaturated water flow, which is a limit case of two-phase flow for negligible nonwetting phase viscosity. 相似文献
2.
Characterizing the pore space of rock samples using three‐dimensional (3D) X‐ray computed tomography images is a crucial step in digital rock physics. Indeed, the quality of the pore network extracted has a high impact on the prediction of rock properties such as porosity, permeability and elastic moduli. In carbonate rocks, it is usually very difficult to find a single image resolution which fully captures the sample pore network because of the heterogeneities existing at different scales. Hence, to overcome this limitation a multiscale analysis of the pore space may be needed. In this paper, we present a method to estimate porosity and elastic properties of clean carbonate (without clay content) samples from 3D X‐ray microtomography images at multiple resolutions. We perform a three‐phase segmentation to separate grains, pores and unresolved porous phase using 19 μm resolution images of each core plug. Then, we use images with higher resolution (between 0.3 and 2 μm) of microplugs extracted from the core plug samples. These subsets of images are assumed to be representative of the unresolved phase. We estimate the porosity and elastic properties of each sample by extrapolating the microplug properties to the whole unresolved phase. In addition, we compute the absolute permeability using the lattice Boltzmann method on the microplug images due to the low resolution of the core plug images. In order to validate the results of the numerical simulations, we compare our results with available laboratory measurements at the core plug scale. Porosity average simulations for the eight samples agree within 13%. Permeability numerical predictions provide realistic values in the range of experimental data but with a higher relative error. Finally, elastic moduli show the highest disagreements, with simulation error values exceeding 150% for three samples. 相似文献
3.
Numerical simulations of dilatational waves in an elastic porous medium containing two immiscible viscous compressible fluids indicate that three types of wave occur, but the modes of dilatory motion corresponding to the three waves remain uncharacterized as functions of relative saturation. In the present paper, we address this problem by deriving normal coordinates for the three dilatational waves based on the general poroelasticity equations of Lo et al. 2005 [13]. The normal coordinates provide a theoretical foundation with which to characterize the motional modes in terms of six connecting coefficients that depend in a well defined way on inertial drag, viscous drag, and elasticity properties. Using numerical calculations of the connecting coefficients in the seismic frequency range for an unconsolidated sand containing water and air as a representative example relevant to hydrologic applications, we confirm that the dilatational wave whose speed is greatest corresponds to the motional mode in which the solid framework and the two pore fluids always move in phase, regardless of water saturation, in agreement with the classic Biot theory of the fast compressional wave in a water-saturated porous medium. For the wave which propagates second fastest, we show, apparently for the first time, that the solid framework moves in phase with water, but out of phase with air [Mode (III)], if the water saturation is below about 0.8, whereas the solid framework moves out of phase with both pore fluids [Mode (IV)] above this water saturation. The transition from Mode (III) to Mode (IV) corresponds to that between the capillarity-dominated region of the water retention curve and the region reflecting air-entry conditions near full water saturation. The second of the two modes corresponds exactly to the slow compressional wave in classic Biot theory, whereas the first mode is possible only in a two-fluid system undergoing capillary pressure fluctuations. For the wave which has the smallest speed, the dilatational mode is dominated by the motions of the two pore fluids, which are always out of phase, a result that is consistent with the proposition that this wave is caused by capillary pressure fluctuations. 相似文献
4.
5.
利用核磁共振测井资料构造储层毛管压力曲线的新方法及其应用 总被引：3，自引：1，他引：2
By analyzing hundreds of capillary pressure curves, the controlling factors of shape and type of capillary pressure curves are found and a novel method is presented to construct capillary pressure curves by using reservoir permeability and a synthesized index. The accuracy of this new method is verified by mercury-injection experiments. Considering the limited quantity of capillary pressure data, a new method is developed to extract the Swanson parameter from the NMR T2 distribution and estimate reservoir permeability. Integrating with NMR total porosity, reservoir capillary pressure curves can be constructed to evaluate reservoir pore structure in the intervals with NMR log data. An in-situ example of evaluating reservoir pore structure using the capillary pressure curves by this new method is presented. The result shows that it accurately detects the change in reservoir pore structure as a function of depth. 相似文献
6.
为了研究孔隙流体对不同渗透率岩石地震波速度的影响,在实验室利用跨频带岩石弹性参数测试系统得到了应变幅值10-6的2~2000Hz频段下的地震波速度和1 MHz频率下的超声波速度,利用差分共振声谱法得到了频率600Hz岩石干燥和完全饱水情况下岩石声学参数.实验表明,在低饱和度下,致密砂岩在地震和超声频段下没有明显的频散;在高饱和度下纵波速度的频散变得明显.从干燥到完全水饱和条件,不同频率测量的致密砂岩的体积模量随岩石孔隙度增高而降低,且体积模量的变化量受岩石微观孔隙结构的影响较大.高孔、高渗砂岩无论在低含水度下还是在高含水饱和度下频散微弱,并且在地震频段下围压对于岩石纵横波速度的影响要大于频率的影响.高孔、高渗砂岩和致密砂岩不同含水饱和度下的频散差异可应用于储层预测,油气检测等方面,同时该研究可以更好地帮助理解岩石的黏弹性行为,促进岩石物理频散理论的发展,提高地震解释的精度. 相似文献
7.
Wavefields in porous media saturated by two immiscible fluids are simulated in this paper. Based on the sealed system theory,
the medium model considers both the relative motion between the fluids and the solid skeleton and the relaxation mechanisms
of porosity and saturation (capillary pressure). So it accurately simulates the numerical attenuation property of the wavefields
and is much closer to actual earth media in exploration than the equivalent liquid model and the unsaturated porous medium
model on the basis of open system theory. The velocity and attenuation for different wave modes in this medium have been discussed
in previous literature but studies of the complete wave-field have not been reported. In our work, wave equations with the
relaxation mechanisms of capillary pressure and the porosity are derived. Furthermore, the wavefield and its characteristics
are studied using the numerical finite element method. The results show that the slow P3-wave in the non-wetting phase can
be observed clearly in the seismic band. The relaxation of capillary pressure and the porosity greatly affect the displacement
of the non-wetting phase. More specifically, the displacement decreases with increasing relaxation coefficient. 相似文献
8.
High resolution images acquired from X-ray μ-CT are able to map the internal structure of porous media on which multiphase flow properties can be computed. While the resolution of a few micrometers may be sufficient for capturing the pore space of many sandstones, most carbonates exhibit a large amount of microporosity; pores which are below the image resolution and are not resolved at specific resolution. Neglecting the effect of micropores on fluid flow and transport properties of these rocks can cause erroneous results in particular at partial saturations. Current image-based pore scale models typically only consider macropores for simulating fluid flow. In this paper, we quantify the effect of microporosity on the effective permeability of the wetting phase for heterogeneous model structures with varying amount of micro-to-macro porosity. A multi-scale numerical approach is proposed to couple an average effect of micropores with an explicit representation of macropores. The Brinkman equation is solved using a lattice Boltzmann formulation to facilitate the coupling of Darcy and Stokes equations in micropores and macropores, respectively. The results show good agreement between the fine scale solution and the results of the upscaled models in which microporous regions are homogenised. The paper analyses in particular the choice of the momentum sink parameter at low wetting phase saturations. It is shown that this parameter can be found using either a flux-based calculation of permeability of microporous regions or chosen purely on the basis of the effective permeability of these regions. 相似文献
9.
复杂孔隙储层往往同时发育孔缝洞等多种孔隙类型，这种孔隙结构的复杂性使得岩石的速度与孔隙度之间的相关性很差.经典的二维岩石物理模版只研究弹性参数与孔隙度和饱和度之间的定量关系，而不考虑孔隙结构的影响，用这样的模版来预测复杂孔隙储层的物性参数时带来很大偏差.本文首先证明多重孔隙岩石的干骨架弹性参数可以用一个等效孔隙纵横比的单重孔隙岩石物理模型来模拟；进而基于等效介质岩石物理理论和Gassmann方程，建立一个全新的三维岩石物理模版，用它来建立复杂孔隙岩石的弹性性质与孔隙扁度及孔隙度和饱和度之间的定量关系；在此基础上，预测复杂储层的孔隙扁度、孔隙度以及孔隙中所包含的流体饱和度.实际测井和地震反演数据试验表明，三维岩石物理模版可有效提高复杂孔隙储层参数的预测精度. 相似文献
10.
Although there is no assumption of pore geometry in derivation of Gassmann's equation, the pore geometry is in close relation with hygroscopic water content and pore fluid communication between the micropores and the macropores. The hygroscopic water content in common reservoir rocks is small, and its effect on elastic properties is ignored in the Gassmann theory. However, the volume of hygroscopic water can be significant in shaly rocks or rocks made of fine particles; therefore, its effect on the elastic properties may be important. If the pore fluids in microspores cannot reach pressure equilibrium with the macropore system, assumption of the Gassmann theory is violated. Therefore, due to pore structure complexity, there may be a significant part of the pore fluids that do not satisfy the assumption of the Gassmann theory. We recommend that this part of pore fluids be accounted for within the solid rock frame and effective porosity be used in Gassmann's equation for fluid substitution. Integrated study of ultrasonic laboratory measurement data, petrographic data, mercury injection capillary pressure data, and nuclear magnetic resonance T2 data confirms rationality of using effective porosity for Gassmann fluid substitution. The effective porosity for Gassmann's equation should be frequency dependent. Knowing the pore geometry, if an empirical correlation between frequency and the threshold pore‐throat radius or nuclear magnetic resonance T2 could be set up, Gassmann's equation can be applicable to data measured at different frequencies. Without information of the pore geometry, the irreducible water saturation can be used to estimate the effective porosity. 相似文献
11.
The semi-empirical Kozeny–Carman (KC) equation is the most famous permeability–porosity relation, which is widely used in the field of flow in porous media and is the starting point for many other permeability models. However, this relation has many limitations from its inception, and the KC constant is an empirical parameter which was proved to be not a constant. In this paper, we briefly reviewed the KC equation, its modifications and various models for the KC constant. We then derived an analytical expression for the permeability in homogeneous porous media based on the fractal characters of porous media and capillary model. The proposed model is expressed as a function of fractal dimensions, porosity and maximum pore size. The analytical KC constant with no empirical constant is obtained from the assumption of square geometrical model. Furthermore, a distinct linear scaling law between the dimensionless permeability and porosity is found. It is also shown that our analytical permeability is more closely related to the microstructures (fractal dimensions, porosity and maximum pore size), compared to those obtained from conventional methods and models. 相似文献
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13.
Ismael Himar Falcon-Suarez Kelvin Amalokwu Jordi Delgado-Martin Ben Callow Katleen Robert Laurence North Sourav K. Sahoo Angus I. Best 《Geophysical Prospecting》2019,67(4):784-803
Synthetic rock samples can offer advantages over natural rock samples when used for laboratory rock physical properties studies, provided their success as natural analogues is well understood. The ability of synthetic rocks to mimic the natural stress dependency of elastic wave, electrical and fluid transport properties is of primary interest. Hence, we compare a consistent set of laboratory multi-physics measurements obtained on four quartz sandstone samples (porosity range 20–25%) comprising two synthetic and two natural (Berea and Corvio) samples, the latter used extensively as standards in rock physics research. We measured simultaneously ultrasonic (P- and S-wave) velocity and attenuation, electrical resistivity, permeability and axial and radial strains over a wide range of differential pressure (confining stress 15–50 MPa; pore pressure 5–10 MPa) on the four brine saturated samples. Despite some obvious physical discrepancies caused by the synthetic manufacturing process, such as silica cementation and anisotropy, the results show only small differences in stress dependency between the synthetic and natural sandstones for all measured parameters. Stress dependency analysis of the dry samples using an isotropic effective medium model of spheroidal pores and penny-shaped cracks, together with a granular cohesion model, provide evidence of crack closure mechanisms in the natural sandstones, seen to a much lesser extent in the synthetic sandstones. The smaller grain size, greater cement content, and cementation under oedometric conditions particularly affect the fluid transport properties of the synthetic sandstones, resulting in lower permeability and higher electrical resistivity for a similar porosity. The effective stress coefficients, determined for each parameter, are in agreement with data reported in the literature. Our results for the particular synthetic materials that were tested suggest that synthetic sandstones can serve as good proxies for natural sandstones for studies of elastic and mechanical properties, but should be used with care for transport properties studies. 相似文献
14.
This study presents a new unsteady-state method for measuring two-phase relative permeability by obtaining local values of the three key parameters (saturation, pressure drop, and phase flux) versus time during a displacement. These three parameters can be substituted to two-phase Darcy Buckingham equation to directly determine relative permeability. To obtain the first two, we use a medical X-ray Computed Tomography (CT) scanner to monitor saturation in time and space, and six differential pressure transducers to measure the overall pressure drop and the pressure drops of five individual sections (divided by four pressure taps on the core) continuously. At each scanning time, the local phase flux is obtained by spatially integrating the saturation profile and converting this to the flux using a fractional flow framework. One advantage of this local method over most previous methods is that the capillary end effect is experimentally avoided; this improvement is crucial for experiments using low viscosity fluids such as supercritical and gas phases. To illustrate the new method, we conduct five CO2-brine primary drainage experiments in a 60.8 cm long and 116 mD Berea sandstone core at 20 °C and 1500 psi. In return, we obtain hundreds of unsteady-state CO2 and brine relative permeability data points that are consistent with steady-state relative permeability data from the same experiments. Due to the large amount of relative permeability data obtained by the new unsteady-state method, the uncertainties of the exponents in the Corey-type fits decrease by up to 90% compared with the steady-state method. 相似文献
15.
低渗透砂岩油气藏已成为油气增储生产的重要勘探开发目标,但孔隙结构复杂使得储层及其有效性难以准确识别.笔者利用物性、压汞、核磁等资料,对东营凹陷南坡沙四段(Es4)低渗透砂岩孔隙结构进行分析,划分出了3种类型.核磁T2谱与毛管压力曲线都在一定程度上反映孔喉分布,但常规方法利用T2谱重构伪毛管压力曲线所得到的孔隙半径与压汞孔喉半径有较大误差,而岩石孔隙自由流体T2与压汞孔喉分布对应关系更好,以此建立了不同孔隙结构类型二者之间不同孔喉尺度对应的关系式(大尺度:线性;小尺度:分段幂函数),可在井筒剖面上通过识别孔隙结构类型,进而利用核磁共振测井(NML)定量反演孔径分布,省去了构建伪毛管曲线环节,为低渗透砂岩储层有效性评价提供了直接依据,也是测井用于定量反演储层微观孔隙结构信息的有益探索. 相似文献
16.
An approach to determining the effective elastic moduli of rocks with double porosity is presented. The double‐porosity medium is considered to be a heterogeneous material composed of a homogeneous matrix with primary pores and inclusions that represent secondary pores. Fluid flows in the primary‐pore system and between primary and secondary pores are neglected because of the low permeability of the primary porosity. The prediction of the effective elastic moduli consists of two steps. Firstly, we calculate the effective elastic properties of the matrix with the primary small‐scale pores (matrix homogenization). The porous matrix is then treated as a homogeneous isotropic host in which the large‐scale secondary pores are embedded. To calculate the effective elastic moduli at each step, we use the differential effective medium (DEM) approach. The constituents of this composite medium – primary pores and secondary pores – are approximated by ellipsoidal or spheroidal inclusions with corresponding aspect ratios. We have applied this technique in order to compute the effective elastic properties for a model with randomly orientated inclusions (an isotropic medium) and aligned inclusions (a transversely isotropic medium). Using the special tensor basis, the solution of the one‐particle problem with transversely isotropic host was obtained in explicit form. The direct application of the DEM method for fluid‐saturated pores does not account for fluid displacement in pore systems, and corresponds to a model with isolated pores or the high‐frequency range of acoustic waves. For the interconnected secondary pores, we have calculated the elastic moduli for the dry inclusions and then applied Gassmann's tensor relationships. The simulation of the effective elastic characteristic demonstrated that the fluid flow between the connected secondary pores has a significant influence only in porous rocks containing cracks (flattened ellipsoids). For pore shapes that are close to spherical, the relative difference between the elastic velocities determined by the DEM method and by the DEM method with Gassmann's corrections does not exceed 2%. Examples of the calculation of elastic moduli for water‐saturated dolomite with both isolated and interconnected secondary pores are presented. The simulations were verified by comparison with published experimental data. 相似文献
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介观尺度孔隙流体流动是地震频段岩石表现出较强速度频散与衰减的主要作用.利用周期性层状孔隙介质模型,基于准静态孔弹性理论给出了模型中孔隙压力、孔隙流体相对运动速度以及固体骨架位移等物理量的数学解析表达式,同时利用Biot理论将其扩展至全频段条件下,克服了传统White模型中介质分界面处流体压力不连续的假设. 在此基础上对准静态与全频段下模型介质中孔隙压力、孔隙流体相对运动速度变化形式及其对弹性波传播特征的影响进行了讨论,为更有效理解介观尺度下流体流动耗散和频散机制提供物理依据.研究结果表明,低频条件下快纵波孔压在介质层内近于定值,慢纵波通过流体扩散改变总孔隙压力, 随频率的增加慢波所形成的流体扩散作用逐渐减弱致使介质中总孔压逐渐接近于快纵波孔压,在较高频率下孔压与应力的二次耦合作用使总孔压超过快纵波孔压.介质中孔隙流体相对运动速度与慢纵波形成的流体相对运动速度变化形式一致;随频率的增加孔隙流体逐渐从排水的弛豫状态过渡到非弛豫状态,其纵波速度-含水饱和度变化形式也从符合孔隙流体均匀分布模式过渡到斑块分布模式,同时介质在不同含水饱和度下的衰减峰值与慢纵波所形成的孔隙流体相对流动速度具有明显的相关性. 相似文献
19.
V. Shulakova J. Sarout L. Pimienta M. Lebedev S. Mayo M.B. Clennell M. Pervukhina 《Geophysical Prospecting》2017,65(1):251-265
CO2 geosequestration is an efficient way to reduce greenhouse gas emissions into the atmosphere. Carbonate rock formations are one of the possible targets for CO2 sequestration due to their relative abundance and ability to serve as a natural trapping reservoir. The injected supercritical CO2 can change properties of the reservoir rocks such as porosity, permeability, tortuosity, and specific surface area due to dissolution and precipitation processes. This, in turn, affects the reservoir characteristics, i.e., their elastic properties, storage capacity, stability, etc. The tremendous progresses made recently in both microcomputed X‐ray tomography and high‐performance computing make numerical simulation of physical processes on actual rock microstructures feasible. However, carbonate rocks with their extremely complex microstructure and the presence of microporosity that is below the resolution of microcomputed X‐ray tomography scanners require novel, quite specific image processing and numerical simulation approaches. In the current work, we studied the effects of supercritical CO2 injection on microstructure and elastic properties of a Savonnières limestone. We used microtomographic images of two Savonnières samples, i.e., one in its natural state and one after injection and residence of supercritical CO2. A statistical analysis of the microtomographic images showed that the injection of supercritical CO2 led to an increase in porosity and changes of the microstructure, i.e., increase of the average volume of individual pores and decrease in the total number of pores. The CO2 injection/residence also led to an increase in the mean radii of pore throats, an increase in the length of pore network segments, and made the orientation distribution of mesopores more isotropic. Numerical simulations showed that elastic moduli for the sample subjected to supercritical CO2 injection/residence are lower than those for the intact sample. 相似文献
20.
Gas exsolution and flow during supersaturated water injection in porous media: I. Pore network modeling 总被引：1，自引：0，他引：1
Weishu ZhaoMarios A. Ioannidis 《Advances in water resources》2011,34(1):2-14
Degassing and in situ development of a mobile gas saturation take place when an aqueous phase saturated with gas at a pressure higher than the subsurface pressure is injected in water-saturated porous media. In the first part of this work, a pore network model is used to study the key physical aspects of this novel and hitherto unexplored way of introducing a gas phase in the subsurface. Following heterogeneous nucleation, growth of gas phase clusters driven by convective diffusion of solute from the bulk aqueous phase, is shown to result in a ramified pattern of gas-occupied pores, which is controlled by capillary and buoyancy forces. The interplay between mass transfer and immiscible displacement processes, namely gas cluster coalescence, mobilization under the action of buoyancy forces and fragmentation resulting from capillary instabilities, is seen to favour the propagation of a stable gas saturation front. Pore network model predictions of the macroscopic mass transfer rate coefficient are in fair agreement with a recently published empirical correlation. 相似文献